g0301_0400.s0330_patching_array.Solution Maven / Gradle / Ivy

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Java-based LeetCode algorithm problem solutions, regularly updated

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package g0301_0400.s0330_patching_array;

// #Hard #Array #Greedy #2022_07_09_Time_1_ms_(60.00%)_Space_44.3_MB_(27.06%)

/**
 * 330 - Patching Array\.
 *
 * Hard
 *
 * Given a sorted integer array `nums` and an integer `n`, add/patch elements to the array such that any number in the 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:**
 *
 * **Input:** nums = [1,3], n = 6
 *
 * **Output:** 1
 *
 * **Explanation:**
 *
 *     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:**
 *
 * **Input:** nums = [1,5,10], n = 20
 *
 * **Output:** 2
 *
 * **Explanation:** The two patches can be [2, 4]. 
 *
 * **Example 3:**
 *
 * **Input:** nums = [1,2,2], n = 5
 *
 * **Output:** 0 
 *
 * **Constraints:**
 *
 * *   `1 <= nums.length <= 1000`
 * *   1 <= nums[i] <= 10⁴
 * *   `nums` is sorted in **ascending order**.
 * *   1 <= n <= 2³¹ - 1
**/
public class Solution {
    public int minPatches(int[] nums, int n) {
        int res = 0;
        long sum = 0;
        int i = 0;
        while (sum < n) {
            // required number
            long req = sum + 1;
            if (i < nums.length && nums[i] <= req) {
                sum += nums[i++];
            } else {
                sum += req;
                res++;
            }
        }
        return res;
    }
}