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.

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

Solution

public class Solution {
    public int minPatches(int[] nums, int n) {
        if (nums == null || n <= 0) return -1;

        long miss = 1;
        int index = 0;
        int result = 0;
        while (miss <= n) {
            if (index < nums.length && nums[index] <= miss) {
                miss += nums[index];
                index++;
            } else {
                result += 1;
                miss = miss << 1;
            }
        }

        return result;
    }
}