#64最小路径和

final class Solution {
    public int minPathSum(int[][] grid) {
        int rows = grid.length;
        int columns = grid[0].length;
        int[][] dp = new int[rows][columns];
        dp[0][0] = grid[0][0];
        for (int row = 1; row < rows; row++) {
            dp[row][0] = dp[row - 1][0] + grid[row][0];
        }
        for (int column = 1; column < columns; column++) {
            dp[0][column] = dp[0][column - 1] + grid[0][column];
        }
        for (int row = 1; row < rows; row++) {
            for (int column = 1; column < columns; column++) {
                dp[row][column] = Math.min(dp[row - 1][column], dp[row][column - 1])
                        + grid[row][column];
            }
        }
        return dp[rows - 1][columns - 1];
    }
}