Leetcode -- Minimum Path Sum

最新推荐文章于 2020-08-21 21:20:07 发布

原创最新推荐文章于 2020-08-21 21:20:07 发布 · 155 阅读

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本文针对LeetCode上的一道题目——最小路径和进行了解析，给出了一种动态规划的解决方案。该方法通过计算每个节点到达目标节点的最小路径和来找到从起点到终点的最优路径。

https://leetcode.com/problems/minimum-path-sum/description/

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.

莫名其妙我居然漏了这一题。这一题其实还是Unique Path(http://blog.youkuaiyun.com/chaochen1407/article/details/43306873) 和 Unique Path II(http://blog.youkuaiyun.com/chaochen1407/article/details/43307579) 的进一步的跟进。原理都是一样的，前两者是f(i, j) = f(i - 1,j) + f(i, j - 1)。这一个就是f(i, j) = min(f(i - 1, j), f(i, j - 1)) + grid(i, j)。所以具体就不阐述了，看代码吧。

    public int minPathSum(int[][] grid) {
        int[] resultRow = new int[grid[0].length];
        resultRow[0] = grid[0][0];
        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid[0].length; j++) {
                if (i == 0 && j == 0) continue;
                
                int fromLeft = j == 0 ? Integer.MAX_VALUE : resultRow[j - 1];
                int fromTop = i == 0 ? Integer.MAX_VALUE : resultRow[j];
                resultRow[j] = Math.min(fromLeft, fromTop) + grid[i][j];
            }
        }
        
        return resultRow[resultRow.length - 1];
    }