#!/usr/bin/env python
# -*- coding: utf-8 -*-
'''
*****************************************
Author:         zhlinh
Email:          zhlinhng@gmail.com
Version:        0.0.1
Created Time:   2016-05-21
Last_modify:    2016-05-21
******************************************
'''

'''
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.
Credits:
Special thanks to @dietpepsi for adding this problem and creating all test cases.
'''

class Solution(object):
    def minPatches(self, nums, n):
        """
        :type nums: List[int]
        :type n: int
        :rtype: int
        """
        top = 1
        i = 0
        res = 0
        while top <= n:
            if i >= len(nums) or nums[i] > top:
                top *= 2
                res += 1
            else:
                top += nums[i]
                i += 1
        return res
