Solving N k Queens Using Dancing Links
少女时代《Dancing Queen》韩文歌词 中文歌词 英文歌词
Dancing Queen演唱：少女时代Girls’ generationLet’s danceHit the beat and take it to the fast line무대위너를처음봤을때내주위에시간들은모두멈추고가슴만뛰어평범한나의인생을바꿔준넌나의댄싱퀸지루한나의일상을깨워준하룻밤의파티내맘을사로잡는댄싱阿그화려한솜씨너의그이기적인맵시그아찔한섹시숨막힐듯해Yeah한참을지나내가무대위에서그때그대처럼춤추고노래해마치꿈같아..정말로평범한나의인생을바꿔준넌나의댄싱퀸지루한나의일상을깨워준하룻밤의꿈내맘을사로잡는댄싱그화려한솜씨너의그이기적인맵시그아찔한섹시리듬에몸을맡겨나Yeah넌나의댄싱퀸누가뭐래도영원히(I don’t care what anyone thinks cause you’re the one who makes me dance.You’re one th e who makes me sing. Can’t nobody be my dancing queen but you.)내마음속의스타넌나의hero 넌나의hero 넌나의hero(I get the “chills” when I see you move, see you groove.The way you shake your body is“Look at me everybody!” Your dancing makes me “hot”.)댄싱, 그화려한댄싱니이기적인맵시그아찔한섹시리듬에몸을맡겨나Yeah날사로잡은댄싱니그화려한솜씨그이기적인맵시아찔한섹시숨막힐듯한너YeahBring it on파티젊음을불태울댄싱파티모두다함께해파티젊음을불태울댄싱파티You can dance, you can jive, having the time of your life你可以跳舞,你可以相当有自己的人生的时候See that girl, watch that scene, dig in the dancing queen看到少女到现场观看,在挖掘舞蹈皇后Friday night and the lights are low周五晚和车灯低Looking out for the place to go好自为之的地方去Where they play the right music, getting in the swing那里发挥有权音乐摆动阻You come in to look for a king你进来找国王Anybody could be that guy有人可以那家伙Night is young and the musics high年轻的、高的作品中晚With a bit of rock music, everything is fine一点点摇滚音乐,感觉良好Youre in the mood for a danceyoure在花样舞蹈And when you get the chance...而当你得到机会::You are the dancing queen, young and sweet, only seventeen你们是跳舞皇后,年轻又甜,只有17Dancing queen, feel the beat from the tambourine跳舞女王感受到击败来自tambourineYou can dance, you can jive, having the time of your life你可以跳舞,你可以相当有自己的人生的时候See that girl, watch that scene, dig in the dancing queen看到少女到现场观看,在挖掘舞蹈皇后Youre a teaser, you turn em onyoure捉弄人,你就转电磁Leave them burning and then youre gone他们焚烧,然后离开了youreLooking out for another, anyone will do好自为之另一个人会做Youre in the mood for a danceyoure在花样舞蹈And when you get the chance...而当你得到机会::You are the dancing queen, young and sweet,only seventeen你们是跳舞皇后,年轻又甜,只有17Dancing queen, feel the beat from the tambourine跳舞女王感受到击败来自tambourineYou can dance, you can jive, having the time of your life你可以跳舞,你可以相当有自己的人生的时候See that girl, watch that scene, dig in the dancing queen看到少女到现场观看,在挖掘舞蹈皇后。
高二年级英语音乐流派与艺术家创作风格深化理解单选题40题
高二年级英语音乐流派与艺术家创作风格深化理解单选题40题1. In a concert hall, the orchestra is playing a piece of music with complex melodies, harmonious polyphony and strict forms. This kind of music often features the use of symphony orchestra and has a long history. Which music genre does it belong to?A. RockB. JazzC. ClassicalD. Pop答案：C。
解析：题干描述的是古典音乐的特点，古典音乐有复杂的旋律、和谐的复调以及严格的形式，常使用交响乐团演奏并且历史悠久。
选项A摇滚音乐通常节奏强烈、旋律简单直接且具有强烈的节拍感。
选项B爵士乐特点是即兴演奏、节奏复杂且独特的爵士和声。
选项D流行音乐风格较为通俗，节奏轻快，和题干描述不符。
本题没有涉及特殊语法知识。
2. A famous piece of music has a solemn and elegant melody. The composer was a master in the Classical period. He often used sonata form in his works. Which of the following composers might he be?A. Ludwig van BeethovenB. Elvis PresleyC. Bob DylanD. Michael Jackson答案：A。
解析：贝多芬是古典时期的著名作曲家，他的作品常常使用奏鸣曲式。
选项B猫王是摇滚和流行音乐领域的歌手，与古典音乐无关。
选项C鲍勃·迪伦是民谣歌手。
闭眼指挥的卡拉扬英语作文200字运用反复修辞
全文分为作者个人简介和正文两个部分：作者个人简介：Hello everyone, I am an author dedicated to creating and sharing high-quality document templates. In this era of information overload, accurate and efficient communication has become especially important. I firmly believe that good communication can build bridges between people, playing an indispensable role in academia, career, and daily life. Therefore, I decided to invest my knowledge and skills into creating valuable documents to help people find inspiration and direction when needed.正文：闭眼指挥的卡拉扬英语作文200字运用反复修辞全文共3篇示例，供读者参考篇1Conducting Karaoke Blind: A Rhythmic Rhapsody of RevelryThere I stood, baton in hand, poised to plunge into the perilous depths of blind karaoke conducting. A thunderous cheer erupted from the crowd as the opening notes reverberatedthrough the room. With eyes tightly shut, I surrendered to the melodic maelstrom, letting the music engulf my senses.Sway, sway, the baton undulated, mimicking the ebb and flow of the tune. Sway, sway, my body swayed in synchronicity, lost in the intoxicating rhythm. The roar of the audience faded into the background as I became one with the song, a conduit for its emotional expression.Crescendo! The music swelled, its intensity mounting like a tidal wave crashing against the shores of my consciousness. Crescendo! My movements crescendoed in tandem, baton slicing through the air with fervent vigor. A kaleidoscope of sound enveloped me, each note a vibrant brushstroke on the canvas of my mind.Diminuendo, the symphony retreated, its power waning like the setting sun. Diminuendo, my gestures softened, caressing the invisible threads that bound me to the melody. In that moment, I was the maestro, the puppet master orchestrating an auditory spectacle.Ritardando, the tempo slowed, each beat lingering like a lover's embrace. Ritardando, my movements mirrored the languid pace, savoring every nuance, every delicate inflection.The audience held its collective breath, spellbound by the sensual interplay of sound and motion.Accelerando! The rhythm quickened, its urgency pulsating through my veins. Accelerando! My baton became a blur, whirling and twirling in a frenzied dance. The exhilaration was palpable, a torrent of adrenaline coursing through my body.Staccato, the notes punctuated the air with staccato precision. Staccato, my movements echoed their staccato cadence, sharp and defined, like the beating of a thousand drums. The crowd roared in approval, feeding off the infectious energy that permeated the room.Legato, the melody flowed like a gentle stream, its notes seamlessly intertwined. Legato, my baton glided through the air, tracing graceful arcs and sweeping curves. A hushed reverence fell upon the audience, transfixed by the ethereal beauty of the moment.Fortissimo, the music reached a thunderous crescendo, its power threatening to shatter the very foundations of the room. Fortissimo, my movements exploded with unbridled passion, every fiber of my being pulsating with the rhythm. The audience was swept away in the maelstrom, their cheers lost in the resounding cacophony.Pianissimo, the notes trickled like raindrops, their delicate whispers caressing my ears. Pianissimo, my gestures became gossamer threads, weaving a tapestry of subtle nuance. The hush that descended was deafening, each soul enraptured by the ethereal intimacy of the moment.Finale! The symphony reached its climactic conclusion, a triumphant blaze of glory. Finale! I poured every ounce of my being into those final, sweeping gestures, my baton a blazing comet streaking across the celestial firmament of sound.As the last note faded into silence, I stood motionless, drenched in the exhilaration of the experience. The thunderous applause that followed was a mere afterthought, for in those fleeting moments, I had transcended the mortal plane, becoming one with the music itself.Blind karaoke conducting was more than just a performance; it was a sacred ritual, a communion with the very essence of sound. With each gesture, I breathed life into the notes, weaving a tapestry of emotion that enveloped all who bore witness. It was a dance, a symphony, a rhapsody of revelry that defied the constraints of sight and soared on the wings of pure, unadulterated feeling.