Strange Printer - Video Solutions

Problem Overview: You are given a string s. A special printer can print a sequence of identical characters in one turn and can overwrite existing characters. The goal is to compute the minimum number of turns required to print the entire string.

Approach 1: Greedy Segment Coverage (O(n^2) time, O(n) space)

This approach relies on the observation that consecutive duplicate characters do not change the number of turns required. You first compress the string by removing adjacent duplicates, which reduces unnecessary states. Then iterate through the compressed string and try to extend segments where the same character appears again later. By greedily covering these matching characters in a single printing turn, you reduce the total number of operations. This strategy works well when the string contains repeating patterns because a single print can overwrite previously printed characters and merge segments.

Approach 2: Dynamic Programming with Memoization (O(n^3) time, O(n^2) space)

The optimal solution uses interval dynamic programming. Define dp[i][j] as the minimum number of turns needed to print the substring from index i to j. Start with the idea that printing s[i] alone requires one turn plus the cost of printing the remaining substring dp[i+1][j]. Then iterate through indices k where s[k] == s[i]. If the printer prints both characters in the same turn, the interval can be split into dp[i][k-1] + dp[k+1][j], reducing redundant prints. Memoization ensures each substring state is computed once, turning the recursive exploration into a manageable O(n^3) process. The DP table has O(n^2) states and each state may scan the interval to merge matching characters.

This problem is a classic example of interval DP similar to matrix chain multiplication or palindrome partitioning. The key trick is recognizing that matching characters allow you to merge print operations across different positions.

Recommended for interviews: Interviewers expect the Dynamic Programming with Memoization solution. It demonstrates strong understanding of interval DP and state transitions. Discussing the greedy idea shows intuition about segment merging, but implementing the DP recurrence correctly proves you can reason about overlapping subproblems. Review related patterns under dynamic programming and string interval problems in string algorithms.