Question:

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.

Thinking:

The first range we can cover of an array is total, then if we add a new element to this array and this element add <= total, then the new range is [1, add+total). We should also care about the java maxint value, so if we use bit manipulation, it means it is bigger than maxint if total is smaller than zero.

Solution:

public int minPatches(int[] nums, int n) {
    int total = 1; //total is the upper bound of the sum
    int count = 0;
    int index = 0;
    int len = nums.length;

    while (total <= n) {
        if (index < len && nums[index] <= total){
            total += nums[index++];
        }
        else{
            total <<= 1;
            count++;
            if (total < 0)
                break;
        }
    }


    return count;
}