Min Cost Climbing Stairs

• LeetCode: Min Cost Climbing Stairs

• Problem:

On a staircase, the i-th step has some non-negative cost cost[i] assigned (0 indexed).

Once you pay the cost, you can either climb one or two steps. 

You need to find minimum cost to reach the top of the floor, and you can either start from the step with index 0, or the step with index 1.

• Note:

1. cost will have a length in the range [2, 1000].

2. Every cost[i] will be an integer in the range [0, 999].

• Examples:

Input: cost = [10, 15, 20]
Output: 15
Explanation: Cheapest is start on cost[1], pay that cost and go to the top.

Input: cost = [1, 100, 1, 1, 1, 100, 1, 1, 100, 1]
Output: 6
Explanation: Cheapest is start on cost[0], and only step on 1s, skipping cost[3].

• Analysis:

Let arr[i] is the minimal cost to arrive at step[i].

The arr[i] = min(cost[i - 1] + arr[i - 1], cost[i - 2] + arr[i - 2])

• Code - Java:

class Solution {
    public int minCostClimbingStairs(int[] cost) {
        int len = cost.length;
        int[] result = new int[len + 1];
        for (int i = 2; i <= len; i++) {
            result[i] = Math.min(cost[i - 1] + result[i - 1], cost[i - 2] + result[i - 2]);
        }
        return result[len];
    }
}

• Code - C++:

class Solution {
public:
    int minCostClimbingStairs(vector<int>& cost) {
        int len = cost.size();
        vector<int> result(len + 1, 0);
        for (int i = 2; i <= len; i++) {
            result[i] = min(cost[i - 1] + result[i - 1], cost[i - 2] + result[i - 2]);
        }
        return result[len];
    }
};

• Code - Python:

class Solution(object):
    def minCostClimbingStairs(self, cost):
        """
        :type cost: List[int]
        :rtype: int
        """
        costLen = len(cost)
        result = [0 for i in range (costLen + 1)]
        for i in range(2, costLen + 1):
            result[i] = min(cost[i - 1] + result[i - 1], cost[i - 2] + result[i - 2])
        return result[costLen]

• Time Complexity: O(N), N is the length of array cost

• Space Complexity: O(N), N is the length of array cost