USACO Section 1.5 Number Triangles （dp）

Number Triangles

Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be 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.

          7

        3   8

      8   1   0

    2   7   4   4

  4   5   2   6   5

In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.

PROGRAM NAME: numtri

INPUT FORMAT

The first line contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. All the supplied integers are non-negative and no larger than 100.

SAMPLE INPUT (file numtri.in)

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

OUTPUT FORMAT

A single line containing the largest sum using the traversal specified.

SAMPLE OUTPUT (file numtri.out)

30

分析：经典dp ，唯一要注意是单个案例输入会超时，可能原因是每次打开文件也要时间。

/*
  ID: dizzy_l1
  LANG: C++
  TASK: numtri
*/
#include<iostream>
#include<cstring>
#include<cstdio>
#define MAXN 1010

using namespace std;

int map[MAXN][MAXN],d[MAXN][MAXN];

int main()
{
    freopen("numtri.in","r",stdin);
    freopen("numtri.out","w",stdout);
    int n,i,j;
    while(scanf("%d",&n)==1)
    {
        for(i=1; i<=n; i++)
            for(j=1; j<=i; j++)
                scanf("%d",&map[i][j]);
        memset(d,0,sizeof(d));
        for(i=n; i>=1; i--)
            for(j=1; j<=i; j++)
                d[i][j]=map[i][j]+max(d[i+1][j],d[i+1][j+1]);
        printf("%d\n",d[1][1]);
    }
    return 0;
}