Find number of contiguous Substrings with repeated patterns

Given a string str consisting of digits, the task is to find the number of contiguous substrings such that the substring can be rearranged into a repetition of some string twice.

Examples:

Input:  str="15512212"
Output: 6
Explanation: Possible 6 substrings are : 

• "1551" can be rearranged to "1515"
• "155122" can be rearranged to "152152"
• "551221" can be rearranged to "512512"
• "1221" can be rearranged to "1212"
• "55" can be  rearranged to "55"
• "22" can be rearranged to "22"

Input:  str="590025995299005"
Output: 14

Approach: This can be solved with the following idea:

The approach used in the code is based on the observation that if a substring can be rearranged into a repetition of some string twice, then toggling any subset of its digits an even number of times will also result in a substring. This observation is used to efficiently compute the count of substrings using bitwise operations and maps.

Steps to implement the above approach:

• Initialize a map m with key-value pair (0, 1).
• Read the input string str.
• Initialize a variable bb to 0.
• Initialize a variable ret to 0.
• For each character c in str, do the following:
  •  Convert the character c to integer v by subtracting the ASCII value of '0' from it.
  • Update bb by toggling the v-th bit in bb using the bitwise XOR operation.
  • If m[bb] exists, increment ret by m[bb].
  • Increment m[bb] by 1.
• Print the value of ret, which is the count of required contiguous substrings.

Below is the implementation of the above approach:

6

Time Complexity: O(n*log(m))
Auxilairy Space: O(m)

Related articles:

• Introduction to Strings – Data Structure and Algorithm Tutorials