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

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.

in order to know if sum of nums[] cover range from 1..n, must iterate 1..n 

 can use one variable boundary to hold the current max sum number we can get.

for example,

[1,2,3, 10]

cur sum boundary

1      1         2

2      3         4

3      6         7

we don't have 7 in the array, so patch 7, then we can get 13 before check next element

10    13     14

       23       24   

Once path 7, we can get 23 as total max

public int minPatches(int[] nums, int n) {
        if(n<=0) return 0;
        nums = (nums == null)? new int[0] :nums;
        int curIndex=0, res = 0;
        long boundaryVal = 1, sum =0;
        while(boundaryVal <= n) {
            if(curIndex < nums.length && nums[curIndex] <=boundaryVal) {
                sum += nums[curIndex++];
                boundaryVal= sum+1;
            } else {
                res++;
                sum += boundaryVal;
                boundaryVal = sum+1;
            }
        }
        return res;
    }