Cow Bowling

Time Limit: 1000MS	Memory Limit: 65536K
Total Submissions: 19855	Accepted: 13164

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

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.

Source

題意：

求一條路徑，使從頭到尾和最大。

思路：

簡單動態規劃。

程式碼：

#include <iostream>
#include <cstring>
#include <string>
using namespace std;
int num[550][550],f[550][550];
int sum;
int main()
{
    int i,j;
    int n;
    cin>>n;
    for(i=1;i<=n;i++)
    {
        for(j=1;j<=i;j++)
            cin>>num[i][j];
    }
    for(j=1;j<=n;j++)f[n][j]=num[n][j];
    for(i=n-1;i>=1;i--)
    {
        for(j=1;j<=i;j++)
            f[i][j]=num[i][j]+max(f[i+1][j],f[i+1][j+1]);
    }
    cout<<f[1][1]<<endl;
}