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Leetcode 2864. Maximum Odd Binary Number

Problem Statement

Given a binary string s, you need to rearrange the characters of s such that the resultant binary number is the largest possible odd binary number.

A binary number is odd if its last digit is 1.

Clarifying Questions

  1. What is the expected input format?
    • The input is a string s consisting only of '0' and '1'.
  2. What should be returned?
    • The function should return the largest possible odd binary number that can be formed by rearranging the characters of s.
  3. Are there any constraints on the length of the string?
    • There may be a problem-specific constraint, but generally, a reasonable length constraint would be manageable within typical limits.

Strategy

To form the largest possible binary number, you need to ensure the most significant bits are 1s. However, to ensure the binary number is odd, its last digit must be 1.

  1. Count the number of 1s and 0s in the string.
  2. Place the largest possible 1s in the highest order positions but preserve at least one 1 to ensure the number ends in 1.
  3. Fill the remaining positions with 0s.

Steps

  1. Count the occurrences of 1s and 0s.
  2. Construct the largest number possible with all 1s first except for one 1 at the end.
  3. Append all 0s.
  4. Ensure the last digit is 1.

Code

Here is a C++ function to implement the strategy described:

#include <string>
#include <algorithm>

std::string maximumOddBinaryNumber(std::string s) {
    int count1 = std::count(s.begin(), s.end(), '1');
    int count0 = s.size() - count1;

    std::string result(count1 - 1, '1'); // Place count1-1 1's first
    result.append(count0, '0'); // Then append count0 0's
    result.append(1, '1'); // Finally append the last 1

    return result;
}

Explanation

  1. Count the 1s and 0s:
    • count1: Total count of 1s in the string.
    • count0: Total count of 0s in the string (can be derived from total length - count1).
  2. Construct the result string:
    • Start with count1 - 1 1s to make the number as large as possible.
    • Append all the 0s.
    • Finally, append a 1 to ensure the number is odd.

Time Complexity

This approach ensures we achieve the largest possible odd binary number by maximizing the number of leading 1s and ensuring the last digit is 1.

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