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Problem Statement:

Given three strings A, B and C. Write a function that checks whether C is an interleaving of A and B. C is said to be interleaving A and B, if it contains all characters of A and B and order of all characters in individual strings is preserved.

Solution:

Related Problems:

• Longest Common Substring
• Longest Common Subsequence

This problem generally requires more thinking than the problems we have seen so far in 2-Strings DP series. The purpose of including this problem in our series is to show how we could use the Template discussed in 2-Strings DP chapter to solve non-trivial problems. I would highly encourage you to go through the chapter on 2-Strings DP Fundamentals and have a strong grasp on the template discussed.

I have put the explanation of the algorithm we would implement in the inline comment in the code itself. We would be using Bottom-up tabulation approach and would solve in the increasing order of length for strings so that when we solve for the higher length order for the strings we could use the already computed results for lower lengths of the strings (optimal sub-structures).

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Space Optimization:

We can do further optimization by solving this problem by using 1D array instead of 2D array. I have discussed the algorithm in the inline comment in the code.

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