篇2The Thunderous Silence: A Maestro's Choreography of SoundThe stage loomed before me, a vast expanse of polished wood and hushed anticipation. As I stepped into the spotlight, the weight of a thousand expectations bore down upon my shoulders. Yet, my eyes remained resolutely shut, for this was no ordinary performance. This was the art of blind conducting, a dance of harmony and dissonance, where the baton became an extension of my very soul.With each sweeping motion, I summoned forth a symphony of sound, a tapestry woven from the threads of discipline and passion. The musicians, my willing accomplices, followed my lead with unwavering precision, their instruments singing in perfect unison. The air itself seemed to vibrate with the intensity of our collective effort, a resonance that transcended mere notes and rhythms.Silence, that ever-present companion, enveloped us like a cloak, its embrace both comforting and unnerving. In the absence of sight, my senses heightened, attuned to the subtlest nuances of the music. Each crescendo, each diminuendo,became a visceral experience, a physical manifestation of the emotions I sought to convey.Repeat, repeat, repeat – the mantra echoed within my mind, a constant reminder of the need for precision, for perfection. Every gesture, every nuance, had to be executed with unwavering conviction, lest the delicate balance be disrupted. The slightest falter, the most minute hesitation, could unravel the intricate tapestry we wove.Yet, within this realm of control and discipline, there existed a paradoxical freedom, a liberation from the constraints of the visible world. Unshackled from the distractions of sight, my mind soared, immersed in the boundless realms of sound and emotion. The music became an extension of my very being, a conduit through which I could express the inexpressible.Repeat, repeat, repeat – the rhythm pulsed through my veins, a primal beat that guided my movements, my body a vessel for the transcendent melodies that flowed forth. Each crescendo, a crescendo of passion; each diminuendo, a whisper of vulnerability. The music swelled and subsided, a living, breathing entity that defied the confines of time and space.In those moments of sublime unity, the boundaries between conductor, musicians, and audience dissolved, replaced by asingular, shared experience. We were no longer mere performers, but co-conspirators in a grand orchestration, weaving a tapestry of sound that transcended the physical realm.Repeat, repeat, repeat – the cycle continued, an endless spiral of creation and interpretation. Each performance, a unique expression of the eternal dance between order and chaos, structure and spontaneity. The baton became an extension of my innermost being, a conduit through which the music flowed, an embodiment of the very essence of artistic expression.As the final notes faded into silence, a hush descended upon the hall, a collective breath held in reverence. In that moment, the world seemed to stand still, suspended in a state of awe and wonder. For in that transcendent silence, we had glimpsed the infinite, the eternal dance of sound and spirit, forever etched into the annals of memory.Repeat, repeat, repeat – the cycle continues, the dance eternal, the symphony everlasting. And in those moments of sublime stillness, I knew that I had become more than a mere conductor; I had become a choreographer of the ineffable, a sculptor of the intangible, a maestro of the thunderous silence.篇3The Blind Conductor of Kalangan: A Symphony of ResilienceIn the heart of a small village nestled amidst the lush green hills of Kalangan, a remarkable story unfolds, a story of perseverance, determination, and the power of music to transcend adversity. It is the tale of Ravi, the blind conductor, whose unwavering spirit has inspired a generation of musicians and touched the souls of countless listeners.Ravi's journey began in darkness, a world without sight, yet his passion for music burned brighter than a thousand suns. From a tender age, he found solace in the melodies that danced through his mind, a sanctuary where he could escape the limitations imposed by his disability. His fingers caressed the ivory keys of an old piano, his ears attuned to every note, every harmony, every dissonance.As he grew older, Ravi's love for music blossomed into an insatiable thirst for knowledge. He studied, he practiced, he immersed himself in the intricacies of composition and the art of conducting. His determination knew no bounds, his dedication unwavering, his spirit unbreakable.It was in the small village of Kalangan that Ravi found his true calling, a place where music was the lifeblood of the community. With his keen ear and his unwavering passion, hegathered a motley crew of musicians, each with their own unique story, their own struggles, their own dreams.Rehearsals were a symphony of their own, a cacophony of instruments and voices, each vying for attention, each striving for perfection. Yet, in the midst of this chaos, Ravi stood tall, his baton raised high, his sightless eyes focused inward, his mind painting a masterpiece of sound.Through his gentle guidance, his unwavering patience, and his extraordinary talent, Ravi molded this ragtag ensemble into a harmonious whole. He taught them to listen, not just with their ears, but with their hearts, to feel the music coursing through their veins like a torrent of emotions.And as the notes soared, as the melodies intertwined, as the crescendos swelled and the diminuendos faded, Ravi became one with the music. His body swayed, his arms danced, his heart beat in