杨辉三角

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/**************************************************************** 
 * Description: C++ implementation of yanghuiRriangle.
 * Author: Alex Li
 * Date: 2023-06-22 12:20:50
 * LastEditTime: 2023-06-22 15:12:09
****************************************************************/

#include<iostream>
#include<iomanip>
using namespace std;
int main(){
    const int n = 15; //二项式次数，实际取最大值14
    const int m = 2 * (n-1); //二项式展开后的项数15，因为元素中间要有n-1个间隔，所以需要29个元素,0~28
    int arr[n][m] = { 0 };
    for (int i =0; i <n; i++){
        arr[i][n-i-1] = 1;   //生成三角形左边数值为1
        arr[i][n+i-1] = 1;   //生成三角形右边数值为1 
     }

    for (int i = 2; i <n; i++){//i从第二行遍历
        for (int j = n - i + 1; j < n-2+i; j = j + 2)//从上一层的两个相邻数值相加得到结果
            arr[i][j] = arr[i - 1][j - 1] + arr[i - 1][j + 1];
    }
    
    for (int i = 0; i < n; i++){//按行遍历
        //输出三角形前面的空格
        for (int j = 0; j < n - i - 1; j++)cout << "    ";
         //n-i-1是三角形左边，n+i+1是三角形右边，j每次跳二格
        for (int j = n - i - 1; j< n+i+1; j = j + 2){
            cout << setw(4) << arr[i][j] << "    ";
        }
        cout << endl;
    }
    return 0;
}