Problem Description
Given a string s, rearrange the characters of s so that any two adjacent characters are not the same. Return any possible rearrangement of s or return "" if not possible.
Key Insights
- The maximum frequency of any character must not exceed half of the total length of the string (rounded up) to ensure adjacent characters are not the same.
- A max heap (priority queue) can be leveraged to always place the most frequent character next, ensuring proper arrangement.
- Use a greedy algorithm to build the rearranged string by selecting characters based on their frequencies.
Space and Time Complexity
Time Complexity: O(n log k), where n is the length of the string and k is the number of unique characters. Space Complexity: O(k), where k is the number of unique characters stored in the heap.
Solution
To solve this problem, we can use a max heap to keep track of the frequency of each character in the string. First, we count the frequency of each character using a hash table. Then, we push the characters into a max heap based on their frequency. In a loop, we will pop the two most frequent characters from the heap and append them to the result string. We will then decrease their counts and push them back into the heap if they still have remaining counts. This process continues until we can no longer add characters without violating the adjacency condition.