递推DP HDOJ 5092 Seam Carving

题目传送门

 /*
     题意：从上到下，找最短路径，并输出路径
     DP：类似数塔问题，上一行的三个方向更新dp，路径输出是关键
 */
 #include <cstdio>
 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cmath>
 #include <string>
 #include <vector>
 #include <queue>
 #include <map>
 #include <set>
 #include <ctime>
 #include <cstdlib>
 using namespace std;

 const int MAXN = 1e2 + ;
 const int INF = 0x3f3f3f3f;
 int a[MAXN][MAXN];
 int dp[MAXN][MAXN];
 int pre[MAXN][MAXN];

 void print(int x, int y)
 {
     if (x == )
     {
         printf ("%d", y);    return ;
     }
     print (x - , pre[x][y]);
     printf (" %d", y);
 }

 int main(void)        //HDOJ 5092 Seam Carving
 {
     //freopen ("C.in", "r", stdin);

     int n, m, t, cas = ;
     scanf ("%d", &t);
     while (t--)
     {
         scanf ("%d%d", &n, &m);
         for (int i=; i<=n; ++i)
             for (int j=; j<=m; ++j)    scanf ("%d", &a[i][j]);
         memset (pre, , sizeof (pre));

         for (int i=; i<=n; ++i)
             for (int j=; j<=m; ++j)    dp[i][j] = INF;
         for (int i=; i<=m; ++i)    dp[][i] = a[][i];

         for (int i=; i<=n; ++i)
         {
             for (int j=m; j>=; --j)
             {
                 for (int k=; k>=-; --k)
                 {
                     if (j + k <  || j + k > m)    continue;
                     if (dp[i][j] > dp[i-][j+k] + a[i][j])
                     {
                         dp[i][j] = dp[i-][j+k] + a[i][j];
                         pre[i][j] = j + k;
                     }
                 }
             }
         }

         int k = m;    int mn = dp[n][m];
         for (int i=m-; i>=; --i)
         {
             if (mn > dp[n][i])    {mn = dp[n][i];    k = i;}
         }

         printf ("Case %d\n", ++cas);
         print (n, k);
         puts ("");
     }

     return ;
 }

 /*
 Case 1
 2 1 1 2
 Case 2
 3 2 1 1 2 1
 */