Campus bikes ii

Array Dynamic Programming Backtracking Bit Manipulation Bitmask

55.9% acceptance

Mar 31, 2026

966

On a campus represented as a 2D grid, there are n workers and m bikes, with n <= m. Each worker and bike is a 2D coordinate on this grid. We assign one unique bike to each worker so that the sum of the Manhattan distances between each worker and their assigned bike is minimized. Return the minimum possible sum of Manhattan distances between each worker and their assigned bike. The Manhattan distance between two points p1 and p2 is Manhattan(p1, p2) = |p1.x - p2.x| + |p1.y - p2.y|.

Solution

Rust

Time O(n²)

Space O(n)

LeetCode

solution.rs

impl Solution {
  pub fn assign_bikes(workers: Vec<Vec<i32>>, bikes: Vec<Vec<i32>>) -> i32 {
    let n = workers.len();
    let m = bikes.len();
    let mut dp = vec![i32::MAX; 1 << m];
    dp[0] = 0;
    for mask in 0..(1usize << m) {
      if dp[mask] == i32::MAX { continue; }
      let worker = mask.count_ones() as usize;
      if worker == n { continue; }
      for k in 0..m {
        if mask & (1 << k) != 0 { continue; }
        let new_mask = mask | (1 << k);
        let dist = (workers[worker][0] - bikes[k][0]).abs()
             + (workers[worker][1] - bikes[k][1]).abs();
        dp[new_mask] = dp[new_mask].min(dp[mask] + dist);
      }
    }
    dp.into_iter()
      .enumerate()
      .filter(|(mask, _)| mask.count_ones() as usize == n)
      .map(|(_, v)| v)
      .min()
      .unwrap()
  }
}