【leetcode】Unique Paths

最新推荐文章于 2020-05-24 11:10:04 发布

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本文通过动态规划算法解决了一种特定类型的路径问题：在一个m×n网格中，从左上角移动到右下角的唯一路径数量。具体而言，机器人只能向下或向右移动，并且最终目标是在给定的网格中找到从起始位置到达终点位置的所有可能路径数量。以一个3×7网格为例，文章详细介绍了如何使用动态规划方法计算此类问题的解决方案。

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time.

The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Accept，动态规划

int dp[101][101] = {1};

int findpath(int m, int n) {
    if (m == 0 || n == 0) {
        return 0;
    }

    if (dp[m][n] > 0) {
        return dp[m][n];
    }
    
    dp[m][n] = findpath(m - 1, n) + findpath(m, n - 1);
    dp[n][m] = dp[m][n];
    return dp[m][n];
}

int uniquePaths(int m, int n) {
    dp[1][1] = 1;
    return findpath(m, n);
}