Given a?m?x?n?grid filled with non-negative numbers, find a path from top left to bottom right which?minimizes?the sum of all numbers along its path.

Note:?You can only move either down or right at any point in time.

?

格子取數問題，另dp[i][j]表示走到(i,j)格子時，取得的最小數字，那么有

dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1])

當i=0時，只能從左邊過來，當j=0時，只能從上面過來

 1 class Solution {
 2 public:
 3     int minPathSum(vector<vector<int> > &grid) {
 4         int m = grid.size();
 5         int n = grid[0].size();
 6         if( m<0 || n<0 ) return 0;
 7         vector< vector<int> > dp(grid);
 8         for(int i=1; i<n; ++i) dp[0][i] += dp[0][i-1];
 9         for(int i=1; i<m; ++i) dp[i][0] += dp[i-1][0];
10         for(int i=1; i<m; ++i)
11             for(int j=1; j<n; ++j)
12                 dp[i][j] += min(dp[i-1][j], dp[i][j-1]);
13         return dp[m-1][n-1];
14     }
15 };

?

轉載于:https://www.cnblogs.com/bugfly/p/4008593.html

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