Minimum Path Sum

//two dimensions dp      public int minPathSum(int[][] grid) {          // Start typing your Java solution below          // DO NOT write main() function          int m = grid.length;          if(m == 0) return 0;          int n = grid[0].length;          int[][] dp = new int[m][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 j = 1; j < n; j++) dp[0][j] = dp[0][j - 1] + grid[0][j];          for(int i = 1; i < m; i++) {              for(int j = 1; j < n; j++) {                  dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];              }          }          return dp[m - 1][n - 1];      }      //use rotate arrays to save space    public int minPathSum(int[][] grid) {        // Start typing your Java solution below        // DO NOT write main() function        int m = grid.length;        if(m == 0) return 0;        int n = grid[0].length;        int[][] dp = new int[2][n];        dp[0][0] = grid[0][0];    int flag = 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++) {flag = i & 1;            dp[flag][0] = dp[flag ^ 1][0] + grid[i][0];for(int j = 1; j < n; j++) {dp[flag][j] = Math.min(dp[flag ^ 1][j], dp[flag][j - 1]) + grid[i][j];}}        return dp[flag][n - 1];    }