🚀 Day 5: Merge Sort & Quick Sort in Java 🎯 Goals for Today

• Understand the Divide and Conquer strategy

• Learn and implement:

  • Merge Sort

  • Quick Sort

• Analyze Time & Space Complexities

• Solve intermediate-level sorting problems

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📘 1. Merge Sort

A stable, divide-and-conquer sorting algorithm.
Time Complexity: O(n log n) in all cases
Space Complexity: O(n) (extra array)

✅ Logic:

• Divide the array into two halves

• Sort each half recursively

• Merge the two sorted halves

🔹 Java Implementation

public class MergeSort {
    public static void mergeSort(int[] arr, int left, int right) {
        if (left < right) {
            int mid = (left + right) / 2;

            // Sort the left and right halves
            mergeSort(arr, left, mid);
            mergeSort(arr, mid + 1, right);

            // Merge them
            merge(arr, left, mid, right);
        }
    }

    public static void merge(int[] arr, int left, int mid, int right) {
        int n1 = mid - left + 1;
        int n2 = right - mid;

        int[] L = new int[n1];
        int[] R = new int[n2];

        for (int i = 0; i < n1; i++) L[i] = arr[left + i];
        for (int j = 0; j < n2; j++) R[j] = arr[mid + 1 + j];

        int i = 0, j = 0, k = left;

        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) arr[k++] = L[i++];
            else arr[k++] = R[j++];
        }

        while (i < n1) arr[k++] = L[i++];
        while (j < n2) arr[k++] = R[j++];
    }
}

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⚡ 2. Quick Sort

Quick and efficient, especially on average cases.
Time Complexity:

• Best/Average: O(n log n)

• Worst: O(n²) (when pivot is worst chosen)
  Space: O(log n) (due to recursive calls)

✅ Logic:

• Choose a pivot

• Partition the array: elements < pivot go left, > pivot go right

• Recursively sort left and right

🔹 Java Implementation

public class QuickSort {
    public static void quickSort(int[] arr, int low, int high) {
        if (low < high) {
            int pi = partition(arr, low, high);

            quickSort(arr, low, pi - 1);
            quickSort(arr, pi + 1, high);
        }
    }

    public static int partition(int[] arr, int low, int high) {
        int pivot = arr[high];
        int i = low - 1; // Index of smaller element

        for (int j = low; j < high; j++) {
            if (arr[j] < pivot) {
                i++;
                // Swap
                int temp = arr[i];
                arr[i] = arr[j];
                arr[j] = temp;
            }
        }

        // Swap pivot to the right place
        int temp = arr[i + 1];
        arr[i + 1] = arr[high];
        arr[high] = temp;

        return i + 1;
    }
}

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📊 3. Merge Sort vs Quick Sort

Feature	Merge Sort	Quick Sort
Time (Best)	O(n log n)	O(n log n)
Time (Worst)	O(n log n)	O(n²)
Space	O(n)	O(log n)
Stable	✅ Yes	❌ No
In-place	❌ No	✅ Yes
Use Case	Linked lists	Arrays

🧠 4. Practice Problems

Try these problems:

1. ✅ Merge Sorted Array

2. ✅ Sort an Array

3. 🔁 Kth Largest Element in Array – Use Quick Select

4. 🧠 Count Inversions in Array – Use Merge Sort logic

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📚 Homework for Day 5

• Implement Merge Sort and Quick Sort

• Solve 2 LeetCode problems involving sorting or partitioning

• Try to write non-recursive quick sort (advanced)

• Visualize Merge vs Quick: Try https://visualgo.net/en/sorting

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🔜 Coming Up on Day 6:

• Recursion Mastery

• Backtracking intro (Subset, Permutations)

• Understanding call stack and dry runs