README.md

Unique Paths

Solution 1: DP

// TC: O(m*n)
// SC: O(m*n)
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];
    }
}

Solution 2

One Dimensional Array

/**
 * Question   : 62. Unique Paths
 * Complexity : Time: O(m*n) ; Space: O(n)
 * Topics     : DP
 */
class Solution {
    public int uniquePaths(int m, int n) {
        int[] dp = new int[n];
        dp[0] = 1;

        for (int j = 1; j < n; j++) {
            dp[j] = dp[j - 1];
        }

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

        return dp[n - 1];
    }
}