perfect synchronicity with the rhythms that filled the air.The audience, spellbound, held their breath, captivated by the sheer power of the performance. They witnessed a miracle unfold before their eyes, a testament to the indomitable spirit of a man who had conquered his disability, who had turned his perceived weakness into his greatest strength.In those moments, when the final chord resonated through the hall, when the applause thundered like a rolling wave, Ravi stood triumphant, a beacon of hope, a living embodiment of what it means to persevere, to overcome, to truly live.For in that small village of Kalangan, Ravi had done more than merely conduct an orchestra; he had conducted a symphony of resilience, a masterpiece of human spirit that resonated far beyond the confines of the concert hall. His story, his music, his unwavering determination, became a rallying cry for all those who dared to dream, who dared to defy the odds, who dared to embrace their own unique rhythms and dance to the beat of their own drums.And as the echoes of his triumphs faded into the night, one thing remained certain: Ravi, the blind conductor of Kalangan, had left an indelible mark on the hearts and souls of all who had witnessed his extraordinary journey, a journey that proved, time and again, that true greatness lies not in what we see, but in how we hear the music of life.。
牛津译林版九年级上册Unit5《Artworld》(Integratedskills)说课稿
牛津译林版九年级上册Unit 5《Art World》（Integrated skills）说课稿一. 教材分析《牛津译林版九年级上册Unit 5 Art World》是一篇关于艺术世界的单元，主要介绍了绘画、音乐、舞蹈等艺术形式。
本单元的主题是艺术，通过学习本单元，学生可以了解不同的艺术形式，提高自己的艺术修养。
本节课的主要内容是Integrated skills部分，通过听、说、读、写等多种方式，让学生全面提高自己的英语能力。
二. 学情分析九年级的学生已经具备了一定的英语基础，但是对于一些专业的艺术术语可能还不太了解。
因此，在教学过程中，我需要帮助学生掌握这些专业术语，并能够运用到实际的语言环境中。
另外，由于本节课的内容涉及到艺术，学生可能对某些部分比较感兴趣，但是在语言表达方面可能还存在一些困难。
因此，我需要引导学生积极参与，提高他们的英语表达能力。
三. 说教学目标1.知识目标：学生能够掌握本节课的主要单词和短语，如pnting、sculpture、dance等，并能够运用到实际的语言环境中。
2.能力目标：学生能够听懂、会说、会读、会写本节课的主要内容，提高自己的英语综合能力。
3.情感目标：学生能够了解不同的艺术形式，提高自己的艺术修养，培养自己的审美能力。
四. 说教学重难点1.教学重点：学生能够掌握本节课的主要单词和短语，并能够运用到实际的语言环境中。
2.教学难点：学生能够理解并运用一些专业的艺术术语，如Impressionism、Baroque等。
五. 说教学方法与手段在本节课的教学过程中，我将以任务型教学法为主，结合交际法、情境教学法等多种教学方法，引导学生积极参与，提高他们的英语表达能力。
同时，我还会运用多媒体教学手段，如图片、音频、视频等，帮助学生更好地理解课文内容，提高他们的学习兴趣。
六. 说教学过程1.Pre-reading：通过展示一些著名的艺术作品，引导学生谈论自己喜欢的艺术形式，激发学生的学习兴趣。
Dancing links
Dancing links很久以前就听过Dancing Links，但一直没去看过，这两天简单学习了下。
算法本身和其名字一样，相当的优美，轻巧，与其说是一个算法，不如说是一种数据结构，十字链表的运用使整个过程真的就像跳舞一样。
推荐momodi的【Dancing Links 在搜索中的应用】精确覆盖：#define maxn 1005 * 105int l[maxn], r[maxn], u[maxn], d[maxn], ch[maxn], rh[maxn];int s[1005], o[1005], head, size, len;void remove(const int &c) {l[r[c]] = l[c];r[l[c]] = r[c];for (int i = d[c]; i != c; i = d[i]) {for (int j = r[i]; j != i; j = r[j]) {u[d[j]] = u[j];d[u[j]] = d[j];s[ch[j]] -= 1;}}}void resume(const int &c) {for (int i = u[c]; i != c; i = u[i]) {for (int j = l[i]; j != i; j = l[j]) {s[ch[j]] += 1;u[d[j]] = j;d[u[j]] = j;}}l[r[c]] = c;r[l[c]] = c;}bool dfs(const int &k) {if (r[head] == head) {return true;}int ss = max_int, c;for (int t = r[head]; t != head; t = r[t]) if (s[t] < ss) {ss = s[t];c = t;}remove(c);for (int i = d[c]; i != c; i = d[i]) {o[k] = i;len = k;for (int j = r[i]; j != i; j = r[j]) remove(ch[j]);if (dfs(k + 1) == true) return true;for (int j = l[i]; j != i; j = l[j]) resume(ch[j]);}resume(c);return false;}int new_node(int up, int down, int left, int right) {u[size] = up;d[size] = down;l[size] = left;r[size] = right;d[up] = u[down] = r[left] = l[right] = size;return size++;}void init(int m) {size = 0;head = new_node(0, 0, 0, 0);for (int j = 1; j <= m; j++) {new_node(j, j, l[head], head);ch[j] = j, s[j] = 0;}}int main(int argc, char** argv) {int n, m, cnt;while (scanf("%d%d", &n, &m) != EOF) {init(m);for (int i = 1, j = 0; i <= n; i++) {cnt = scan_int();int row = -1;while (cnt--) {j = scan_int();ch[size] = j, s[j] += 1;if (row == -1) {row = new_node(u[ch[j]], ch[j], size, size);rh[row] = i;}else {int k = new_node(u[ch[j]], ch[j], l[row], row); rh[k] = i;}}}bool ans = dfs(1);if (ans == true) {printf("%d", len);for (int i = 1; i <= len; i++) printf(" %d", rh[o[i]]);printf("\n");} else printf("NO\n");}return (EXIT_SUCCESS);}hust1017 【Exact cover】纯模板题。
A phase I escalating single-dose and weekly Wxed-dose study of cetuximab pharmacokinetics
Cancer Chemother Pharmacol (2009) 64:557–564DOI 10.1007/s00280-008-0904-6ORIGINAL ARTICLEA phase I escalating single-dose and weekly W xed-dose study of cetuximab pharmacokinetics in Japanese patientswith solid tumorsKuniaki Shirao · Takayuki Yoshino · Narikazu Boku · Ken Kato · Tetsuya Hamaguchi · Hisateru Yasui · Nobuyuki Yamamoto · Yusuke Tanigawara · Arno Nolting ·Shinichiro YoshinoReceived: 4 August 2008 / Accepted: 12 December 2008 / Published online: 24 January 2009© Springer-Verlag 2009AbstractPurpose Cetuximab is a therapeutic immunoglobulin G1 monoclonal antibody that recognizes the epidermal growth factor receptor (EGFR). This phase I dose-escalation study was designed to assess the safety and pharmacokinetics (PK) of cetuximab in Japanese patients with EGFR-expressing, advanced, solid tumors and also to look for evi-dence of antitumor e Y cacy.Patients and methods Thirty patients were enrolled in the study; 29 with colorectal adenocarcinomas and one with an adenocarcinoma of the lung. Patients received an initial/ weekly infusion of cetuximab at dose levels of 100/100 (dose level 1), 250/250 (dose level 2), 400/250 (dose level 3), 500/250 (dose level 4) or 400/250 (dose level 5) mg/m2, for 7 or more weeks, with an interval between the initial and second infusion of 1 (dose level 5 representing the stan-dard regimen) or 2weeks (dose levels 1–4 of the non-stan-dard regimens).Results No dose-limiting toxicities (DLTs) were observed during the evaluation period. All patients had at least one adverse event (AE). The most common cetuximab-related AEs were skin toxicity (93% of patients), including acnei-form dermatitis (83% of patients). Two patients experi-enced cetuximab-related grade 3 AEs of skin toxicity and diarrhea after DLT evaluation. C max and AUC0–1 after the initial infusion showed dose-proportional increases. Mean total body clearance (CL) values decreased with dose at the lower dose levels. At doses of ¸400mg/m2, CL values appeared to level o V. Mean trough concentrations for dose level 5 were constant from week 4 (day 29) onward. Two patients (8%) achieved partial response (at 100/100mg/ m2). The overall disease control rate (partial response+ stable disease) was 58%.Conclusion The