64. 最小路径和

动态规划：

• 状态定义：dp[i][j]表示从左上角到达第i行第j列位置的路径和，dp[m-1][n-1]即为答案。
• 状态转移：dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]，注意首行首列的特殊情况。
• 状态初始化：dp[0][0] = grid[0][0]

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                if (i == 0 && j == 0) continue;
                if (i == 0) {
                    dp[i][j] = dp[i][j - 1] + grid[i][j];
                    continue;
                }
                if (j == 0) {
                    dp[i][j] = dp[i - 1][j] + grid[i][j];
                    continue;
                }
                dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];
            }
        }
        return dp[m - 1][n - 1];
    }
}