DevExCode

70. Climbing Stairs

MathDynamic ProgrammingMemoization

Explanation

To solve this problem, we can use dynamic programming. We can define a DP array where dp[i] represents the number of distinct ways to reach step i. We can then build up this array iteratively by considering the number of ways to reach the current step based on the number of ways to reach the previous two steps.

  1. Initialize a DP array of size n+1 to store the number of ways to reach each step.
  2. Set dp[0] = 1 and dp[1] = 1 as there is only 1 way to reach the first and second steps.
  3. Iterate from i = 2 up to n and calculate dp[i] based on the sum of dp[i-1] and dp[i-2], as you can climb either 1 or 2 steps at a time.
  4. Return dp[n] as the final answer.

Time Complexity: O(n)
Space Complexity: O(n)

View Leetcode Problem
class Solution {
    public int climbStairs(int n) {
        if (n <= 1) {
            return 1;
        }
        
        int[] dp = new int[n + 1];
        dp[0] = 1;
        dp[1] = 1;
        
        for (int i = 2; i <= n; i++) {
            dp[i] = dp[i - 1] + dp[i - 2];
        }
        
        return dp[n];
    }
}

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