minimum-path-sum

/**
 * 給定一個由非負整數填充的m x n的二維數組，
 * 如今要從二維數組的左上角走到右下角，
 * 請找出路徑上的全部數字之和最小的路徑。
 * 注意：你每次只能向下或向右移動。
 *
 * 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.
 */

/**
 * 給定一個由非負整數填充的m x n的二維數組，
 * 如今要從二維數組的左上角走到右下角，
 * 請找出路徑上的全部數字之和最小的路徑。
 * 注意：你每次只能向下或向右移動。
 *
 * 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.
 */

public class Main52 {

    public static void main(String[] args) {
        int[][] grid = new int[3][7];
        System.out.println(Main52.minPathSum(grid));
    }

    public static int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;

        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        //第一行
        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i-1] + grid[0][i];
        }
        //第一列
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i-1][0] + grid[i][0];
        }

        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];

    }
}