current study demonstrated that cetux-imab PK and safety pro W les are similar between Japanese and non-Japanese patient populations. It would appear thatK. Shirao · K. Kato · T. Hamaguchi · H. YasuiDivision of Gastrointestinal Oncology,National Cancer Center Hospital, Tokyo, JapanT. Yoshino · N. BokuDivision of Gastrointestinal Oncology, Shizuoka Cancer Center, Shizuoka, JapanN. YamamotoThoracic Oncology Division, Shizuoka Cancer Center, Shizuoka, JapanY. TanigawaraDepartment of Hospital Pharmacy, School of Medicine,Keio University, Tokyo, JapanA. NoltingExploratory Medicine Global Human Pharmacology,Merck KGaA, Darmstadt, Germany S. YoshinoMedical Department, Merck Serono Co., Ltd, Tokyo, Japan Present Address:K. Shirao (&)Department of Medical Oncology, Faculty of Medicine, Oita University, 1-1, Idaigaoka, Hasama-machi, Yufu, Oita 879-5593, Japane-mail: kshirao@med.oita-u.ac.jpPresent Address:T. YoshinoNational Cancer Center Hospital East, Chiba, Japan Present Address:H. YasuiMedical Oncology Division,National Hospital Organization Kyoto Medical Center, Kyoto, Japanthe standard dose of an initial 2-h infusion of 400mg/m2 followed thereafter by weekly 1-h infusions of 250mg/m2 for non-Japanese patients is feasible for future clinical stud-ies in Japanese patients.Keywords Cetuximab · Japanese · EGFR · Safety · Pharmacokinetics · ColorectalIntroductionOver recent years, the development of rationally selected targeted agents such as monoclonal antibodies and small molecule tyrosine kinase inhibitors has o V ered new possi-bilities in relation to improving the e Y cacy of the standard cytotoxic regimens used in the treatment of metastatic colo-rectal cancer (mCRC). The epidermal growth factor recep-tor (EGFR)-targeted immunoglobulin G1 monoclonal antibody cetuximab (Erbitux®) is one such targeted agent.Cetuximab competitively inhibits the binding of endoge-nous EGFR ligands and thus prevents receptor dimerization and downstream signaling [1, 2]. Antibody-binding to the tumor cell may also result in a clinically-important anti-body-dependent cell-mediated cytotoxicity reaction (ADCC) [3, 4]. Randomized mCRC studies in mainly Cau-casian populations have shown that cetuximab, adminis-tered in accordance with the standard dosing regimen of an initial 2-h infusion of 400mg/m2 of body surface area (BSA) followed thereafter by weekly 1-h infusions of 250mg/m2, is e V ective as monotherapy [5, 6] or in combi-nation with irinotecan [5, 7], following the failure of previ-ous chemotherapy regimens. Furthermore, in the W rst-line setting, the phase III CRYSTAL study has shown that the addition of cetuximab to infusional 5-X uorouracil/folinic acid/irinotecan (FOLFIRI) signi W cantly improves the response rate, progression-free survival (PFS) time and R0 resection rate in mCRC patients, compared with FOLFIRI alone [8]. Similarly, randomized studies have demonstrated the e Y cacy of cetuximab in combination with radiotherapy in the treatment of locally advanced squamous cell carci-noma of the head and neck (SCCHN) [9] and in combina-tion with platinum-based therapy in the W rst-line treatment of recurrent and/or metastatic SCCHN [10].Two recent studies in the US have explored the pharma-cokinetics (PK) of single-dose administration of cetuximab in patients with solid tumors, with particular attention paid to the elimination phase [11, 12]. Both studies supported the saturation of EGFR binding at a clinically achievable dose level. A signi W cant association was also noted between cetuximab clearance and both BSA and weight, supporting the use of these parameters in calculating individual cetuximab doses [12]. The primary objective of the current phase I study was to investigate the safety and tolerability of cetuximab in a population of Japanese patients with EGFR-expressing solid tumors. Secondary objectives were to evaluate the PK of cetuximab in Japa-nese patients the (mirroring the recent US PK analyses with an escalating single dose); expression of human antichi-meric antibodies (HACA); the incidence of dose-limiting toxicity (DLT); and the antitumor e Y cacy of cetuximab. Patients and methodsPatient eligibilityOnly Japanese patients, aged between 20 and 74years, with a histologically or cytologically con W rmed advanced solid EGFR-expressing tumor, refractory to a standard therapy or for which no standard therapy existed, were eligible. They required an Eastern Cooperative Oncology Group perfor-mance status of 0–2; a life expectancy of at least 3months after the start of study; adequate hematological (leukocyte count: ¸3,000 and <12,000mm¡3; neutrophil count:¸1,500mm¡3; platelet count: ¸100,000mm¡3; hemoglo-bin: ¸9g/dL), hepatic (aspartate aminotransferase and ala-nine aminotransferase: ·2.5 times the upper limit of the reference range; serum total bilirubin: ·1.5 times the upper limit of the reference range), and renal (serum creatinine:·1.5 times the upper limit of the reference range) function. Patients were required to be available for hospitalization until day 22 of the study, to have no carry-over e V ect from prior therapy and to not have received treatment with blood transfusions, blood products or blood cell factors such as granulocyte colony stimulating factor during 2weeks prior to enrollment. All patients gave their written informed con-sent prior to study entry.Patients were excluded if they had: symptomatic brain metastasis, a previous history of cancerous meningitis, poorly controlled epileptic seizures or clinically signi W cant mental or central nervous system disorders or if they had previously received monoclonal antibody therapy (includ-ing cetuximab). They were also ineligible if they had seri-ous cardiac or cardiovascular disease, diabetes mellitus, hypertension, active infection or symptomatic blood coag-ulation disorder, acute pulmonary disorder, interstitial pneumonia, or pulmonary W brosis; active, double cancers;a previous history of malignant tumors (other than non-melanoma skin cancer, uterine cervical carcinoma or gastrointestinal intramucosal carcinoma) with a sign of recurrence within the last 5years; a large volume of pleu-ral e V usion or ascites or were positive for hepatitis B virus, hepatitis C virus or human immunode W ciency virus. Patients were also excluded if they required chronic treatment with systemic steroids; were pregnant or lactating; if they wished to have a child; or if they had an alcohol or drugaddiction or a