leetcode-dp-64

import java.util.Arrays;
import java.util.HashMap;

/**
 * <p>给定一个包含非负整数的 <code><em>m</em> x <em>n</em></code> 网格 <code>grid</code> ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。</p>
 *
 * <p><strong>说明：</strong>每次只能向下或者向右移动一步。</p>
 *
 * <p> </p>
 *
 * <p><strong>示例 1：</strong></p>
 * <img alt="" src="https://assets.leetcode.com/uploads/2020/11/05/minpath.jpg" style="width: 242px; height: 242px;" />
 * <pre>
 * <strong>输入：</strong>grid = [[1,3,1],[1,5,1],[4,2,1]]
 * <strong>输出：</strong>7
 * <strong>解释：</strong>因为路径 1→3→1→1→1 的总和最小。
 * </pre>
 *
 * <p><strong>示例 2：</strong></p>
 *
 * <pre>
 * <strong>输入：</strong>grid = [[1,2,3],[4,5,6]]
 * <strong>输出：</strong>12
 * </pre>
 *
 * <p> </p>
 *
 * <p><strong>提示：</strong></p>
 *
 * <ul>
 * <li><code>m == grid.length</code></li>
 * <li><code>n == grid[i].length</code></li>
 * <li><code>1 <= m, n <= 200</code></li>
 * <li><code>0 <= grid[i][j] <= 100</code></li>
 * </ul>
 * <div><div>Related Topics</div><div><li>数组</li><li>动态规划</li><li>矩阵</li></div></div><br><div><li>👍 1300</li><li>👎 0</li></div>
 */

//leetcode submit region begin(Prohibit modification and deletion)
class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;

        //二维数组作为 备忘录
        int[][] memo = new int[m][n];
        for (int[] row : memo) {
            Arrays.fill(row, -1);
        }

        return dp(grid, m - 1, n - 1, memo);
    }

    int dp(int[][] grid, int i, int j, int[][] memo) {
        if (i == 0 && j == 0) {
            return grid[0][0];
        }

        if (i < 0 || j < 0) {
            return Integer.MAX_VALUE;
        }

        if (memo[i][j] != -1) {
            return memo[i][j];
        }


        memo[i][j] = Math.min(dp(grid, i - 1, j, memo), dp(grid, i, j - 1, memo)) + grid[i][j];
        return memo[i][j];
    }
}
//leetcode submit region end(Prohibit modification and deletion)