18-The Triangle-水

最新推荐文章于 2020-05-03 16:51:48 发布

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最新推荐文章于 2020-05-03 16:51:48 发布

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分类专栏： dp

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本文介绍了一个寻找三角形网格中从顶部到底部的最大路径和的问题。通过动态规划的方法，递推计算每一步到达的位置能获得的最大累积数值。最终输出的是到达底部任一位置的最大可能累积值。

7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
(Figure 1)
Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.

输入描述:

Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99.

输出描述:

Your program is to write to standard output. The highest sum is written as an integer.

样例输入:

复制

样例输出:

提示:

没有提示哦

来源:

未知

上传者：苗栋栋

思路：从上往下递推

代码：

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<algorithm> 
using namespace std;
int a[109][109],dp[108][108];
int main()
{
	int n;
	scanf("%d",&n);
	for(int i = 1;i <= n;++i)
	{
		for(int j = 1;j <= i;++j)
		{
			scanf("%d",&a[i][j]);
			dp[i][j] = a[i][j];
		}
	}
	int max1 = 0;
	for(int i = 1;i <= n;++i)
	{
		for(int j = 1;j <= i;++j)
		{
			dp[i][j] = max(dp[i-1][j]+a[i][j],dp[i-1][j-1]+a[i][j]);
			max1 = max(max1,dp[i][j]);
		}
	}
	printf("%d\n",max1);
	return 0;
}