Minimum swaps to sort by digit sum

Array Hash Table Sorting

50.4% acceptance

Feb 25, 2026

143

You are given an array nums of distinct positive integers. You need to sort the array in increasing order based on the sum of the digits of each number. If two numbers have the same digit sum, the smaller number appears first in the sorted order. Return the minimum number of swaps required to rearrange nums into this sorted order. A swap is defined as exchanging the values at two distinct positions in the array.

Solution

Rust

Time O(n²)

Space O(n)

LeetCode

solution.rs

impl Solution {
  pub fn min_swaps(nums: Vec<i32>) -> i32 {
    fn digit_sum(mut x: i32) -> i32 {
      let mut s = 0;
      while x > 0 { s += x % 10; x /= 10; }
      s
    }
    let n = nums.len();
    // Build sorted target
    let mut sorted = nums.clone();
    sorted.sort_by(|&a, &b| digit_sum(a).cmp(&digit_sum(b)).then(a.cmp(&b)));
    // For each value in nums, find its target index
    // Build position map: value -> target index
    use std::collections::HashMap;
    let mut pos: HashMap<i32, usize> = HashMap::new();
    for (i, &v) in sorted.iter().enumerate() { pos.insert(v, i); }
    // Count cycles in permutation
    let perm: Vec<usize> = nums.iter().map(|v| pos[v]).collect();
    let mut visited = vec![false; n];
    let mut swaps = 0;
    for i in 0..n {
      if visited[i] || perm[i] == i { visited[i] = true; continue; }
      let mut cycle_len = 0;
      let mut j = i;
      while !visited[j] {
        visited[j] = true;
        j = perm[j];
        cycle_len += 1;
      }
      swaps += cycle_len - 1;
    }
    swaps
  }
}