Minimum number of subsequences required to convert one string to another

Given two strings A and B consisting of only lowercase letters, the task is to find the minimum number of subsequences required from A to form B.

Examples: 

Input: A = "abbace" B = "acebbaae" 
Output: 3 
Explanation: 
Sub-sequences "ace", "bba", "ae" from string A used to form string B

Input: A = "abc" B = "cbacbacba" 
Output: 7 
 

Approach:  

• Maintain an array for each character of A which will store its indexes in increasing order.
• Traverse through each element of B and increase the counter whenever there is a need for new subsequence.
• Maintain a variable minIndex which will show that elements greater than this index can be taken in current subsequence otherwise increase the counter and update the minIndex to -1.

Below is the implementation of the above approach. 

3

Time Complexity: O(N1+N2) // N1 is the length of string A and N2 is the length of string B

Auxiliary Space: O(26)