Strange Printer

Strange Printer

What is this problem about?

The Strange Printer coding problem presents a unique challenge involving a specialized printer that can only print a sequence of the same character at a time. The printer can cover any existing characters within a specified range, effectively overwriting them. The objective is to determine the minimum number of turns needed to print a given target string. This problem is particularly interesting because it forces you to think about how to optimally layer character "washes" to achieve a complex pattern with the fewest possible operations.

Why is this asked in interviews?

As a "Hard" difficulty problem, the Strange Printer interview question is frequently used by top-tier companies like Microsoft, Meta, and Google to assess a candidate's depth in Dynamic Programming. It specifically tests your ability to handle "Interval DP," a technique used when the optimal solution for a range depends on how that range is partitioned or how its endpoints interact. Interviewers want to see if you can identify that printing the same character at the beginning and end of a range can potentially save a turn, which is the key insight for this problem.

Algorithmic pattern used

This problem follows the String, Dynamic Programming interview pattern, specifically utilizing Interval DP. The state dp[i][j] represents the minimum turns to print the substring from index i to index j. The base case is a single character, which takes one turn. For longer strings, you split the interval at various points k and sum the results. However, the critical optimization occurs when the characters at s[i] and s[j] are the same; in this case, the turn used to print s[i] can be extended to cover s[j] as well, reducing the total turns.

Example explanation

Suppose we want to print the string "ABA".

1. A simple way would be: Print "AAA" (1 turn), then print "B" at the second position (1 turn). Total = 2 turns.
2. If we didn't notice the "A"s match, we might think: Print "A" (1 turn), print "B" (1 turn), print "A" (1 turn). Total = 3 turns. The algorithm recognizes that since the first and last characters are both 'A', any turn spent printing the first 'A' can "reach" the last 'A' for free, as long as the intermediate characters are handled. For "AABBAA", the printer could print "AAAAAA" in one turn, then focus on the "BB" section.

Common mistakes candidates make

The most frequent error is treating this as a greedy problem, such as trying to print the most frequent character first. Another common mistake is not correctly identifying the overlap condition (when s[i] == s[j]). Some candidates also fail to optimize the string by removing consecutive identical characters (e.g., "aaabbb" is functionally the same as "ab" for this problem), which can simplify the logic and improve performance. Failure to handle the base cases of the DP table also leads to incorrect results.

Interview preparation tip

To master Interval DP questions, start with easier problems like "Longest Palindromic Subsequence." These problems build the intuition for how a range [i, j] is built from [i+1, j], [i, j-1], and [i+1, j-1]. Always look for properties at the boundaries of your interval. In your interview, draw out the DP table and trace a small example like "ABA" or "ABCA" to ensure your transition logic correctly accounts for matching characters at different split points.