Create k-ary_heap

k-ary_heap

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+// C++ program to demonstrate all operations of k-ary Heap 
+// Time complexity of build heap is O(n)
+#include<bits/stdc++.h> 
+
+using namespace std; 
+
+// function to heapify (or restore the max- heap 
+// property). This is used to build a k-ary heap 
+// and in extractMin() 
+// att[] -- Array that stores heap 
+// len   -- Size of array 
+// index -- index of element to be restored 
+//          (or heapified) 
+void restoreDown(int arr[], int len, int index, 
+                                        int k) 
+{ 
+    // child array to store indexes of all 
+    // the children of given node 
+    int child[k+1]; 
+
+    while (1) 
+    { 
+        // child[i]=-1 if the node is a leaf 
+        // children (no children) 
+        for (int i=1; i<=k; i++) 
+            child[i] = ((k*index + i) < len) ? 
+                    (k*index + i) : -1; 
+
+        // max_child stores the maximum child and 
+        // max_child_index holds its index 
+        int max_child = -1, max_child_index ; 
+
+        // loop to find the maximum of all 
+        // the children of a given node 
+        for (int i=1; i<=k; i++) 
+        { 
+            if (child[i] != -1 && 
+                arr[child[i]] > max_child) 
+            { 
+                max_child_index = child[i]; 
+                max_child = arr[child[i]]; 
+            } 
+        } 
+
+        // leaf node 
+        if (max_child == -1) 
+            break; 
+
+        // swap only if the key of max_child_index 
+        // is greater than the key of node 
+        if (arr[index] < arr[max_child_index]) 
+            swap(arr[index], arr[max_child_index]); 
+
+        index = max_child_index; 
+    } 
+} 
+
+// Restores a given node up in the heap. This is used 
+// in decreaseKey() and insert() 
+void restoreUp(int arr[], int index, int k) 
+{ 
+    // parent stores the index of the parent variable 
+    // of the node 
+    int parent = (index-1)/k; 
+
+    // Loop should only run till root node in case the 
+    // element inserted is the maximum restore up will 
+    // send it to the root node 
+    while (parent>=0) 
+    { 
+        if (arr[index] > arr[parent]) 
+        { 
+            swap(arr[index], arr[parent]); 
+            index = parent; 
+            parent = (index -1)/k; 
+        } 
+
+        // node has been restored at the correct position 
+        else
+            break; 
+    } 
+} 
+
+// Function to build a heap of arr[0..n-1] and alue of k. 
+void buildHeap(int arr[], int n, int k) 
+{ 
+    // Heapify all internal nodes starting from last 
+    // non-leaf node all the way upto the root node 
+    // and calling restore down on each 
+    for (int i= (n-1)/k; i>=0; i--) 
+        restoreDown(arr, n, i, k); 
+} 
+
+// Function to insert a value in a heap. Parameters are 
+// the array, size of heap, value k and the element to 
+// be inserted 
+void insert(int arr[], int* n, int k, int elem) 
+{ 
+    // Put the new element in the last position 
+    arr[*n] = elem; 
+
+    // Increase heap size by 1 
+    *n = *n+1; 
+
+    // Call restoreUp on the last index 
+    restoreUp(arr, *n-1, k); 
+} 
+
+// Function that returns the key of root node of 
+// the heap and then restores the heap property 
+// of the remaining nodes 
+int extractMax(int arr[], int* n, int k) 
+{ 
+    // Stores the key of root node to be returned 
+    int max = arr[0]; 
+
+    // Copy the last node's key to the root node 
+    arr[0] = arr[*n-1]; 
+
+    // Decrease heap size by 1 
+    *n = *n-1; 
+
+    // Call restoreDown on the root node to restore 
+    // it to the correct position in the heap 
+    restoreDown(arr, *n, 0, k); 
+
+    return max; 
+} 
+
+// Driver program 
+int main() 
+{ 
+    const int capacity = 100; 
+    int arr[capacity] = {4, 5, 6, 7, 8, 9, 10}; 
+    int n = 7; 
+    int k = 3; 
+
+    buildHeap(arr, n, k); 
+
+    printf("Built Heap : \n"); 
+    for (int i=0; i<n; i++) 
+        printf("%d ", arr[i]); 
+
+    int element = 3; 
+    insert(arr, &n, k, element); 
+
+    printf("\n\nHeap after insertion of %d: \n", 
+            element); 
+    for (int i=0; i<n; i++) 
+        printf("%d ", arr[i]); 
+
+    printf("\n\nExtracted max is %d", 
+                   extractMax(arr, &n, k)); 
+
+    printf("\n\nHeap after extract max: \n"); 
+    for (int i=0; i<n; i++) 
+        printf("%d ", arr[i]); 
+
+    return 0; 
+}