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Dynamic Programming•Pattern: DP / Fibonacci•Medium

Climbing stairs with variable steps

Problem Intuition & Objective

Count ways to climb n stairs taking 1 or 2 steps at a time.

Time ComplexityO(n)
Optimal
Space ComplexityO(1)
Memory Bounds
Optimal Algorithmic Approach

Fibonacci DP.

Core Invariants & Edge Cases

  • dp[i] = dp[i-1] + dp[i-2] — Fibonacci pattern
  • Can generalize to k-step variants
  • Space-optimized to O(1) with two variables
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