PatchingArray.java

/**
 * 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.
 *
 * Tags: Greedy
 */
public class PatchingArray {

    /**
     * Build the largest range possible and find the smallest missing number
     * if missing >= nums[i], range can be extended to missing + nums[i]
     * else add missing number, range can be extended to missing * 2
     * stop till missing > n
     */
    public int minPatches(int[] nums, int n) {
        int total = 0, i = 0;
        for (long miss = 1; miss <= n; total++) {
            miss += (i < nums.length && nums[i] <= miss) ? nums[i++] : miss;
        }
        return total - i;
    }
}