Patching Array

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.

Ideas: Greedy, sum can be added by exist items, so next one should be sum+1.

public int minPatches(int[] nums, int n) {
    long sum = 1;
    int i=0, patch = 0;

    while(sum <= n) {
        if(i < nums.length && sum >= nums[i]) {
            sum += nums[i];
            i++;
        } else {
            patch++;
            sum += sum; // Here, add sum, because we use sum <= n.
        }
    }

    return patch;
}