POJ 1163 / NYOJ 16 The Triangle（数字三角形）

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

大致题意：给出一个数n，表示这个数字三角形有n层，每层的数字个数逐渐递增。从第一行的数开始，每次可以往右下或坐下走一格，直到走到最后一行，把沿途经过的数全部加起来，如何走才能使得这个歌尽量大？

#include<iostream>
#include<algorithm>
#include<cstdio>
using namespace std;
const int MAX = 110;
int dp[MAX][MAX],a[MAX][MAX];
int main()
{
    int i,j,n;
    while(scanf("%d",&n)!=EOF)
    {
        for(i=0;i<n;i++)
        {
            for(j=0;j<=i;j++)
                scanf("%d",&a[i][j]);
        }
        for(i=n-2;i>=0;i--)
        {
            for(j=0;j<=i;j++)
            {
                a[i][j]=a[i][j]+max(a[i+1][j],a[i+1][j+1]);
            }
        }
        printf("%d
",a[0][0]);
    }
    return 0;
}