LeetCode Patching Array

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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.

Java Solution

The following algorithm is from https://discuss.leetcode.com/topic/35494/solution-explanation

We define miss to be the smallest number that will miss, which means, given an input {1…m}, we can build all sums in [0, miss).  For the next number x in the array, if x <= miss, then we can build sums in the range [0, miss + x), thus there is no need to add a number.

If the array is empty, or the next number x in the array is larger than miss, we have to add a number to get miss. The best strategy is to add miss itself. Then our next range is [0, miss + miss)

I also used an example below to describe how this method works.