62.unique-paths.java

/*
 * @lc app=leetcode id=62 lang=java
 *
 * [62] Unique Paths
 *
 * https://leetcode.com/problems/unique-paths/description/
 *
 * algorithms
 * Medium (46.42%)
 * Total Accepted:    274.4K
 * Total Submissions: 583.7K
 * Testcase Example:  '3\n2'
 *
 * 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 7 x 3 grid. How many possible unique paths are there?
 *
 * Note: m and n will be at most 100.
 *
 * Example 1:
 *
 *
 * 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 -> Right -> Down
 * 2. Right -> Down -> Right
 * 3. Down -> Right -> Right
 *
 *
 * Example 2:
 *
 *
 * Input: m = 7, n = 3
 * Output: 28
 *
 */
class Solution {
  public int uniquePaths(int m, int n) {
    int[][] dp = new int[m][n];
    for (int i = 0; i < n; i++) {
      dp[m-1][i] = 1;
    }
    for (int i = 0; i < m; i++) {
      dp[i][n-1] = 1;
    }

    for (int i = m - 2; i >= 0; i--) {
      for (int j = n - 2; j >= 0; j--) {
        dp[i][j] = dp[i+1][j] + dp[i][j+1];
      }
    }

    return dp[0][0];
  }
}