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Climbing Stairs⚓︎

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Description⚓︎

You are climbing a staircase. It takes n steps to reach the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Example 1:

  • Input: n = 2
  • Output: 2
  • Explanation: There are two ways to climb to the top.
1
2
1. 1 step + 1 step
2. 2 steps

Example 2:

  • Input: n = 3
  • Output: 3
  • Explanation: There are three ways to climb to the top.
1
2
3
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

Constraints:

  • 1 <= n <= 45

Solution⚓︎

Way 1⚓︎

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class Solution {
public:
    int dp[50];
    int climbStairs(int n) {
        dp[1] = 1;
        dp[2] = 2;
        for (int i = 3; i <= n; i++) {
            dp[i] = dp[i - 1] + dp[i - 2];
        }
        return dp[n];
    }
};
  • Time complexity: \(O(n)\);
  • Space complexity: \(O(n)\).

Way 2⚓︎

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class Solution {
public:
    int climbStairs(int n) {
        if (n <= 1) return 1;
        int a = 1, b = 2;
        for (int i = 3; i <= n; i++) {
            int sum = a + b;
            a = b;
            b = sum;
        }
        return b;
    }
};
  • Time complexity: \(O(n)\);
  • Space complexity: \(O(1)\).