Solving the CodeForces 276B Problem: Price and Quality Comparison for Laptops

Are you facing challenges with the CodeForces problem 276B, which involves determining if there exists a laptop with a higher quality at a lower or equal price? This article will guide you through the steps to solve this interesting problem. We will walk you through input parsing, sorting, and validation to find the solution. Additionally, we provide a Python implementation for better understanding and reference.

Problem Summary

The problem at hand requires you to analyze a set of laptops each with a unique price and quality rating. Your goal is to identify if there exists a laptop whose price is less than or equal to another laptop's price yet has a higher quality rating. If such a pair is found, the answer is 'Yes'; otherwise, it's 'No'.

Steps to Solve the Problem

Input Parsing

Begin by reading the number of laptops, denoted as n. Each laptop's price and quality are then inputted, which needs to be stored for subsequent processing. Here’s how you can parse the input:

First, read the number of laptops, n. For every laptop, read its price and quality values. Organize these values into a list of tuples where each tuple contains the price and quality of a single laptop.

Sorting

To solve the problem effectively, it's crucial to sort the list of laptops based on their price. If two laptops have the same price, the order of quality does not matter for this problem. Utilize Python's built-in sort function for this purpose.

Checking for Valid Pairs

After sorting the list, iterate through the sorted list to check if there is a laptop with a lower quality than the one appearing before it in the sorted list. If a valid pair is found, the answer is 'Yes'; otherwise, it remains 'No'.

Implementation

A sample implementation in Python can be as follows:

def solve():    import sys    input      data  input().splitlines()    n  int(data[0])    laptops  []    for i in range(1, n   1):        price, quality  map(int, data[i].split())        ((price, quality))    # Sort laptops by price    ()    # Check for a valid pair    for i in range(1, n):        if laptops[i][1]  laptops[i - 1][1]:  # Compare quality            print('Yes')            return    print('No')

Explanation of the Code

Input Handling: The input function reads all input at once, and the splitlines method is used to separate the information into different lines. The first line contains the number of laptops, and the subsequent lines contain the price and quality of each laptop. Sorting: The laptops are sorted based on their price using Python's built-in sort method, which is efficient. Validation: The loop checks adjacent laptops in the sorted list. If any laptop has a lower quality than the one before it, it means it has a higher price, and we output 'Yes'. Otherwise, it remains 'No'.

Complexity

Time Complexity: The sorting step takes O(n log n) time, and the iteration takes O(n) time, leading to an overall complexity of O(n log n).

Space Complexity: The space used is O(n) for storing the laptops.

This approach efficiently determines the relationship between price and quality for the given laptops and produces the correct output based on the conditions specified in the problem statement.