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patching-array.py
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patching-array.py
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# Time: O(s + logn), s is the number of elements in the array
# Space: O(1)
# 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.
class Solution(object):
def minPatches(self, nums, n):
"""
:type nums: List[int]
:type n: int
:rtype: int
"""
patch, miss, i = 0, 1, 0
while miss <= n:
if i < len(nums) and nums[i] <= miss:
miss += nums[i]
i += 1
else:
miss += miss
patch += 1
return patch