716016. Fraction pairs with sum 1
Medium
Fraction Pairs with Sum 1
Slug: fraction-pairs-with-sum-1
Difficulty: Medium
Id: 716016
Topic Tags: Mathematical, Map
Company Tags: Microsoft
Summary
Given a list of fractions in the form [numerator/denominator], find all unique pairs of fractions that add up to 1. The problem is about finding fraction pairs with sum 1 and involves mathematical concepts like fractions and mapping.
Detailed Explanation
To solve this problem, we can iterate through the list of fractions, considering each pair as a potential solution. We'll keep track of the fractions we've seen so far using a HashMap to store the denominators as keys and their corresponding numerators as values.
Here's the step-by-step breakdown:
- Initialize an empty HashMap
fractionMapto store the fractions. - Iterate through the list of fractions:
- For each fraction, extract the numerator and denominator.
- Calculate the reciprocal of the current fraction (i.e., swap the numerator and denominator).
- Check if the reciprocal is already in the
fractionMap. If it is, that means we've found a pair of fractions that add up to 1. Add this pair to our result set.
- After iterating through all the fractions, return the result set containing all unique pairs of fractions with sum 1.
Time complexity: O(n), where n is the number of fractions in the list. Space complexity: O(n), as we need to store the fractions and their denominators in the HashMap.
Optimized Solutions
Java
import java.util.*;
public class FractionPairs {
public static List<List<Integer>> fractionPairs(int[][] fractions) {
Map<Integer, Integer> fractionMap = new HashMap<>();
Set<List<Integer>> result = new HashSet<>();
for (int[] fraction : fractions) {
int numerator = fraction[0];
int denominator = fraction[1];
int reciprocalNumerator = denominator;
int reciprocalDenominator = numerator;
if (!fractionMap.containsKey(reciprocalDenominator)) {
fractionMap.put(reciprocalDenominator, reciprocalNumerator);
} else {
result.add(Arrays.asList(fraction[0], fraction[1], fractionMap.get(reciprocalDenominator), reciprocalDenominator));
}
}
return new ArrayList<>(result);
}
}