g1901_2000.s1982_find_array_given_subset_sums.Solution Maven / Gradle / Ivy

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Java-based LeetCode algorithm problem solutions, regularly updated

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package g1901_2000.s1982_find_array_given_subset_sums;

// #Hard #Array #Divide_and_Conquer #2022_05_21_Time_70_ms_(64.91%)_Space_83.3_MB_(70.18%)

import java.util.Arrays;

/**
 * 1982 - Find Array Given Subset Sums\.
 *
 * Hard
 *
 * You are given an integer `n` representing the length of an unknown array that you are trying to recover. You are also given an array `sums` containing the values of all 2ⁿ **subset sums** of the unknown array (in no particular order).
 *
 * Return _the array_ `ans` _of length_ `n` _representing the unknown array. If **multiple** answers exist, return **any** of them_.
 *
 * An array `sub` is a **subset** of an array `arr` if `sub` can be obtained from `arr` by deleting some (possibly zero or all) elements of `arr`. The sum of the elements in `sub` is one possible **subset sum** of `arr`. The sum of an empty array is considered to be `0`.
 *
 * **Note:** Test cases are generated such that there will **always** be at least one correct answer.
 *
 * **Example 1:**
 *
 * **Input:** n = 3, sums = [-3,-2,-1,0,0,1,2,3]
 *
 * **Output:** [1,2,-3]
 *
 * **Explanation:** [1,2,-3] is able to achieve the given subset sums: 
 *
 * - []: sum is 0 
 *
 * - [1]: sum is 1 
 *
 * - [2]: sum is 2 
 *
 * - [1,2]: sum is 3 
 *
 * - [-3]: sum is -3 
 *
 * - [1,-3]: sum is -2 
 *
 * - [2,-3]: sum is -1 
 *
 * - [1,2,-3]: sum is 0 
 *   
 * Note that any permutation of [1,2,-3] and also any permutation of [-1,-2,3] will also be accepted.
 *
 * **Example 2:**
 *
 * **Input:** n = 2, sums = [0,0,0,0]
 *
 * **Output:** [0,0]
 *
 * **Explanation:** The only correct answer is [0,0].
 *
 * **Example 3:**
 *
 * **Input:** n = 4, sums = [0,0,5,5,4,-1,4,9,9,-1,4,3,4,8,3,8]
 *
 * **Output:** [0,-1,4,5]
 *
 * **Explanation:** [0,-1,4,5] is able to achieve the given subset sums.
 *
 * **Constraints:**
 *
 * *   `1 <= n <= 15`
 * *   sums.length == 2ⁿ
 * *   -10⁴ <= sums[i] <= 10⁴
**/
public class Solution {
    public int[] recoverArray(int n, int[] sums) {
        Arrays.sort(sums);
        int m = sums.length;
        int zeroShift = 0;
        int[] res = new int[n];
        for (int i = 0; i < n; ++i) {
            int diff = sums[1] - sums[0];
            int p = 0;
            int k = 0;
            int zpos = m;
            for (int j = 0; j < m; ++j) {
                if (k < p && sums[k] == sums[j]) {
                    k++;
                } else {
                    if (zeroShift == sums[j]) {
                        zpos = p;
                    }
                    sums[p++] = sums[j] + diff;
                }
            }
            if (zpos >= m / 2) {
                res[i] = -diff;
            } else {
                res[i] = diff;
                zeroShift += diff;
            }
            m /= 2;
        }
        return res;
    }
}