public class MinPathSum_64 {

/**

* 动态规划

* 1、状态矩阵：dp为m*n，dp[i][j]代表走到(i, j)的最小路径和

* 2、状态转移方程：只能向右或者向下走

* i != 0 && j != 0 -> dp[i][j] = min(dp[i - 1][j], dp[i][j-1]) + grid[i][j]

* i = 0 && j != 0 -> dp[i][j] = dp[i][j - 1] + grid[i][j]

* j != 0 && j = 0 -> dp[i][j] = dp[i - 1][j] + grid[i][j]

* i = 0 && j = 0 -> dp[i][j] = grid[i][j]

* @param grid

* @return

*/

public int minPathSum(int[][] grid) {

for(int i = 0; i < grid.length; i++) {

for(int j = 0; j < grid[0].length; j++) {

if(i == 0 && j == 0) continue;

else if(i == 0) grid[i][j] = grid[i][j - 1] + grid[i][j];

else if(j == 0) grid[i][j] = grid[i - 1][j] + grid[i][j];

else grid[i][j] = Math.min(grid[i - 1][j], grid[i][j - 1]) + grid[i][j];

}

}

return grid[grid.length - 1][grid[0].length - 1];

}

}