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Strange Printer

Difficulty: Hard

Problem Description

There is a strange printer that can print sequences of the same character. Given a string s, the task is to find the minimum number of turns needed for the printer to print the entire string.

Key Insights

  • The printer can only print the same character in one turn.
  • Overlapping prints can cover previously printed characters.
  • The problem can be solved using dynamic programming to minimize the number of turns based on character sequences.

Space and Time Complexity

Time Complexity: O(n^3), where n is the length of the string, due to the dynamic programming approach. Space Complexity: O(n^2) for the DP table.

Solution

The problem can be approached using dynamic programming. We define a 2D array dp[i][j] that represents the minimum number of turns required to print the substring s[i...j]. The main idea is to consider all possible split points in the substring and combine results from subproblems. If the characters at the boundaries match, we can potentially reduce the number of turns needed.

  1. Initialize a DP table where dp[i][i] = 1 since a single character requires one turn.
  2. Iterate through increasing lengths of substrings.
  3. For each substring, try all possible split points and update the DP table based on previous results.

Code Solutions

def strangePrinter(s: str) -> int:
    n = len(s)
    dp = [[0] * n for _ in range(n)]
    
    for i in range(n):
        dp[i][i] = 1  # A single character requires one turn
    
    for length in range(2, n + 1):  # length of the substring
        for i in range(n - length + 1):
            j = i + length - 1  # end index
            dp[i][j] = dp[i][j - 1] + 1  # Assume we print last character separately
            for k in range(i, j):
                if s[k] == s[j]:  # If characters match, reduce turns
                    dp[i][j] = min(dp[i][j], dp[i][k] + (1 if k + 1 <= j - 1 else 0))
    
    return dp[0][n - 1]
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