881766. Lexicographical Rank Of String
Lexicographical Rank Of String
Summary
The problem is to find the lexicographical rank of a given string. The lexicographical rank of a string is its position in a sorted list of all strings that can be formed by rearranging the characters of the original string. For example, if the input string is "cat", the possible permutations are "act", "atc", "cac", "cta", "tac", and the lexicographical rank would be 3 (since "tac" is the third permutation in the sorted list).
Detailed Explanation
The problem can be solved by generating all permutations of the input string using backtracking, and then sorting these permutations. The lexicographical rank is the position of the given string in this sorted list.
Here's a step-by-step breakdown of the solution:
- Generate all permutations of the input string using backtracking.
- Sort the generated permutations in lexicographical order.
- Find the position of the given string in the sorted list of permutations.
- Return the position as the lexicographical rank of the original string.
Here's a simple example to illustrate this:
Input string: "cat" Permutations: ["act", "atc", "cac", "cta", "tac"] Sorted permutations: ["act", "atc", "cac", "cta", "tac"] Position of "cat" in the sorted list: 4 Lexicographical rank: 4
Time complexity: O(n!), where n is the length of the input string. This is because we need to generate all permutations, and there are n! possible permutations for a string of length n. Space complexity: O(n), as we need to store the generated permutations.
Optimized Solutions
Java
import java.util.Arrays;
public class LexicographicalRank {
public static int lexicographicalRank(String s) {
char[] chars = s.toCharArray();
Arrays.sort(chars);
return Arrays.binarySearch(new String(chars), s);
}
}