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Min Cost Climbing Stairs

Difficulty: Easy

Problem Description

You are given an integer array cost where cost[i] is the cost of i-th step on a staircase. Once you pay the cost, you can either climb one or two steps. You can either start from the step with index 0, or the step with index 1. Return the minimum cost to reach the top of the floor.

Key Insights

  • You can start from either the first or second step.
  • The cost to reach a step can be derived from the costs of the previous one or two steps.
  • This problem can be solved using dynamic programming to keep track of the minimum cost at each step.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

The problem can be solved using a dynamic programming approach. We can maintain two variables to keep track of the minimum cost to reach the last two steps. Starting from the base cases (the cost to reach the first and second step), we iteratively calculate the minimum cost for each subsequent step by considering the cost to reach the step from either of the two previous steps.

The algorithm uses constant space, as we only need to store the last two computed costs at any time, and it runs in linear time relative to the number of steps.

Code Solutions

def minCostClimbingStairs(cost):
    n = len(cost)
    # Base cases
    first = cost[0]
    second = cost[1]
    
    for i in range(2, n):
        current = cost[i] + min(first, second)
        first = second
        second = current
    
    return min(first, second)
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