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+/**
+ * @file Min Binary Heap.c
+ * @brief Implementation of a Min Binary Heap using a dynamic array in C.
+ * * A Min Heap is a complete binary tree where the value of each node is less
+ * than or equal to the values of its children. The smallest element is always
+ * at the root. This implementation supports: Insert, Extract Min, Peek Min,
+ * Search, and Display. It uses dynamic memory management to create and destroy
+ * the heap structure.
+ */
+
+#include <limits.h>  // For INT_MAX (used for error checking/sentinel value)
+#include <stdio.h>
+#include <stdlib.h>
+
+// --- STRUCTURE DEFINITION ---
+
+/**
+ * @brief Represents the Min Heap structure.
+ * * The heap is stored in a 0-indexed array where:
+ * Parent(i) = (i - 1) / 2
+ * LeftChild(i) = 2 * i + 1
+ * RightChild(i) = 2 * i + 2
+ */
+typedef struct MinHeap
+{
+    int* arr;      // Pointer to the dynamic array holding the heap elements
+    int size;      // Current number of elements in the heap
+    int capacity;  // Maximum number of elements the array can hold
+} MinHeap;
+
+// --- UTILITY FUNCTIONS ---
+
+/**
+ * @brief Swaps two integer values.
+ */
+void swap(int* a, int* b)
+{
+    int temp = *a;
+    *a = *b;
+    *b = temp;
+}
+
+/**
+ * @brief Calculates the index of the parent node.
+ */
+int parent(int i) { return (i - 1) / 2; }
+
+/**
+ * @brief Calculates the index of the left child.
+ */
+int left_child(int i) { return 2 * i + 1; }
+
+/**
+ * @brief Calculates the index of the right child.
+ */
+int right_child(int i) { return 2 * i + 2; }
+
+// --- HEAP LIFE CYCLE MANAGEMENT ---
+
+/**
+ * @brief Creates a new MinHeap structure with a given capacity.
+ * @param capacity The maximum number of elements the heap can hold.
+ * @return Pointer to the newly created MinHeap.
+ */
+MinHeap* createMinHeap(int capacity)
+{
+    // Allocate memory for the structure itself
+    MinHeap* h = (MinHeap*)malloc(sizeof(MinHeap));
+    if (h == NULL)
+    {
+        perror("Failed to allocate MinHeap structure");
+        exit(EXIT_FAILURE);
+    }
+
+    // Set properties
+    h->capacity = capacity;
+    h->size = 0;
+
+    // Allocate memory for the underlying array
+    h->arr = (int*)malloc(capacity * sizeof(int));
+    if (h->arr == NULL)
+    {
+        perror("Failed to allocate array memory");
+        free(h);  // Clean up the structure memory
+        exit(EXIT_FAILURE);
+    }
+
+    return h;
+}
+
+/**
+ * @brief Frees the memory allocated for the MinHeap.
+ * @param h Pointer to the MinHeap to be destroyed.
+ */
+void destroyMinHeap(MinHeap* h)
+{
+    if (h == NULL)
+        return;
+    free(h->arr);  // Free the dynamic array first
+    free(h);       // Free the structure memory
+    printf("\nMinHeap successfully destroyed. Memory freed.\n");
+}
+
+// --- HEAP PROPERTY MAINTENANCE ---
+
+/**
+ * @brief Corrects the Min Heap property by moving the element at index i DOWN
+ * the tree. This is primarily used after Extract Min. Time Complexity: O(log n)
+ * @param h Pointer to the MinHeap.
+ * @param i The index of the element to heapify down.
+ */
+void heapify_down(MinHeap* h, int i)
+{
+    int l = left_child(i);
+    int r = right_child(i);
+    int smallest = i;  // Assume current node is the smallest
+
+    // Check if left child exists and is smaller than the current smallest
+    if (l < h->size && h->arr[l] < h->arr[smallest])
+    {
+        smallest = l;
+    }
+
+    // Check if right child exists and is smaller than the current smallest
+    if (r < h->size && h->arr[r] < h->arr[smallest])
+    {
+        smallest = r;
+    }
+
+    // If the smallest is not the current node, swap and recursively move down
+    if (smallest != i)
+    {
+        swap(&h->arr[i], &h->arr[smallest]);
+        heapify_down(h, smallest);
+    }
+}
+
+/**
+ * @brief Corrects the Min Heap property by moving the element at index i UP the
+ * tree. This is primarily used after Insert. Time Complexity: O(log n)
+ * @param h Pointer to the MinHeap.
+ * @param i The index of the element to heapify up.
+ */
+void heapify_up(MinHeap* h, int i)
+{
+    // Check if current node is not root AND if element is smaller than its
+    // parent
+    while (i > 0 && h->arr[parent(i)] > h->arr[i])
+    {
+        // Swap the current element with its parent
+        swap(&h->arr[parent(i)], &h->arr[i]);
+
+        // Move up to the parent's index and repeat
+        i = parent(i);
+    }
+}
+
+// --- CORE HEAP OPERATIONS ---
+
+/**
+ * @brief Inserts a new key into the MinHeap.
