Minimum Path Sum 求方格总从左上到右下的最短路径 简单动态规划

题目：

链接

解答：

简单的动态规划：

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

初始化：

 dp[0][0] = grid[0][0];

 dp[i][0] = dp[i - 1][0] + grid[i][0];
 dp[0][i] = dp[0][i - 1] + grid[0][i];

代码：

  class Solution {  public:  int minPathSum(vector<vector<int> > &grid) {  int m = grid.size();  if (m == 0)  return 0;  int n = grid[0].size();  vector<vector<int> > dp(m, vector<int>(n));  dp[0][0] = grid[0][0];  for (int i = 1; i < m; i++)  dp[i][0] = dp[i - 1][0] + grid[i][0];  for (int i = 1; i < n; i++)  dp[0][i] = dp[0][i - 1] + grid[0][i];  for (int i = 1; i < m; i++)  {  for (int j = 1; j < n; j++)  {  dp[i][j] = min(dp[i - 1][j] , dp[i][j - 1]) + grid[i][j];  }  }  return dp[m - 1][n - 1];  }  };