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

Difficulty: interview

Starter code:

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

Solutions:
class Solution:
     def minPatches(self, nums, n):
         """
         :type nums: List[int]
         :type n: int
         :rtype: int
         """
         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):
         """
         :type nums: List[int]
         :type n: int
         :rtype: int
         """
         miss, res, i = 1, 0, 0
         while miss <= n:
             if i < len(nums) and nums[i] <= miss:
                 miss += nums[i]
                 i += 1
             else:
                 miss += miss
                 res += 1
         return res

class Solution:
     def minPatches(self, nums, n):
         """
         :type nums: List[int]
         :type n: int
         :rtype: int
         """
         miss, res, i = 1, 0, 0
         while miss <= n:
             if i < len(nums) and nums[i] <= miss:
                 miss += nums[i]
                 i += 1
             else:
                 miss += miss
                 res += 1
         
         return res

class Solution:
     def minPatches(self, nums, n):
         """
         :type nums: List[int]
         :type n: int
         :rtype: int
         """
         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):
         """
         :type nums: List[int]
         :type n: int
         :rtype: int
         """
         maxValue = 0
         i = 0
         count = 0
         while maxValue < n:
             # print(i, count, nums[i]-1, maxValue)
             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):
         """
         :type nums: List[int]
         :type n: int
         :rtype: int
         """
         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