数字三角形

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.
给出一个数字三角形，你从[1,1]开始出发，走到最后一行。每次站在一个点上时，可以向下走，或者向右下走。
将经过的数字加起来，希望其和最大。

输入

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

输出

#include<bits/stdc++.h>
using namespace std;
int a[1001][1001],n,f[10001][1001],ans=-1;
int main() {
    scanf("%d",&n);
    for(int i=1; i<=n; i++)
        for(int j=1; j<=i; j++)
            scanf("%d",&a[i][j]);
    memset(f,-1,sizeof(f));
    f[1][1]=a[1][1];
    for(int i=2; i<=n; i++)
        for(int j=1; j<=i; j++)
            f[i][j]=max(f[i-1][j-1],f[i-1][j])+a[i][j];
    for(int i=1; i<=n; i++)
        ans=max(ans,f[n][i]);
    printf("%d
",ans);
    return 0;
}

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