The Triangle POJ1163

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. 

Input

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. 

Output

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

Sample Input

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

Sample Output

30

题意:

在上面的数字三角形中寻找一条从顶部到底边的路径，使得

路径上所经过的数字之和最大

题解:这算是dp水题了 

#include<bits/stdc++.h>

using namespace std;
#define MAX 100+5

int D[MAX][MAX];
int maxSum[MAX][MAX];

int main(){
int n;
scanf("%d",&n);
for(int i = 1;i<=n;i++)
    for(int j = 1;j<=n;j++)
        scanf("%d",&D[i][j]);
    for(int i = 1;i<=n;i++)
        maxSum[n][i]=D[n][i];
    for(int i = n-1;i>=1;i--)
        for(int j = 1;j<=i;j++)
            maxSum[i][j]=max(maxSum[i+1][j],maxSum[i+1][j+1]+D[i][j]);
        printf("%d\n",maxSum[1][1]);
    return 0;
}