Cow Bowling POJ - 3176

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

Hint

Explanation of the sample:

          7

         *

        3   8

       *

      8   1   0

       *

    2   7   4   4

       *

  4   5   2   6   5

The highest score is achievable by traversing the cows as shown above.

 

数塔问题。

可以从后向前更新，而状态很明显，dp[ i ][ j ]表示在（i，j）位置时的最大值。

所以：dp[i][j]=max(dp[i+1][j]+map[i+1][j],dp[i+1][j+1]+map[i+1][j+1]);

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;

int n;
int map[400][400],dp[400][400];

void solve()
{   int ans=0;
    for(int i=n-2;i>=0;i--)
        for(int j=0;j<=i;j++)
            dp[i][j]=max(dp[i+1][j]+map[i+1][j],dp[i+1][j+1]+map[i+1][j+1]);
    ans=dp[0][0]+map[0][0];
    cout<<ans<<endl;
}

int main()
{   cin>>n;
    for(int i=0;i<n;i++)
        for(int j=0;j<i+1;j++)
            scanf("%d",&map[i][j]);
    memset(dp,0,sizeof(dp));        
    
    solve();
}