Check whether two strings can be made equal by reversing substring of equal length from both strings
Give two strings S1 and S2, the task is to check whether string S1 can be made equal to string S2 by reversing substring from both strings of equal length.
Note: A substring can be reversed any number of times.
Input: S1 = “abbca”, S2 = “acabb”
The string S1 and S2 can be made equal by:
Reverse S1 in the range [2, 4] (length = 3), S1 = “abacb”
Reverse S2 in the range [1, 3] (length = 3), S2 = “abacb”
S1 = “abacb” and S2 = “abacb”, after reversing.
Hence, both can be made equal.
Input: “S1 = “abcd”, S2 = “abdc”
- The idea is to make both the strings equal by sorting both of them.
- First, check if both the strings have the same set of characters or not. If not, then answer is “No”.
- Fix the length of substring to reverse to 2. Now, this means swapping adjacent characters.
- Now, number of moves needed to sort a string by reversing substring of size 2 or in other words, swapping adjacent characters, is the Inversion Count of the string.
- If both strings have the same inversion count, then the answer is “Yes”.
- If they have different inversion counts, making them equal is only possible if at least one of the following conditions matches:
- First, if the parity of the inversion count is the same, that is both even or odd, then answer is “Yes”. We’ll continue swapping any pair of elements in the sorted string until the other one is sorted. Since, the difference of inversion count will be even, so swapping any pair twice doesn’t produce any change.
- Second, if the parity is not the same, then there has to be at least a character with a frequency greater than 1 in any of the string. We’ll just swap them until the other one gets sorted. Since swapping identical character doesn’t make any change.
Below is the implementation of the above approach: