Find array given subset sums

Array Divide and Conquer

49.5% acceptance

Feb 25, 2026

632

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.

Solution

Rust

Time O(n²)

Space O(n)

LeetCode

solution.rs

impl Solution {
  pub fn recover_array(n: i32, sums: Vec<i32>) -> Vec<i32> {
    use std::collections::BTreeMap;
    
    fn solve(mut sums: Vec<i32>, n: usize) -> Vec<i32> {
      if n == 0 {
        return vec![];
      }
      sums.sort();
      let d = sums[1] - sums[0]; // difference between two smallest
      
      for &elem in &[d, -(d)] {
        let mut freq: BTreeMap<i32, i32> = BTreeMap::new();
        for &s in &sums {
          *freq.entry(s).or_insert(0) += 1;
        }
        
        let mut without = vec![];
        let mut ok = true;
        
        for &s in &sums {
          let cnt = freq.get_mut(&s).unwrap();
          if *cnt == 0 { continue; }
          *cnt -= 1;
          
          if elem >= 0 {
            // s → without, s+elem → with
            without.push(s);
            if let Some(cnt2) = freq.get_mut(&(s + elem)) {
              if *cnt2 > 0 { *cnt2 -= 1; }
              else { ok = false; break; }
            } else { ok = false; break; }
          } else {
            // s → with, s+(-elem) = s+d → without
            without.push(s + d);
            if let Some(cnt2) = freq.get_mut(&(s + d)) {
              if *cnt2 > 0 { *cnt2 -= 1; }
              else { ok = false; break; }
            } else { ok = false; break; }
          }
        }
        
        if ok && without.contains(&0) {
          let mut result = solve(without, n - 1);
          result.push(elem);
          return result;
        }
      }
      
      vec![]
    }
    
    solve(sums, n as usize)
  }
}