HDU-2032 Yang Hui triangle

最新推荐文章于 2020-02-05 14:20:34 发布

原创最新推荐文章于 2020-02-05 14:20:34 发布 · 123 阅读

0 ·

CC 4.0 BY-SA版权

ACM 专栏收录该内容

73 篇文章

订阅专栏

本文介绍了一种使用C++编程语言实现杨辉三角的方法。通过递推公式计算每层数值，展示了一个完整的程序代码，能够根据输入的层数输出相应规模的杨辉三角。适合初学者理解和实践。

See the article on https://dyingdown.github.io/2019/12/20/HDU-2032%20Yang-Hui-triangle/

Yang Hui triangle

Remember the Yang Hui triangle you learned in middle school? The specific definition is not described here, you can refer to the following figure:

[外链图片转存失败,源站可能有防盗链机制,建议将图片保存下来直接上传(img-KgzZqIXC-1576812717168)(https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSp8ifUZL3-2LFdhmkXlBN0fqY_EPEwvMV3MtqLqFrn1YbcUIJu&s)]

Input

The input data contains multiple test instances. The input of each test instance contains only a positive integer n (1 <= n <= 30), which represents the number of layers of the Yang Hui triangle to be output.

Output

Corresponding to each input, please output the Yanghui triangle of the corresponding number of layers. The integers of each layer are separated by a space, and a blank line is added after each Yanghui triangle.

Analysis

As you can see from the picture, for each unit, there is :
$y [i] [j] = y [i - 1] [j - 1] + y [i - 1] [j]$

Code

#include<bits/stdc++.h>

using namespace std;

long long y[50][50];
void Yang() {
	for(int i = 0; i < 50; i ++) {
		y[i][0] = 0;
	}
	y[0][1] = 1;
	for(int i = 1; i <= 30; i ++) {
		for(int j = 1; j <= i; j ++) {
			y[i][j] = y[i - 1][j - 1] + y[i - 1][j];
		}
	}

}
int main() {
	Yang();
	int n;
	while(cin >> n) {
		for(int i = 1; i <= n; i ++) {
			for(int j = 1; j <= i; j ++) {
				if(j == 1) cout << y[i][j];
				else cout << " " << y[i][j];
			}
			cout << endl;
		}
		cout << endl;
	}
	return 0;
}