previous history of drug allergy or anaphy-lactic symptoms.Study designThis study was a two-center, phase I dose-escalation study of cetuximab in patients with advanced solid cancer. As this was the W rst such investigation in Japanese patients, a low dose level of 100mg/m 2 as an initial dose and 100mg/m 2 as a repeated weekly dose was selected to begin the study. All patients received 50mg oral diphenhydramine hydrochloride (H1-antagonist) 30–60min before each cetuximab infusion as a preventive measure in relation to infusion-related reactions. At W rst infusion, patients received 100 (dose level 1), 250 (dose level 2), 400 (dose level 3 or 5) or 500 (dose level 4) mg/m 2 of cetuximab as a 2-h intravenous infusion. Subsequent weekly 1-h infusions of 100 (dose level 1) or 250 (dose level 2–5) mg/m 2 of cetuximab began according to the schedule in Fig.1 and continued to day 50, which was considered to be su Y cient to assess cetuximab PK. For dose levels 1–4, patients had a 2-week interval between W rst and second infusion for the purposes of evaluation of single-dose PK. Patients in dose level 5 received cetuximab according to the standard 400/250mg/m 2 schedule, with a 1-week interval between W rst and second infusions, curtailing the collection of single-dose PK at 7days in this group.Six patients were assigned to each dose level 1–4, with the W rst cohort receiving cetuximab at the lowest dose level.If DLT was observed in ¸2 patients during the DLT evalu-ation period of 6weeks from the W rst administration until 1week after the W fth administration, no further patients were to be enrolled and this dose level was de W ned as the MTD. Otherwise, the dose was escalated to the next dose level (1–2, 2–3 or 3–4). If the MTD was not established at dose level 4, six patients received the standard 400/250mg/m 2 regimen at dose level 5. DLT was de W ned as either:grade 4 or three incidences of grade 3 skin toxicity events,or the omission of three consecutive infusions due to grade 3 skin toxicity; adverse drug reactions ¸grade 3 (except forskin toxicity, electrolyte abnormality, anorexia, nausea, and alkaline phosphatase) or the development of acute pulmo-nary disease, interstitial pneumonia and other pulmonary symptoms. Infusion-related reactions were not regarded as DLTs as they were considered to be largely dose-indepen-dent. If progressive disease (PD) was not observed between the initial dose and W fth administration (or sixth administra-tion for dose level 5), the study medication was to be con-tinued as long as the patient gave consent, again after an observation period of 1week. During the study period, the following drugs and therapies were not permitted; thera-peutic modalities for malignant tumor, other antibody ther-apy, chemotherapy, hormonal therapy, immunological therapy, radiotherapy, hyperthermia and surgical therapy,and systemic steroids. The drugs and therapies used for symptomatic relief of concurrent diseases or complications were permitted before and during the study with minimal modi W cation of dosage and mode of administration.Study evaluationsResponse was assessed in evaluable patients by the investi-gators according to RECIST guidelines [13] and had to be con W rmed by a repeated consecutive assessment conducted a minimum of 28days after the W rst assessment. Adverse events (AEs) were graded according to the National Cancer Institute—Common Toxicity Criteria version 2 (Japan Clinical Oncology Group—translation version). Safety variables assessed included; AEs, abnormal laboratory val-ues and vital signs (blood pressure, heart rate, respiratory rate, body temperature, 12-lead electrocardiogram, chest X-ray).Pharmacokinetic analysisBlood samples (5mL) were drawn prior to the W rst cetux-imab infusion and at 1, 1:58, 2:30, 3, 4, 6, 8, 24, 48, 96,168, 264 and 336h (not 264 and 336h for dose level 5)after the initiation of infusion. Subsequent samples were taken before cetuximab infusions on days 15 (dose level 5Fig.1Dosage and schedule of on-study cetuximab administrationonly), 22, 29, 36, 43 and 50 and during the post-treatment observation period or at the time of withdrawal from the study. Cetuximab serum concentration data were generated using a validated sandwich enzyme-linked immunosorbent assay (ELISA) carried out by MDS PS Pharma Services Switzerland AG (Fehraltorf, Switzerland) essentially as described [14].ResultsPatients and demographicsEGFR expression was detected immunohistochemically in the tumor tissue of 43 of 47 screened patients (91%). Of these 43 patients, 30 ful W lled all the inclusion criteria and were enrolled in the study; all received at least one dose of the study drug. Summarized for all patients in Table 1, the demographic characteristics of the individual treatment groups were generally similar. There were no major di V er-ences between the dose levels with regard to medical his-tory other than cancer. Twenty-nine patients were su V ering from adenocarcinoma of the colon or rectum and the remaining patient had adenocarcinoma of the lung. The majority of patients had metastatic disease at study entry,and 8 (27%), 10 (33%) and 9 (30%) patients had 1, 2 and 3organs involved, respectively. Most commonly involved organs were the lung in 22, liver in 20 and the lymph nodes in 15 patients. All patients had received previous chemo-therapy or hormonal therapy; 29 had undergone surgery, 6had received radiotherapy, and three had received other treatments. Similar percentages of patients received con-comitant medication across dose levels, except for a higher incidence of the use of antihypertensive medications at dose levels 4 and 5.Dose-limiting toxicity assessmentThe safety population comprised all 30 patients, each of whom had received at least one dose of the study medica-tion. Four patients did not complete the DLT evaluation period after withdrawing from treatment as a consequence of PD after one (one patient) or three infusions (three patients). DLT analyses were therefore performed on 26evaluable patients (5 patients each at dose levels 2–5 and 6 patients at dose level 1). The median duration of treat-ment was 14.0weeks and the median cumulative cetux-imab dose was 2,450mg/m 2. No DLT was reported during the evaluation period and consequently, the MTD was not reached even at the highest dose level. Eighteen patients continued treatment with cetuximab after com-pletion of the preset weekly repeated treatment schedule (on day 50).Adverse eventsAEs and cetuximab-related AEs were reported in 30(100%) and 29 (97%) patients, respectively. The most com-mon AEs according to system organ class (SOC) distribu-tion were skin and subcutaneous tissue disorders and investigations (both reported for 28/30, 93% of patients)followed by gastrointestinal disorders and general disorders and administration site conditions (both 26/28 patients,87%).The most common cetuximab-related AEs observed (summarized in Table 2) were acneiform dermatitis (83%),rash and skin reaction (both 47%), dry skin (40%), pruritus (33%), paronychia (37%), pyrexia (57%), diarrhea (33%)and fatigue and stomatitis (both 30%). Hypersensitivity reaction (HSR) was reported in only one patient at dose level 1. This patient experienced HSR twice: a grade 1 HSR on the day of the W rst cetuximab infusion and a grade 2HSR on the second day after administration at week 6. Both reactions resolved. Pyrexia and headache appeared to more common at the higher dose levels and were mainly reported in a close temporal relationship with cetuximab infusion,suggesting that they may have been infusion-related events.Grade 3 or 4 AEs were reported in nine patients after DLT evaluation and in two cases, were considered to beTable 1Patients characteristics ECOG PS Eastern Cooperative Oncology Group performance status,NSCLC non-small cell lung cancerCharacteristic N =30Gender, N (%)Male 15 (50.0)Female 15 (50.0)Age (years)Median (min–max)54 (36–73)ECOG PS, N (%)020 (67.7)19 (30.0)21 (3.3)Diagnosis, N (%)Colorectal cancer 29 (96.7)NSCLC1 (3.3)Prior therapy, N (%)Chemotherapy 30 (100)5-Fluorouracil 27S-17UFT 7Irinotecan 28Oxaliplatin 1Radiotherapy6 (20)cetuximab-related (grade 3 diarrhea, one patient at doselevel 1; grade 3 acneiform dermatitis, pruritus and rash, one patient at dose level 4).Although cetuximab-related AEs did not lead to discon-tinuation of cetuximab in any patient, the primary reason for discontinuation in two patients was an aggravation of disease symptoms. The weekly dose for one patient (dose level 4) was reduced from 250 to 200mg/m 2 at the 38th week of administration due to grade 3 skin toxicity in accordance with the study protocol. There were no other dose reductions. One patient died within 30days of the end of study treatment from an unrelated respiratory failure due to progressive lung metastases.PharmacokineticsA full PK pro W le suitable for PK analysis following initial cetuximab infusion was available from all patients. Individ-ual PK parameters after non-compartmental and compart-mental analysis were in good agreement. In general, inter-patient variability in the cetuximab concentration values was not large. Cetuximab serum concentration time pro W les are displayed in Fig.2. Mean trough concentrations for dose level 5 were constant from week 4 (day 22) onwards (Fig.3).PK parameters, based on non-compartment analysis and data obtained at 2weeks later (day 15) in dose level 1–4and at a week later (day 8) in dose level 5, are shown in Table 3. Dose-proportional increases in mean C max (range 49.0–396.7 g/mL) were observed across the dose range of 100–500mg/m². Moderate deviations from dose propor-tional increases were observed for AUC 0–1 (range 3,469–3,4817 g/mL h), especially at the low doses. However, in general, maximum serum concentrations following infusion and the exposure to cetuximab as measured by AUC 0¡1are predictable for each dose used. Mean CL values decreased with dose at the lower dose levels. At doses of ¸400mg/m 2, CL values appeared to level o V . Mean termi-nal half-life (t 1/2) values increased from 54 to 111h over the 100–500mg/m 2 dose range. At the dose of 400mg/m 2(equivalent to the standard regimen), the mean t 1/2 values were 101 (dose level 3) and 106h (dose level 5). Values for the volume of distribution at steady state (V ss ) were inde-pendent of dose and consistent with distribution of cetux-imab in the theoretical vascular space.Pre- and post-dose samples for the determination of HACA levels were available for 21 patients. The analytical results suggested that there had been no induction of such antibodies in these patients.E Y cacySix patients were excluded from the e Y cacy analysis,three because follow-up evaluation was not available (allTable 2Relevant common any grade and grade 3/4 cetuximab-related adverse events aDose; initial dose/weekly doseAdverse eventNumber of patients with any grade (grade 3/4)Any gradetotal (%)Grade 3/4 total (%)Dose level 12345Dose a (mg/m 2)100/100N =6250/250N =6400/250N =6500/250N =6400/250N =6N =30Any adverse event 5 (1)66 6 (1)696.7 6.7Acneiform dermatitis 564 5 (1)583.3 3.3Rash3252 (1)246.7 3.3Skin reaction 3332346.7Dry skin1214440.0Pruritus 213 3 (1)133.3 3.3Paronychia 34436.7Pyrexia 245656.7Diarrhea 2 (1)122333.3 3.3Fatigue 1142130.0Stomatitis 311430.0Anorexia 24226.7Nausea 123123.3Vomiting132123.3colorectal cancer), and three because the disease at baseline was not measurable (two colorectal cancer and one lung adenocarcinoma). Twenty-four patients were thereforeevaluable for e Y cacy. Two patients treated at dose level 1showed partial response, giving an overall response rate of 8.3% in the e Y cacy-evaluable population [95% con W dence interval (CI): 1.0, 27.0]. Furthermore, 12 patients achieved stable disease (3, 3, 1, 3 and 2 patients at dose levels 1–5,respectively) to give an overall disease control rate of 58.3% (95% CI: 36.6, 77.9).DiscussionCetuximab has been shown to be e V ective and generally well tolerated in mixed but mainly Caucasian patient groups and the PK pro W le of this agent administered as a single dose of 20–500mg/m 2 has been extensively charac-terized in a variety of separate studies in such populations [15]. Two recent studies have examined cetuximab single-dose PK in US patients with solid tumors using a similarTable 3Mean (standard deviation) pharmacokinetic parameters at day 15 (non-compartment analysis)CV coeY cient of variation, C max maximum concentration, AUC 0–1 area under the concentration-time curve, t 1/2 terminal half-life, CL total body clearance, V ss volume of distribution at steady state aDose level 5: pharmacokinetic parameters are based on concentration data measured up to timepoint 168h (day 8) following the initial 400mg/m 2 doseDose level (dose mg/m 2)1 (100) N =62 (250) N =63 (400) N =64 (500) N =65 (400)a N =6C max ( g/mL)49.0 (8.5)157.0 (31.9)287.2 (37.9)396.7 (83.6)297.8 (30.5)% CV1720132110AUC 0–1 ( g/mL £h)3,469 (583)12,132 (2,300)25,823 (6,525)34,817 (11,498)29,213 (6,431)% CV 1719253322t 1/2 (h)54 (17)74 (12)101 (31)111 (19)106 (24)CL (L/h)0.046 (0.007)0.035 (0.009)0.026 (0.009)0.026 (0.013)0.022 (0.005)V ss (L)3.46 (0.59)3.98 (0.78)3.34 (0.48)3.51 (0.56)3.1 (0.5)dose-escalation protocol to that employed in the current study [11, 12]. Patients in both of these studies received either: 50, 100, 250, 400 or 500mg/m2 initial infusions, fol-lowed after a 3-week interval by weekly infusions of 250mg/m2. The similarity in schedules and type of patient included in these analyses allows a comparative evaluation of cetuximab PK and safety in the non-Japanese and Japa-nese patient groups. Mean C max values were comparable for initial cetuximab dose levels of 100 and 250mg/m² in the two populations. However, at the higher doses of 400 and 500mg/m2, C max values were higher in the Japanese (287 and 397 g/mL) compared with the non-Japanese popula-tions 205/229 and 243/246 g/mL, respectively). Likewise, mean AUC0–1 values were comparable at the lower doses but higher in the Japanese compared with the non-Japanese patient groups at the 500mg/m2 dose level (34,817 vs. 30,870 and 24,740 g/mL h).However, the results of the current study con W rm that the PK pro W le in Japanese patients is broadly similar to that obtained for non-Japanese patient groups. In particular, lin-ear relationships for both mean C max and AUC0–1 with dose that were previously noted in the non-Japanese popu-lations were also observed in the Japanese population, indi-cating that the exposure to cetuximab is predictable across the dose-range. Dose-dependent relationships were observed in the current study for t1/2 and CL at lower doses, with the apparent leveling of CL seen at the higher doses mirroring the earlier studies in non-Japanese patients and supportive of receptor saturation at these doses. In addition, V ss was independent of dose and consistent with a distribu-tion of cetuximab in the theoretical vascular space, which is similarly consistent with the data from non-Japanese popu-lations. The cetuximab mean trough concentrations follow-ing repeated weekly doses of 250mg/m2 (dose level 5) in the Japanese population were constant from fourth week (day 29) onwards and were in good agreement with previ-ously reported pharmacologically active trough concentra-tion values following the standard dosing regimen (equal to dose level 5) of cetuximab [16].In relation to safety, cetuximab was generally well toler-ated at all dose levels in Japanese patients and the MTD was not reached at the highest dose-level tested (500mg/m2 initial infusion followed by 250mg/m2 weekly). No spe-ci W c toxicities were identi W ed in Japanese patients com-pared with mainly Caucasian groups, and the incidence of cetuximab-related grade 3/4 AEs was low (2/30 patients) and as expected. The most common AEs at any grade according to SOC distribution were skin and subcutaneous tissue disorders, which were reported for 93% of patients. Acneiform dermatitis, which was noted in 83% of patients, was the most commonly occurring cetuximab-related AE. Although skin reactions are a class e V ect of EGFR-targeted agents, the level of incidence of this mainly mild adverse drug reaction in this study is in the upper range of what has been commonly reported for mixed but mainly Caucasian populations. A considerable number of studies in a range of cancer types including mCRC have noted a correlation between the incidence and severity of acne-like rash or skin reactions and e Y cacy [5, 8, 16–19]. The high level of skin toxicity noted in Japanese patients may therefore be a promising indicator for cetuximab e Y cacy in this popula-tion, a hypothesis that should be addressed in future clinical studies. The disease control rate of 58% achieved for cetux-imab monotherapy in Japanese patients is encouraging in this context. On balance, the safety pro W le for all dose regi-mens in the current study was essentially consistent with the safety pro W le of cetuximab as described in the previous comparable studies in non-Japanese patient populations [11, 12].In conclusion, the current study has demonstrated that cetuximab PK and safety pro W les are similar between Japa-nese and non-Japanese patient populations. Given this assessment, it would appear that the standard dose of an ini-tial 2-h infusion of 400mg/m2 followed thereafter by weekly 1-h infusions of 250mg/m2 is feasible for future clinical studies in Japanese patients.References1.Goldstein NI, Prewett M, Zuklys K, Rockwell P, Mendelsohn J(1995) Biological e Y cacy of a chimeric antibody to the epidermal growth factor receptor in a human tumor xenograft model. Clin Cancer Res 1:1311–13182.Li S, Schmitz KR, Je V rey PD, Wiltzius JJ, Kussie P, Ferguson KM(2005) Structural basis for inhibition of the epidermal growth fac-tor receptor by cetuximab. Cancer Cell 7:301–3113.Kang X, Patel D, Ng S, Melchior M, Ludwig D, Hicklin D (2007)High a Y nity Fc receptor binding and potent induction of antibody-dependent cellular cytotoxicity (ADCC) in vitro by anti-epidermal growth factor receptor antibody cetuximab. J Clin Oncol 25:(Abstr 3041)4.Kurai J, Chikumi H, Hashimoto K, Yamaguchi K, Yamasaki A,Sako T, Touge H, Makino H, Takata M, Miyata M, Nakamoto M, Burioka N, Shimizu E (2007) Antibody-dependent cellular cyto-toxicity mediated by cetuximab against lung cancer cell lines. Clin Cancer Res 13:1552–15615.Cunningham D, Humblet Y, Siena S, Khayat D, Bleiberg H,Santoro A, Bets D, Mueser M, Harstrick A, Verslype C, Chau I, Van Cutsem E (2004) Cetuximab monotherapy and cetuximab plus irinotecan in irinotecan-refractory metastatic colorectal cancer. N Engl J Med 351:337–3456.Jonker DJ, Karapetis CS, Moore M, Zalcberg JR, Tu D, Berry S,Koski S, Krahn M, Simes J, Tebbutt N, Van Hazel G, O’Callaghan CJ (2007) Randomized phase III trial of cetuximab monotherapy plus best supportive care [BSC] versus BSC alone in patients with pretreated metastatic epidermal growth factor receptor [EGFR]-positive colorectal carcinoma. A trial of the National Cancer Institute of Canada Clinical Trials Group (NCIC CTG) and the Australasian Gastro-Intestinal Trials Group (AGITG). 98th AACR Annual Meeting, 14–18 April 2007, Los Angeles, USA (Abstr LB-1). Updated information presented at meeting。
一篇不错的 Dancing Links 介绍文章 [
决方法只有搜索! 且看如下搜索代码：
3 EXACT COVER PROBLEM 4
if (A is empty) { \\A is the 0-1 matrix.
