Solution via MaxHeap in C and Complexity Analysis

• ``````#define PARENT(x) x
``````

#define LCHILD(x) 2 * x + 1
#define RCHILD(x) 2 * x + 2

typedef struct node {

``````int data ;
``````

} node ;

typedef struct maxHeap {

``````int size ;
node *elem ;
``````

} maxHeap ;

maxHeap initMinHeap(int size) {

``````maxHeap hp ;
hp.size = 0 ;
return hp ;
``````

}

void swap1(node *n1, node *n2) {

``````node temp = *n1 ;
*n1 = *n2 ;
*n2 = temp ;
``````

}

void heapify(maxHeap *hp, int i) {

``````int largest = (LCHILD(i) < hp->size && hp->elem[LCHILD(i)].data > hp->elem[i].data) ? LCHILD(i) : i ;
if(RCHILD(i) < hp->size && hp->elem[RCHILD(i)].data > hp->elem[largest].data) {
largest = RCHILD(i) ;
}
if(largest != i) {
swap1(&(hp->elem[i]), &(hp->elem[largest])) ;
heapify(hp, largest) ;
}
``````

}

void buildMaxHeap(maxHeap *hp, int *arr, int size) {
int i ;

``````// Insertion into the heap without violating the shape property
for(i = 0; i < size; i++) {
if(hp->size) {
hp->elem = (node*)realloc(hp->elem, (hp->size + 1) * sizeof(node)) ;
} else {
hp->elem =(node*) malloc(sizeof(node)) ;
}
node nd ;
nd.data = arr[i] ;
hp->elem[(hp->size)++] = nd ;
}

// Making sure that heap property is also satisfied
for(i = (hp->size - 1) / 2; i >= 0; i--) {
heapify(hp, i) ;
}
``````

}

int findKthLargest(int* nums, int numsSize, int k) {

``````maxHeap hp=initMinHeap(numsSize);
buildMaxHeap(&hp,nums,numsSize);
for (int i = 0; i < k-1; i++) {
//cout<<"largest:"<<hp.elem[0].data<<endl;
swap1(&hp.elem[0], &hp.elem[hp.size-1]);
hp.size--;
// Making sure that heap property is also satisfied
for(int j = (hp.size - 1) / 2; j >= 0; j--) {
heapify(&hp, j) ;
}
}
return hp.elem[0].data;
``````

}

``````    Complexity Analysis :

finding the largest element in a heap is O(1)
Heaplify Complexity O(logn)
Building of heap O(n)
[Although the worst case complexity looks like O(nLogn), upper bound of time complexity is O(n).]
Extracting K elements from a heap, and returning the heap of non-extracted elements, would take O(K·log(N)) time.
``````

Thus overall Timecomplexity of this solution :
O(n + klogn)

• your solution will not work in case of duplicate let suppose arr is 0 -1 0 and we want to extract
3rd largest element so your solution will give 0 but ans should be -1

• read the question , it says
"Note that it is the kth largest element in the sorted order, not the kth distinct element."
thanks

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