330. Patching Array【M】【84】【leetcode】

最小补丁数以覆盖所有整数范围

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本文讨论了如何使用最少的补丁来填充一个已排序的正整数数组，使其能形成从1到指定整数n的所有可能组合之和。通过实例解释了补丁添加策略和所需数量的计算。

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.

Credits:
Special thanks to @dietpepsi for adding this problem and creating all test cases.

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class Solution(object):
    def minPatches(self, nums, n):
        res = 0
        cur = 1
        total = 1
        i = 0
        while total <= n:
            if i < len(nums) and nums[i] <= total : #cur not in nums:
                #res += 1
                total += nums[i]
                i += 1
            else:
                res += 1
                total += total
            #print nums,total
        return res