+ * Time Complexity: O(log n)
+ * @param h Pointer to the MinHeap.
+ * @param key The value to be inserted.
+ */
+void insert(MinHeap* h, int key)
+{
+    if (h->size == h->capacity)
+    {
+        printf("Error: Heap is full (Capacity: %d). Cannot insert %d.\n",
+               h->capacity, key);
+        return;
+    }
+
+    // 1. Place the new element at the next available spot (end of the array)
+    h->size++;
+    int i = h->size - 1;
+    h->arr[i] = key;
+
+    // 2. Restore the heap property by moving the element up
+    heapify_up(h, i);
+    printf("Inserted %d. Heap size: %d\n", key, h->size);
+}
+
+/**
+ * @brief Removes and returns the minimum element (root) from the MinHeap.
+ * Time Complexity: O(log n)
+ * @param h Pointer to the MinHeap.
+ * @return The minimum element, or INT_MAX if the heap is empty.
+ */
+int extract_min(MinHeap* h)
+{
+    if (h->size <= 0)
+    {
+        printf("Error: Heap is empty. Cannot extract.\n");
+        return INT_MAX;
+    }
+
+    // 1. Store the minimum element (root)
+    int root = h->arr[0];
+
+    // 2. Replace the root with the last element
+    h->arr[0] = h->arr[h->size - 1];
+
+    // 3. Decrease the size
+    h->size--;
+
+    // 4. Restore the heap property by moving the new root down
+    heapify_down(h, 0);
+
+    return root;
+}
+
+/**
+ * @brief Returns the minimum element (root) without removing it.
+ * Time Complexity: O(1)
+ * @param h Pointer to the MinHeap.
+ * @return The minimum element, or INT_MAX if the heap is empty.
+ */
+int peek_min(MinHeap* h)
+{
+    if (h->size <= 0)
+    {
+        printf("Error: Heap is empty.\n");
+        return INT_MAX;
+    }
+    return h->arr[0];  // Simply return the root element
+}
+
+/**
+ * @brief Performs a linear search for a key in the heap.
+ * Time Complexity: O(n)
+ * @param h Pointer to the MinHeap.
+ * @param key The value to search for.
+ * @return The array index of the key if found, or -1 otherwise.
+ */
+int search(MinHeap* h, int key)
+{
+    // Linear search through the underlying array
+    for (int i = 0; i < h->size; i++)
+    {
+        if (h->arr[i] == key)
+        {
+            return i;  // Found at index i
+        }
+    }
+    return -1;  // Not found
+}
+
+/**
+ * @brief Prints all elements of the heap in array order (not tree order).
+ * Time Complexity: O(n)
+ * @param h Pointer to the MinHeap.
+ */
+void display(MinHeap* h)
+{
+    if (h->size == 0)
+    {
+        printf("Heap is empty.\n");
+        return;
+    }
+    printf("Current Heap elements (Array Order, size=%d): ", h->size);
+    for (int i = 0; i < h->size; i++)
+    {
+        printf("%d ", h->arr[i]);
+    }
+    printf("\n");
+}
+
+// --- MAIN FUNCTION FOR DEMONSTRATION ---
+
+int main()
+{
+    // Define the initial capacity
+    int capacity = 10;
+    MinHeap* heap = createMinHeap(capacity);
+
+    printf("--- Min Binary Heap Demonstration ---\n");
+    printf("1. Initializing Heap with Capacity: %d\n", capacity);
+
+    // 2. Insert Operations
+    printf("\n2. Inserting elements: 10, 5, 20, 2, 4, 8\n");
+    insert(heap, 10);
+    insert(heap, 5);
+    insert(heap, 20);
+    insert(heap, 2);
+    insert(heap, 4);
+    insert(heap, 8);
+    display(heap);
+    // Expected Array Order: [2, 4, 8, 10, 5, 20] (Min Heap Property satisfied)
+
+    // 3. Peek Min Operation (O(1))
+    printf("\n3. Peek Min (O(1)): %d\n", peek_min(heap));
+    display(heap);
+
+    // 4. Extract Min Operations (O(log n))
+    int min1 = extract_min(heap);
+    printf("\n4. Extracted Min (O(log n)): %d\n", min1);
+    display(heap);
+
+    int min2 = extract_min(heap);
+    printf("Extracted Min: %d\n", min2);
+    display(heap);
+
+    // 5. Search Operation (O(n))
+    int search_val = 10;
+    int index = search(heap, search_val);
+    if (index != -1)
+    {
+        printf("5. Search: Value %d found at array index %d.\n", search_val,
+               index);
+    }
+    else
+    {
+        printf("5. Search: Value %d not found.\n", search_val);
+    }
+
+    search_val = 99;
+    index = search(heap, search_val);
+    if (index != -1)
+    {
+        printf("5. Search: Value %d found at array index %d.\n", search_val,
+               index);
+    }
+    else
+    {
+        printf("5. Search: Value %d not found.\n", search_val);
+    }
+
+    // 6. Final cleanup (Crucial for memory management)
+    destroyMinHeap(heap);
+
+    return 0;
+}