Maximum possible number by binary concatenation

Array Bit Manipulation Enumeration

65.5% acceptance

Feb 23, 2026

115

You are given an array of integers nums of size 3. Return the maximum possible number whose binary representation can be formed by concatenating the binary representation of all elements in nums in some order. Note that the binary representation of any number does not contain leading zeros.

Solution

Rust

Time O(2^n)

Space O(n)

LeetCode

solution.rs

impl Solution {
  pub fn max_good_number(mut nums: Vec<i32>) -> i32 {
    fn bits(x: i32) -> u32 { (32 - x.leading_zeros()) as u32 }
    // Sort by which concatenation order gives larger number
    nums.sort_unstable_by(|&a, &b| {
      let ab = (a as i64) << bits(b) | b as i64;
      let ba = (b as i64) << bits(a) | a as i64;
      ba.cmp(&ab)
    });
    let mut result = 0i32;
    for x in nums {
      result = (result << bits(x)) | x;
    }
    result
  }
}