LWC 63：746. 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.

Example 1:

Input: cost = [10, 15, 20] Output: 15 Explanation: Cheapest is start on cost1, pay that cost and go to the top.

Example 2:

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].

Note:

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

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

思路： 好吧，此题所说的跳到top指的是跳到数组末尾的下一个位置。动态规划，记录当前位置所需要花费的最小代价，要么从前一个位置来，要么从前两个位置来，代码如下：

Java版本：

    public int minCostClimbingStairs(int[] cost) {
        int n = cost.length;
        int[] dp = new int[n + 16];
        for (int i = 2; i <= n; ++i) {
            dp[i] = Math.min(dp[i - 1] + cost[i - 1], dp[i - 2] + cost[i - 2]);
        }
        return dp[n];
    }

Python版本：

    def minCostClimbingStairs(self, cost):
        """
        :type cost: List[int]
        :rtype: int
        """
        n = len(cost)
        dp = [0] * (n + 1)
        for i in xrange(2, n + 1):
            dp[i] = min(dp[i - 1] + cost[i - 1], dp[i - 2] + cost[i - 2])

        return dp[n]