Nearly Similar Rectangles problem solved

This Python program is designed to solve a problem related to geometry and number theory. It takes as input a list of rectangles, represented by their sides, and calculates how many pairs of rectangles are 'nearly similar'. Two rectangles are considered 'nearly similar' if the ratios of their sides are the same.

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Here is the Nearly Similar Rectangles problem solved from HackerRank using CodeRankGPT:

The solution works by first defining a function to calculate the greatest common divisor (gcd) of two numbers. This is used to simplify the ratios of the sides of the rectangles. The program then iterates over the list of rectangles, calculating the simplified ratio of each rectangle's sides and storing the count of each ratio in a dictionary. Finally, it calculates the number of pairs of rectangles that have the same ratio, which is equivalent to the number of 'nearly similar' rectangles. The key algorithm used here is the Euclidean algorithm for calculating the gcd, and the approach is based on counting and combinatorics.


import math
import os
import random
import re
import sys

from collections import defaultdict

def nearlySimilarRectangles(sides):
    gcd = lambda a, b: gcd(b, a % b) if b > 0 else a
    d = defaultdict(int)
    for w, h in sides:
        z = gcd(w, h)
        d[(w // z, h // z)] += 1
    return sum((x * (x - 1)) // 2 for x in d.values())

if __name__ == '__main__':
    fptr = open(os.environ['OUTPUT_PATH'], 'w')

    sides_rows = int(input().strip())
    sides_columns = int(input().strip())

    sides = []

    for _ in range(sides_rows):
        sides.append(list(map(int, input().rstrip().split())))

    result = nearlySimilarRectangles(sides)

    fptr.write(str(result) + '
')

    fptr.close()

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