The Triangle

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The Triangle

时间限制： 1000 ms  |  内存限制： 65535 KB

难度： 4

描述

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

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

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

样例输入

5
7
3 8
8 1 0 
2 7 4 4
4 5 2 6 5

样例输出

30

解析：这是一个简单动态规划问题（数塔），和我博客另外一题（免费馅饼）类似，思路就是倒着计算，数塔每个位置变为他能成为的最大数，最后dp[1][1]就是结果。

#include<stdio.h>
#include<cstring>
#include<algorithm>
using namespace std;
int dp[105][105],n; 
int main()
{
	while(~scanf("%d",&n)){
		memset(dp,0,sizeof(dp));
		for(int i = 1; i <= n; i++){
			for(int j = 1; j <= i; j++){
				scanf("%d",&dp[i][j]);
			}
		}
			
			for(int i = n - 1; i >= 1; i--){
				
				for(int j = 1; j <= i; j++){
					dp[i][j] = dp[i][j] + max(dp[i+1][j],dp[i+1][j+1]);
				}
			
			}
		printf("%d\n",dp[1][1]);
	}
		
}