K-Similar Strings - Video Solutions

Problem Overview: You are given two anagram strings s1 and s2. A swap can exchange any two characters in s1. The goal is to compute the minimum number of swaps required to transform s1 into s2. Since both strings contain the same characters, the challenge is finding the smallest sequence of swaps that fixes mismatched positions.

Approach 1: Breadth-First Search (BFS) State Search (O(n!) time, O(n!) space)

This problem can be modeled as a shortest-path search where each string configuration is a node in a graph. Start from s1 and generate new states by swapping characters. A Breadth-First Search guarantees the first time you reach s2 uses the minimum number of swaps. To reduce branching, locate the first index where the current string differs from s2. Only swap that character with a later index that moves the correct target character into place. Each valid swap produces a new string state that gets pushed into a queue if it hasn't been visited. A visited set prevents revisiting permutations. This pruning drastically reduces the search space compared to exploring all possible swaps.

The key insight is that you should only fix the earliest mismatch instead of trying every swap pair. That greedy restriction turns a factorial search into a manageable BFS traversal. Each level of BFS represents one additional swap, so the level where s2 appears is the answer.

Approach 2: Greedy Depth-First Search (DFS) with Pruning (O(n!) worst-case time, O(n) recursion space)

A backtracking approach using Depth-First Search can also solve the problem efficiently with aggressive pruning. At each step, find the first mismatch between the current string and s2. Try swapping that character with positions later in the string that match the needed target character. After performing a swap, recursively continue fixing the remaining suffix. If the current swap count already exceeds the best solution found so far, prune that branch.

This greedy restriction ensures every swap immediately fixes at least one mismatch, preventing unnecessary permutations. Combined with pruning and early termination, the DFS approach often runs faster in practice because it avoids maintaining large BFS queues. The implementation relies heavily on efficient character swapping and careful backtracking.

Since the input is a string anagram pair, both approaches rely on the observation that optimal swaps always correct mismatched characters rather than introducing new mismatches.

Recommended for interviews: The BFS approach is the most common explanation in interviews because it clearly models the problem as a shortest transformation sequence. It demonstrates strong understanding of state-space search and pruning. The DFS with pruning solution is more optimized and often faster in practice, but BFS tends to be easier to reason about and prove correct during an interview discussion.