poj3176——dp

Cow Bowling

Description

The cows don‘t use actual bowling balls when they go bowling. They each take a number (in the range 0..99), though, and line up in a standard bowling-pin-like triangle like this:

          7

        3   8

      8   1   0

    2   7   4   4

  4   5   2   6   5

Then the other cows traverse the triangle starting from its tip and moving "down" to one of the two diagonally adjacent cows until the "bottom" row is reached. The cow‘s score is the sum of the numbers of the cows visited along the way. The cow with the highest score wins that frame.

Given a triangle with N (1 <= N <= 350) rows, determine the highest possible sum achievable.

Input

Line 1: A single integer, N

Lines 2..N+1: Line i+1 contains i space-separated integers that represent row i of the triangle.

Output

Line 1: The largest sum achievable using the traversal rules

Sample Input

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

Sample Output

30题意：求从三角形顶端向下走的最大和dp水题

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<stdlib.h>

using namespace std;

const int maxn=1010;
int N;
int a[maxn][maxn];
int dp[maxn][maxn];

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(dp,0,sizeof(dp));
    for(int i=N;i>=1;i--){
        for(int j=1;j<=i;j++){
            dp[i][j]=max(dp[i+1][j],dp[i+1][j+1])+a[i][j];//因dp初始化时已清零，所以第N+1层为0
        }
    }
    printf("%d\n",dp[1][1]);
    return 0;
}