The Triangle（DP-数塔问题）

题目链接：http://poj.org/problem?id=1163

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

就是你身处最三角形的顶端，你可以选择向下紧邻两个的左边或右边走，然后求你所走路标的最大总和

该题错在从第n行开始去进行迭代，但是从倒数第二行开始即可；

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
using namespace std;
int dp[99][99];
int main()
{
    int n,i,j,a[100][100];
    memset(dp,0,sizeof(dp));
    scanf("%d",&n);
    for(i=1;i<=n;i++){
        for(j=1;j<=i;j++){
            scanf("%d",&dp[i][j]);
        }
    }
    for(i=n-1;i>=1;i--){
        for(j=1;j<=i;j++){
            dp[i][j]+=max(dp[i+1][j],dp[i+1][j+1]);
        }
    }
    printf("%d\n",dp[1][1]);
    return 0;
}