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Java-based LeetCode algorithm problem solutions, regularly updated

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package g0001_0100.s0062_unique_paths;

// #Medium #Top_100_Liked_Questions #Top_Interview_Questions #Dynamic_Programming #Math
// #Combinatorics #Algorithm_II_Day_13_Dynamic_Programming #Dynamic_Programming_I_Day_15
// #Level_1_Day_11_Dynamic_Programming #Big_O_Time_O(m*n)_Space_O(m*n)
// #2023_08_11_Time_0_ms_(100.00%)_Space_39.2_MB_(67.74%)

/**
 * 62 - Unique Paths\.
 *
 * Medium
 *
 * 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?
 *
 * **Example 1:**
 *
 * ![](https://assets.leetcode.com/uploads/2018/10/22/robot_maze.png)
 *
 * **Input:** m = 3, n = 7
 *
 * **Output:** 28 
 *
 * **Example 2:**
 *
 * **Input:** m = 3, n = 2
 *
 * **Output:** 3
 *
 * **Explanation:**
 *
 *     From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
 *     1. Right -> Down -> Down
 *     2. Down -> Down -> Right
 *     3. Down -> Right -> Down 
 *
 * **Example 3:**
 *
 * **Input:** m = 7, n = 3
 *
 * **Output:** 28 
 *
 * **Example 4:**
 *
 * **Input:** m = 3, n = 3
 *
 * **Output:** 6 
 *
 * **Constraints:**
 *
 * *   `1 <= m, n <= 100`
 * *   It's guaranteed that the answer will be less than or equal to 2 * 10⁹.
**/
public class Solution {
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        for (int i = 0; i < m; i++) {
            dp[i][0] = 1;
        }
        for (int j = 0; j < n; j++) {
            dp[0][j] = 1;
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m - 1][n - 1];
    }
}