動機

有點魔法的一題

Problem

Given a sorted integer array nums and an integer n, add/patch elements to the array such that any number in the range [1, n] inclusive can be formed by the sum of some elements in the array.

Return the minimum number of patches required.

 

Example 1:

Input: nums = [1,3], n = 6Output: 1Explanation:Combinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4.Now if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,3], [1,2,3].Possible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6].So we only need 1 patch.

Example 2:

Input: nums = [1,5,10], n = 20Output: 2Explanation: The two patches can be [2, 4].

Example 3:

Input: nums = [1,2,2], n = 5Output: 0

 

Constraints:

  • 1 <= nums.length <= 1000
  • 1 <= nums[i] <= 104
  • nums is sorted in ascending order.
  • 1 <= n <= 231 - 1

Sol

假設現在可以組合出的數字是1~miss，所以有兩個case 如果目前的數字在可以組合出的範圍中，就直接加上去 如果不在，就是加最大的數字，miss

class Solution:
    def minPatches(self, nums: List[int], n: int) -> int:
        miss = 1
        i = 0
        ret = 0
        while miss <= n:
            if i < len(nums) and nums[i] <= miss:
                miss += nums[i]
                i += 1
            else:
                miss += miss
                ret += 1
        return ret