杨辉三角的各种算法实现

/*Name: 杨辉三角算法集锦Copyright: 始发于goal00001111的专栏；允许自由转载，但必须注明作者和出处Author: goal00001111Date: 27-11-08 19:04Description:分别使用了二维数组，一维数组，队列，二项式公式，组合公式推论和递归方法等9种算法算法思路详见代码注释——注释很详细，呵呵*/#include<iostream>#include<iomanip>using namespace std;const int MAXROW = 40;void PrintBlank(int n);int Com(int n, int m);int Try(int row, int cel);void Fun_1(int row);void Fun_2(int row);void Fun_3(int row);void Fun_4(int row);void Fun_5(int row);void Fun_6(int row);void Fun_7(int row);void Fun_8(int row);void Fun_9(int row);int main(){int row;cin >> row;Fun_1(row);cout << endl;Fun_2(row);cout << endl;Fun_3(row);cout << endl;Fun_4(row);cout << endl;Fun_5(row);cout << endl;Fun_6(row);cout << endl;Fun_7(row);cout << endl;Fun_8(row);cout << endl;Fun_9(row);system("pause");return 0;}//输出n个空格void PrintBlank(int n){for (int i=0; i<n; i++)cout << ' ';}//使用二维数组输出杨辉三角void Fun_1(int row){const int DIS = 6;int blank = 32;int a[MAXROW][MAXROW] = {0};for (int i=0; i<row; i++){PrintBlank(blank-=DIS/2);//输出第i行空格for (int j=0; j<=i; j++){if (j == 0 || j == i)a[i][j] = 1;else //规律: 左上与正上元素之和a[i][j] = a[i-1][j-1] + a[i-1][j];cout << setw(DIS) << a[i][j];if (j == i)cout << endl;}}}//使用队列输出杨辉三角void Fun_2(int row){const int DIS = 6;int max = row + 2;int blank = 30;int *a = new int[max];int front, rear;front = 0; a[0] = 1;rear = 1; a[1] = 1;PrintBlank(blank);//输出第一行空格while (front != (rear+1)%max){if (a[front] == 1 && a[(front+1)%max] == 1)//到i-1行尾部{rear = (rear+1)%max; a[rear] = 1; //第i行尾部rear = (rear+1)%max; a[rear] = 1; //队尾进入第i+1行cout << setw(DIS) << 1 << endl; //输出第i-1行尾部front = (front+1)%max; //对头进入第i行PrintBlank(blank-=DIS/2);//输出第i行空格}//处理中间数据rear = (rear+1)%max; a[rear] = a[front] + a[(front+1)%max];if (front != rear)//队列非空时输出cout << setw(DIS) << a[front]; //输出对头front = (front+1)%max; //删除对头元素}delete []a;}//使用两个一维数组代替二维数组输出杨辉三角void Fun_3(int row){const int DIS = 6;int blank = 33;int *a = new int[row]; //存储下一行int *b = new int[row];//存储输出行b[0] = 1;for (int n=1; n<=row; n++){//输出第n行PrintBlank(blank-=DIS/2);cout << setw(DIS) << b[i];cout << endl;if (n == row)//已经到最后一行则不再复制continue;//生成第n+1行数据a[0] = b[0];for (int i=1; i<n; i++)a[i] = b[i] + b[i-1];a[n] = 1;//复制第n+1行数据for (int i=0; i<=n; i++)b[i] = a[i];}delete []a;delete []b;}//使用一个一维数组和两个临时变量代替二维数组输出杨辉三角：很巧妙void Fun_4(int row){const int DIS = 6;int blank = 30;int *a = new int[row]; //存储输出行int left, right;//输出第一行PrintBlank(blank);//输出第1行空格cout << setw(DIS) << 1 << endl;a[0] = 1;//左侧数据永远为1for (int