Java Combinatorial Pair Counting

Introduction

Hello, coding enthusiast! In our journey to master coding and problem-solving, we've arrived at an interesting challenge today. We're going to focus heavily on combinatorial problems in practice. Specifically, we're examining combinatorial problems that involve working with large datasets and multiple pairs of numbers. We'll learn how to solve significant problems efficiently by implementing smart use of data structures like HashMap and sidestepping expensive operations like iterating over large arrays. Are you ready? Let's dive in!

Task Statement

i \ne j

Understanding the Solution: The Idea

n \cdot (n - 1) / 2

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Solution Building: Step 2

With the first step completed, our next move is to populate the HashMap by iterating over the array of pairs. For each pair, we'll examine its two elements and either append the current index to the list of indices for this number (if it’s already in the HashMap) or start a new list for it (if it isn't).

Here's how we modify our function to carry out this operation:

Java

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class NonCommonPairs {
    public static int nonCommonPairs(List<Map.Entry<Integer, Integer>> arr) {
        Map<Integer, List<Integer>> indices = new HashMap<>();
        int totalPairs = arr.size() * (arr.size() - 1) / 2;
        
        for (int idx = 0; idx < arr.size(); ++idx) {
            Map.Entry<Integer, Integer> pair = arr.get(idx);
            for (int num : new int[]{pair.getKey(), pair.getValue()}) {
                indices.computeIfAbsent(num, k -> new ArrayList<>()).add(idx);
            }
        }
        
        // (The rest of the code will be added in the next step)
        return totalPairs; // Temporary return to avoid compilation error
    }

    public static void main(String[] args) {
        // Code for testing will be added later
    }
}

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class NonCommonPairs {
    public static int nonCommonPairs(List<Map.Entry<Integer, Integer>> arr) {
        Map<Integer, List<Integer>> indices = new HashMap<>();
        int totalPairs = arr.size() * (arr.size() - 1) / 2;
        
        for (int idx = 0; idx < arr.size(); ++idx) {
            Map.Entry<Integer, Integer> pair = arr.get(idx);
            for (int num : new int[]{pair.getKey(), pair.getValue()}) {
                indices.computeIfAbsent(num, k -> new ArrayList<>()).add(idx);
            }
        }
        
        // (The rest of the code will be added in the next step)
        return totalPairs; // Temporary return to avoid compilation error
    }

    public static void main(String[] args) {
        // Code for testing will be added later
    }
}

Solution Building: Step 3

Finally, with all the data in place, we arrive at our final step of calculation. We need to calculate the total pairs of indices that share at least one common element. For that, we'll consider each number in the array and count the number of times those numbers occur in different pairs. We'll use the same formula as before.

Finally, we subtract these common pairs from the total pairs to get our answer — the count of pairs without a common number.

Adding this last part to our function gives us the solution:

Java

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.AbstractMap.SimpleEntry;

public class NonCommonPairs {
    public static int nonCommonPairs(List<Map.Entry<Integer, Integer>> arr) {
        Map<Integer, List<Integer>> indices = new HashMap<>();
        int totalPairs = arr.size() * (arr.size() - 1) / 2;
        
        for (int idx = 0; idx < arr.size(); ++idx) {
            Map.Entry<Integer, Integer> pair = arr.get(idx);
            for (int num : new int[]{pair.getKey(), pair.getValue()}) {
                indices.computeIfAbsent(num, k -> new ArrayList<>()).add(idx);
            }
        }

        int commonPairs = 0;
        for (Map.Entry<Integer, List<Integer>> entry : indices.entrySet()) {
            int size = entry.getValue().size();
            commonPairs += size * (size - 1) / 2;
        }
        
        return totalPairs - commonPairs;
    }

    public static void main(String[] args) {
        List<Map.Entry<Integer, Integer>> arr = new ArrayList<>();
        arr.add(new SimpleEntry<>(2, 5));
        arr.add(new SimpleEntry<>(1, 6));
        arr.add(new SimpleEntry<>(3, 2));
        arr.add(new SimpleEntry<>(4, 2));
        arr.add(new SimpleEntry<>(5, 1));
        arr.add(new SimpleEntry<>(6, 3));
        
        System.out.println("Count of non-common pairs: " + nonCommonPairs(arr));
    }
}

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.AbstractMap.SimpleEntry;

public class NonCommonPairs {
    public static int nonCommonPairs(List<Map.Entry<Integer, Integer>> arr) {
        Map<Integer, List<Integer>> indices = new HashMap<>();
        int totalPairs = arr.size() * (arr.size() - 1) / 2;
        
        for (int idx = 0; idx < arr.size(); ++idx) {
            Map.Entry<Integer, Integer> pair = arr.get(idx);
            for (int num : new int[]{pair.getKey(), pair.getValue()}) {
                indices.computeIfAbsent(num, k -> new ArrayList<>()).add(idx);
            }
        }

        int commonPairs = 0;
        for (Map.Entry<Integer, List<Integer>> entry : indices.entrySet()) {
            int size = entry.getValue().size();
            commonPairs += size * (size - 1) / 2;
        }
        
        return totalPairs - commonPairs;
    }

    public static void main(String[] args) {
        List<Map.Entry<Integer, Integer>> arr = new ArrayList<>();
        arr.add(new SimpleEntry<>(2, 5));
        arr.add(new SimpleEntry<>(1, 6));
        arr.add(new SimpleEntry<>(3, 2));
        arr.add(new SimpleEntry<>(4, 2));
        arr.add(new SimpleEntry<>(5, 1));
        arr.add(new SimpleEntry<>(6, 3));
        
        System.out.println("Count of non-common pairs: " + nonCommonPairs(arr));
    }
}

import java.util.ArrayList; import java.util.HashMap; import java.util.List; import java.util.Map; public class NonCommonPairs { public static int nonCommonPairs(List<Map.Entry<Integer, Integer>> arr) { Map<Integer, List<Integer>> indices = new HashMap<>(); int totalPairs = arr.size() * (arr.size() - 1) / 2; // (The rest of the code will be added in subsequent steps) return totalPairs; // Temporary return to avoid compilation error } public static void main(String[] args) { // Code for testing will be added later } }

Introduction

Task Statement

Understanding the Solution: The Idea

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Solution Building: Step 1

Solution Building: Step 2

Solution Building: Step 3

Lesson Summary