算法——Patching Array

给定一个已排序的整数数组和一个值n，插入几个元素使得的可以组成的[1，n]中所有的数。求加入最小的数量元素完成该功能。
Given a sorted positive integer array nums and an integer n, add/patch elements to the array such that any number in 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:
nums = [1, 3], n = 6
Return 1.

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

Example 3:
nums = [1, 2, 2], n = 5
Return 0.

python代码如下：

class Solution(object):
    def minPatches(self, nums, n):
        """
        :type nums: List[int]
        :type n: int
        :rtype: int
        """
        _sum, ans, index = 0, 0, 0
        while _sum < n:
            while index < len(nums) and nums[index] <= _sum + 1:
                _sum += nums[index]
                index += 1
            if _sum < n:
                ans += 1
                _sum = _sum * 2 + 1
        return ans