n=1; n<row; n++){left = a[0];//生成第n行数据for (int i=1; i<n; i++)//设置中间数据{right = a[i];a[i] = left + right;//left=a[i-1]，right=a[i]left = right;}a[n] = 1;//设置右侧的数据1//输出第n行PrintBlank(blank-=DIS/2);cout << setw(DIS) << a[i];cout << endl;}delete []a;}//使用一个一维数组和两个临时变量代替二维数组输出杨辉三角：方法同Fun_4，但更具有技巧，有点难懂void Fun_5(int row){const int DIS = 6;int blank = 33;int *a = new int[row]; //存储输出行for (int i=1; i<row; i++)//赋初值0，这个很重要，因为后面有用到a[i] = 0;a[0] = 1;int left, right;for (int n=1; n<=row; n++){left = 0;//生成第n行数据for (int i=0; i<n; i++){right = a[i];a[i] = left + right;//left=a[i-1]，right=a[i]left = right;}//输出第n行PrintBlank(blank-=DIS/2);for (int i=0; i<n; i++)cout << setw(DIS) << a[i];cout << endl;}delete []a;}//使用一个一维数组输出杨辉三角；两侧的1不变，计算中间的元素void Fun_6(int row){const int DIS = 6;int blank = 30;int *a = new int[row];//输出第一行PrintBlank(blank);//输出第1行空格cout << setw(DIS) << 1 << endl;a[0] = 1;//最左侧为1，永远不变for (int n=1; n<row; n++){a[n] = 1; //设置最右侧的1for (int i=n-1; i>0; i--)//设置中间的元素，由于a[i]的值变化，故应从右到左计算{a[i] += a[i-1]; //杨辉三角的规律}//输出第n+1行PrintBlank(blank-=DIS/2);for (int i=0; i<=n; i++)cout << setw(DIS) << a[i];cout << endl;}delete []a;}//使用二项式定理输出杨辉三角void Fun_7(int row){const int DIS = 6;int blank = 30;//输出第一行PrintBlank(blank);//输出第1行空格cout << setw(DIS) << 1 << endl;for (int i=1; i<row; i++){PrintBlank(blank-=DIS/2);//输出第i行空格for (int j=0; j<i; j++){cout << setw(DIS) << Com(i, j);}cout << setw(DIS) << 1 << endl;//输出每行最后一个1}}//输出组合c(n,m)int Com(int n, int m){int s1 = 1;int s2 = 1;m = (m > n/2) ? (n - m) : m;//取小的，以减少计算量for (int i=1; i<=m; i++){s1 *= n;s2 *= i;if (s1 % s2 == 0)//防止溢出{s1 /= s2;s2 = 1;}n--;}return s1;}//使用组合公式推论输出杨辉三角:C(n,m) = (n-m+1)/m * C(n,m-1) void Fun_8(int row){const int DIS = 6;int blank = 30;//输出第一行PrintBlank(blank);//输出第1行空格cout << setw(DIS) << 1 << endl;for (int n=1; n<row; n++){int c = 1;PrintBlank(blank-=DIS/2);//输出第i行空格cout << setw(DIS) << c; //输出每行第一个1for (int m=1; m<n; m++)//输出中间元素{c = c * (n - m + 1) / m;cout << setw(DIS) << c;}cout << setw(DIS) << 1 << endl;//输出每行最后一个1 }}//使用递归方法输出杨辉三角:C(n,k) = 1 (k=0或者n=k);C(n,k) = C(n-1,k-1) + C(n-1,k) void Fun_9(int row){const int DIS = 6;int blank = 33;for (int n=0; n<row; n++){PrintBlank(blank-=DIS/2);//输出第i行空格for (int m=0; m<=n; m++)//输出中间元素{cout << setw(DIS) << Try(n, m);}cout << endl;//输出每行最后一个1}}//递归函数，输出杨辉三角:C(n,k) = 1 (k=0或者n=k);C(n,k) = C(n-1,k-1) + C(n-1,k) int Try(int n, int k){if (k == 0 || k == n)//在左右两侧返回1return 1;return Try(n-1,k-1) + Try(n-1,k);//递推公式}。