K-Similar Strings

K-Similar Strings

1. What is this problem about?

The K-Similar Strings interview question is a string transformation challenge. Two strings $s1$ and $s2$ are "k-similar" if $s1$ can be transformed into $s2$ by performing exactly $k$ swaps of two characters in $s1$. You are given two anagrams, $s1$ and $s2$, and you need to find the minimum number of swaps required to make them equal.

2. Why is this asked in interviews?

Companies like Google and DoorDash use the K-Similar Strings coding problem to test a candidate's mastery of Breadth-First Search (BFS) on state spaces. It's not a simple greedy problem; choosing the wrong swap can lead to a sub-optimal total. It evaluates whether you can represent string states as nodes in a graph and find the shortest path between them.

3. Algorithmic pattern used

This problem follows the BFS on State Space pattern.

1. Initial State: The string $s1$ is your starting node.
2. Target State: The string $s2$ is your destination.
3. Queue: Use a queue to explore strings level by level. Each level represents one swap.
4. Pruning: At each step, find the first index $i$ where s1[i] != s2[i]. Only try swapping s1[i] with indices $j > i$ where s1[j] == s2[i].
5. Visited Set: Keep track of strings you've already seen to avoid cycles and redundant work.

4. Example explanation

s1 = "abc", s2 = "bca"

1. Level 0: "abc".
2. First mismatch at index 0 ('a' vs 'b').
3. Possible swaps for index 0: swap with index 1 (value 'b').
4. Result: "bac". Level 1 queue: ["bac"].
5. From "bac", first mismatch at index 1 ('a' vs 'c').
6. Swap with index 2 (value 'c').
7. Result: "bca". Target reached! Result: 2 swaps.

5. Common mistakes candidates make

• Greedy swapping: Assuming that any swap that fixes one character is correct. Some swaps fix one but make others harder to fix.
• No pruning: Trying every possible $N^2$ swap at each step, which makes the BFS too slow.
• Ignoring Anagram property: Failing to realize that because the strings are anagrams, a sequence of swaps always exists.

6. Interview preparation tip

State-space search problems are common in "Hard" interviews. Practice identifying when a problem can be modeled as a shortest path in a graph where nodes are the current configuration of the data. This is a vital Graph interview pattern.