【欧拉计划】18. Maximum path sum I

（本题取 $n=16$）

【思路】暴力 DFS，时间复杂度为 $\mathcal O(2^n)$。

【优化】采用 $\mathcal O(n^2)$ 的 DP：

#include<stdio.h>
int dp[16][16],ans;
int max(int a,int b){return a>b?a:b;}
const int matrix[16][16]=
{
    {0},
    {0,75},
    {0,95,64},
    {0,17,47,82},
    {0,18,35,87,10},
    {0,20,04,82,47,65},
    {0,19,01,23,75,03,34},
    {0,88,02,77,73,07,63,67},
    {0,99,65,04,28,06,16,70,92},
    {0,41,41,26,56,83,40,80,70,33},
    {0,41,48,72,33,47,32,37,16,94,29},
    {0,53,71,44,65,25,43,91,52,97,51,14},
    {0,70,11,33,28,77,73,17,78,39,68,17,57},
    {0,91,71,52,38,17,14,91,43,58,50,27,29,48},
    {0,63,66,04,68,89,53,67,30,73,16,69,87,40,31},
    {0,04,62,98,27,23,9,70,98,73,93,38,53,60,04,23}
};
int main()
{
    for(int i=1;i<=15;++i)
    {
        for(int j=1;j<=i;++j)
        {
            dp[i][j]=max(dp[i-1][j-1],dp[i-1][j])+matrix[i][j];
        }
    }
    for(int i=1;i<=15;++i)ans=max(ans,dp[15][i]);
    printf("%d",ans);
    return 0;
}