lc 330. patching array

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.

Input: nums = [1,3], n = 6

Output: 1

Explanation:

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.

We can use dp to handle it. miss means the minimum number we can not get at present (we can get all of the numbers smaller than miss).

If miss >= nums[i], we can update miss by miss + nums[i] as we can add nums[i] to all of the numbers we can get before.

If miss < nums[i] or i == len(nums), we can not get larger miss without patching, therefore, we should add miss to the array, thus we can
cover all of the numbers in [1, miss 2 - 1], so the current miss should be 2 miss.

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class :
    def minPatches(self, nums: List[int], n: int) -> int:
        miss, add, i = 1, 0, 0
        while miss <= n:
            if i < len(nums) and miss >= nums[i]:
                miss, i = miss + nums[i], i + 1
            else:
                miss, add = miss * 2, add + 1
        return add