Description
You are given an integer array cost where cost[i] is the cost of ith 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.
Examples
Example 1:
Input: cost = [10,15,20]
Output: 15
Explanation: You will start at index 1.
- Pay 15 and climb two steps to reach the top, the total cost is 15.
Example 2:
Input: cost = [1,100,1,1,1,100,1,1,100,1]
Output: 6
Explanation: You will start at index 0.
- Pay 1 and climb two steps to reach index 2.
- Pay 1 and climb two steps to reach index 4.
- Pay 1 and climb two steps to reach index 6.
- Pay 1 and climb one step to reach index 7.
- Pay 1 and climb two steps to reach index 9.
- Pay 1 and climb one step to reach the top.
The total cost is 6.
Approach
For this problem, we can either go through bottom-up or top-down approach to find the minimum cost. Iterate over the array starting at the 2nd index. The problem statement says we are allowed to start at the 0th or 1st step, so we know the minimum cost to reach those steps is 0.
At the end, return the final element of minimumCost. Remember, we are treating this "step" as the top floor that we need to reach.
Solution
class Solution:
def minCostClimbingStairs(self, cost: List[int]) -> int:
n = len(cost)
dp = [0] * (n + 1)
dp[0] = 0
dp[1] = 0
for i in range(2, n + 1):
dp[i] = min(dp[i - 1] + cost[i - 1], dp[i - 2] + cost[i - 2])
return dp[n]
