Overview

This problem requires processing library lending records in order and outputting the remaining book count for each genre in each library, along with the total number of failed lending attempts.

Analysis

The problem simply involves processing each lending request in order, but the following points require attention: - If the book count is 0, the lending fails and the book count does not change - If the book count is 1 or more, the lending succeeds and the book count is decreased by 1 - Since the input size can be large (up to 200,000 lending requests), efficient processing is necessary

A straightforward approach (directly updating the book count for each lending request) is sufficiently efficient since each operation can be processed in constant time. In particular, updating the book count only requires array element access and subtraction, so it can be processed quickly.

Algorithm

1. Read the input data and store the book counts for each library in a 2D array
2. Process lending requests sequentially:
   • Check the book count for the target library and genre
   • If the book count is greater than 0, decrease it by 1
   • If the book count is 0, increment the failure count
3. Output the book counts for each library after processing
4. Output the total number of failures

Complexity

• Time complexity: \(O(Q + \sum_{i=1}^{N} M_i)\)
  • Input reading: \(O(\sum_{i=1}^{N} M_i)\)
  • Lending processing: \(O(Q)\)
  • Output: \(O(\sum_{i=1}^{N} M_i)\)
• Space complexity: \(O(\sum_{i=1}^{N} M_i)\)
  • Memory for storing the book data

Implementation Notes

• Since array indices are 0-based, subtract 1 from the input library number v and subtract 1 from the genre number d to compute the correct indices

• Strictly check whether the book count is 0 (to avoid negative numbers)

• Improve efficiency by reading and processing input data all at once

• Use the join method when converting lists to strings for output

  Source Code

import sys

def main():
    data = sys.stdin.read().split()
    if not data:
        return
    
    index = 0
    N = int(data[index]); index += 1
    libraries = []
    total_books = 0
    
    for i in range(N):
        M_i = int(data[index]); index += 1
        books = list(map(int, data[index:index+M_i]))
        index += M_i
        libraries.append(books)
        total_books += M_i
        
    Q = int(data[index]); index += 1
    fail_count = 0
    
    for i in range(Q):
        v = int(data[index]); index += 1
        d = int(data[index]); index += 1
        library_index = v - 1
        genre_index = d - 1
        
        if libraries[library_index][genre_index] > 0:
            libraries[library_index][genre_index] -= 1
        else:
            fail_count += 1
            
    for books in libraries:
        print(" ".join(map(str, books)))
        
    print(fail_count)

if __name__ == "__main__":
    main()

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