easyDSA

How do you solve the climbing stairs problem?

Q: How do you solve the climbing stairs problem?

**Intuition.** To reach step n you arrived either from step n-1 (a 1-step) or step n-2 (a 2-step). So the number of ways to reach n is the sum of the ways to reach those two — which is exactly the **Fibonacci** recurrence. ways(n) = ways(n-1) + ways(n-2) 1 way <text x="155" y="125" fill=

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Explain the Fibonacci DP.

dpclimbing-stairs

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O(1)-space DP

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def climb_stairs(n):
    a, b = 1, 1
    for _ in range(2, n + 1):
        a, b = b, a + b
    return b


# --- demo ---
print(climb_stairs(2), climb_stairs(3), climb_stairs(5))   # 2 3 8

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