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:


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.

Example 2:


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


Example 3:


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

Source: leetcode | Difficulty: MEDIUM_HARD
Tags: Data structures

Greedy algorithms

Starter code: class Solution:
    def minPatches(self, nums: List[int], n: int) -> int:
        

Solutions:
class Solution:

	def minPatches(self, nums, n):
		(res, cur, i) = (0, 1, 0)
		while cur <= n:
			if i < len(nums) and nums[i] <= cur:
				cur += nums[i]
				i += 1
			else:
				cur *= 2
				res += 1
		return res


class Solution:

	def minPatches(self, nums, n):
		(missed, added, i) = (1, 0, 0)
		while missed <= n:
			if i < len(nums) and nums[i] <= missed:
				missed += nums[i]
				i += 1
			else:
				missed += missed
				added += 1
		return added


class Solution:

	def minPatches(self, nums, n):
		maxValue = 0
		i = 0
		count = 0
		while maxValue < n:
			if i >= len(nums):
				while maxValue < n:
					maxValue += maxValue + 1
					count += 1
			elif nums[i] - 1 > maxValue:
				maxValue += maxValue + 1
				count += 1
			elif nums[i] - 1 == maxValue:
				maxValue += nums[i]
				i += 1
			elif nums[i] - 1 < maxValue:
				maxValue += nums[i]
				i += 1
		return count


class Solution:

	def minPatches(self, nums, n):
		current_max = 1
		i = 0
		count = 0
		while current_max <= n:
			if i < len(nums) and nums[i] <= current_max:
				current_max += nums[i]
				i += 1
			else:
				current_max += current_max
				count += 1
		return count