the problem is solved;
return ;
}
choose a column, c,
that is unremoved and has fewest elements.;
remove(C[j]); } if (dfs(k + 1)) { 4 SUDOKU TO EXACT COVER PROBLEM 8
3 EXACT COVER PROBLEM 7
} } } void resume(const int &c) { for (int i = U[c]; i != c; i = U[i]) {
for (int j = L[i]; j != i; j = L[j]) { ++S[C[j]]; U[D[j]] = j; D[U[j]] = j;
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舞蹈韵律生活调的英语作文
Dancing is a universal language that transcends cultural and linguistic barriers, bringing people together in a harmonious celebration of movement and rhythm.It is an art form that has been practiced for centuries,evolving with time and culture,yet remaining a constant source of joy and expression for those who partake in it.The rhythm of life is often likened to a dance,with its ups and downs,its moments of stillness and bursts of activity.Just as a dancer moves to the beat of music,we navigate the ebb and flow of our daily lives,finding our own rhythm and balance.The art of dance can teach us valuable lessons about life,resilience,and the power of selfexpression.In the realm of dance,there are countless styles,each with its own unique characteristics and cultural significance.From the graceful movements of ballet to the energetic steps of hiphop,from the traditional folk dances of various countries to the contemporary styles of modern dance,the diversity of dance is a testament to the creativity and adaptability of the human spirit.Ballet,with its roots in the Italian Renaissance courts of the15th century,has evolved into a highly technical and disciplined form of dance.It requires immense physical strength,flexibility,and control,as well as a deep understanding of musicality and artistic expression.Ballet dancers often spend years perfecting their craft,embodying the discipline and dedication that can be applied to any aspect of life.Hiphop,on the other hand,emerged from the urban streets of New York City in the 1970s,reflecting the cultural and social experiences of its practitioners.It is a vibrant and dynamic form of dance that emphasizes improvisation,individuality,and the power of collective expression.Through hiphop,dancers can communicate their personal stories and experiences,fostering a sense of community and shared identity.Folk dances,which are deeply rooted in the traditions and histories of their respective cultures,offer a window into the lives and values of the people who practice them.These dances often involve intricate patterns and formations,requiring a high level of coordination and teamwork.By participating in folk dances,individuals can connect with their cultural heritage and gain a deeper appreciation for the richness of human diversity.Modern dance,a form that emerged in the early20th century as a reaction against the rigidity of classical ballet,emphasizes the exploration of personal expression and the use of unconventional movements.Modern dancers often experiment with different techniques and styles,pushing the boundaries of what is considered dance.This spirit of innovation and creativity can inspire us to approach our own lives with an open mind and a willingness to embrace change.In addition to the aesthetic and cultural aspects of dance,it also offers numerous physical and mental health benefits.Dancing regularly can improve cardiovascular health, increase flexibility and strength,and promote overall wellbeing.Moreover,the act of dancing can be a powerful stress reliever,allowing individuals to express their emotions and connect with their inner selves.In conclusion,the dance of life is a beautiful and complex interplay of movement,rhythm, and emotion.By embracing the art of dance,we can learn to move with grace and confidence through the various stages of our lives,finding joy and fulfillment in the process.Whether it be through the discipline of ballet,the energy of hiphop,the traditions of folk dances,or the creativity of modern dance,the lessons and experiences gained from dancing can enrich our lives and help us to find our own unique rhythm in the world.。
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N+1 Parallel Solution
Almost exactly the same as Sequential except:
ForFor-loop over Pawn Placements is distributed over p processors Evidence suggests that more solutions are found when the Pawns are near the center of the chess board
Motivation
NASA EPSCoR grant
Began working with Chatham and Skaggs in November
Doyle added DLX (Dancing Links) at beginning of semester
New to me (and the rest of the team, I think) A lot more work!
Backtracking
An example of backtracking is used in a depthdepth-first search in a binary tree:
Let t be a binary tree depthfirst(t) { if (t is not empty) { access root item of t; depthfirst(left(t)); depthfirst(right(t)); } }
N+1 Queens, Parallel vs. Sequential C++
1.0E+05 1.0E+03 1.0E+01 1.0E-01 1.0E-03 C++,backtrack C++, BT, || 6 7 8 9 10 11 12 13 14 15
N+K – what to do?
N+k presents a very large problem
Solutions
Solutions – A class of Queen placements such that no two Queens can attack each other. Fundamental Solutions – A class of solutions such that all members of the class are simply rotations or reflections of one another.
i.e. It calls itself
Recursion in Art
Recursion in Computer Science
// precondition: n >= 0 // postcondition: n! is returned factorial (int n) { if (n == 1) or (n == 0) return 1; else return (n*factorial(n-1)); (n*factorial(n}
Search for a better way…
Dancing Links
Why “Dancing Links?”
Structure & Algorithm
Comprehendible (Open for Debate…)
Increased performance
Parallel computing is utilized mainly for performance advantages… so, why run a subsubpar algorithm (backtracking) when the goal is to achieve the quickest run-time? run-
Category of Problems
8 Queens
8 attacking queens on an 8x8 chess board
N Queens
N attacking queens on an NxN chess board
N+1 Queens
N+1 attacking queens on an NxN chess board 1 Pawn used to block two or more attacking queens
Column Headers
Column Headers are nodes linked horizontally with the Header node Members:
Solving N+k Queens Using Dancing Links
Matthew Wolff CS 499c May 3, 2006
Agenda
Motivation Definitions Problem Definition Solved Problems with Results Future Work
Another loop over Pawn placements More checking for fundamental solutions
8x8 Board, 1 Pawn
Main Focus: N+k Queens
Why?
Instead of focusing on specific solutions (N+1, N+2, ...), we will be able to solve any general statement (N+k) of the “Queens Problem.” Implementing a solution is rigorous and utilizes many important techniques in computer science such as parallel algorithm development, recursion, and backtracking
Similar to 8 Queens Use a more general board of size NxN
Same algorithm as 8 Queens
N+1 Queens
What happens when you add a pawn?
For a large enough board, we can add an extra Queen Slightly more complex
1 Pawn meant an extra for loop around everything k Pawns would imply k for loops around everything
Dynamic for loops? “That’s Unpossible” – Ralph Wiggum
More solutions implies more computations, thus more time Pawns are specially numbered for more optimization
Pawn Placements for Parallel N+1 Queens Solution
Made popular by Knuth via his circa 2000 article
“The Universe”
MultiMulti-Dimensional structure composed of circular, doubly linked-lists linkedEach row and column is a circular, doubly linkedlinked-list
N+k Queens
N+k attacking queens on an NxN chess board k Pawns used to block numerous attacking queens
8 Queens Example
/nqueen_demo/nqueens.html
Chatham, Fricke, Skaggs
Proved N+k queens can be placed on an NxN board with k pawns.
What did I do?
Translate Chatham’s Python Code (for N+1) into a sequential C++ program Modify sequential C++ code to run in Parallel with MPI Design and implement the N+k Queens solution (Iterative)k * (Recursive)N = No. Dancing Links
N+1 Sequential Solution
Optimized to exploit the geometry of the problem
Pawns may not be placed in first or last column or row Pawns are only placed on roughly 1/8 of the board (in a wedge shape)
Backtracking Example
Output:
A–B–D–E–H–I–C–F-G
4 Queens Backtracking Example
Solved by iterating over all solutions, using backtracking