समस्या कथन
यह देखते हुए कि पूर्णांक डेटा स्ट्रीम से पढ़े जाते हैं। प्रभावी तरीके से इसके लिए पढ़े जाने वाले तत्वों का माध्यिका खोजें
धारा का पहला तत्व पढ़ने के बाद - 10 -> माध्यिका - 10
धारा का दूसरा तत्व पढ़ने के बाद - 10, 20 -> माध्यिका - 15
धारा का तीसरा तत्व पढ़ने के बाद - 10, 20, 30 -> माध्यिका - 20, इसी तरह...
एल्गोरिदम
1. Use a max heap on left side to represent elements that are less than effective median, and a min heap on right side to represent elements that are greater than effective median 2. After processing an incoming element, the number of elements in heaps differ utmost by 1 element 3. When both heaps contain same number of elements, we pick average of heaps root data as effective median 4. When the heaps are not balanced, we select effective median from the root of heap containing more elements
उदाहरण
#include <iostream>
using namespace std;
#define MAX_HEAP_SIZE (128)
#define ARRAY_SIZE(a) sizeof(a)/sizeof(a[0])
inline void Exch(int &a, int &b){
int aux = a;
a = b;
b = aux;
}
bool Greater(int a, int b){
return a > b;
}
bool Smaller(int a, int b){
return a < b;
}
int Average(int a, int b){
return (a + b) / 2;
}
int Signum(int a, int b){
if( a == b ) {
return 0;
}
return a < b ? -1 : 1;
}
class Heap{
public:
Heap(int *b, bool (*c)(int, int)) : A(b), comp(c){
heapSize = -1;
}
virtual ~Heap(){
if( A ) {
delete[] A;
}
}
virtual bool Insert(int e) = 0;
virtual int GetTop() = 0;
virtual int ExtractTop() = 0;
virtual int GetCount() = 0;
protected:
int left(int i){
return 2 * i + 1;
}
int right(int i){
return 2 * (i + 1);
}
int parent(int i){
if( i <= 0 ) {
return -1;
}
return (i - 1)/2;
}
int *A;
bool (*comp)(int, int);
int heapSize;
int top(void){
int max = -1;
if( heapSize >= 0 ) {
max = A[0];
}
return max;
}
int count(){
return heapSize + 1;
}
void heapify(int i){
int p = parent(i);
if( p >= 0 && comp(A[i], A[p]) ) {
Exch(A[i], A[p]);
heapify(p);
}
}
int deleteTop(){
int del = -1;
if( heapSize > -1) {
del = A[0];
Exch(A[0], A[heapSize]);
heapSize--;
heapify(parent(heapSize+1));
}
return del;
}
bool insertHelper(int key){
bool ret = false;
if( heapSize < MAX_HEAP_SIZE ) {
ret = true;
heapSize++;
A[heapSize] = key;
heapify(heapSize);
}
return ret;
}
};
class MaxHeap : public Heap{
private:
public:
MaxHeap() : Heap(new int[MAX_HEAP_SIZE], &Greater) { }
~MaxHeap() { }
int GetTop(){
return top();
}
int ExtractTop(){
return deleteTop();
}
int GetCount(){
return count();
}
bool Insert(int key){
return insertHelper(key);
}
};
class MinHeap : public Heap{
private:
public:
MinHeap() : Heap(new int[MAX_HEAP_SIZE], &Smaller) { }
~MinHeap() { }
int GetTop(){
return top();
}
int ExtractTop(){
return deleteTop();
}
int GetCount(){
return count();
}
bool Insert(int key){
return insertHelper(key);
}
};
int getMedian(int e, int &m, Heap &l, Heap &r){
int sig = Signum(l.GetCount(), r.GetCount());
switch(sig){
case 1:
if( e < m ) {
r.Insert(l.ExtractTop());
l.Insert(e);
} else {
r.Insert(e);
}
m = Average(l.GetTop(), r.GetTop());
break;
case 0:
if( e < m ) {
l.Insert(e);
m = l.GetTop();
} else {
r.Insert(e);
m = r.GetTop();
}
break;
case -1:
if( e < m ) {
l.Insert(e);
} else {
l.Insert(r.ExtractTop());
r.Insert(e);
}
m = Average(l.GetTop(), r.GetTop());
break;
}
return m;
}
void printMedian(int A[], int size){
int m = 0;
Heap *left = new MaxHeap();
Heap *right = new MinHeap();
for(int i = 0; i < size; ++i) {
m = getMedian(A[i], m, *left, *right);
cout << m << endl;
}
delete left;
delete right;
}
// Driver code
int main(){
int A[] = {10, 20, 30};
int size = ARRAY_SIZE(A);
cout "Result:\n";
printMedian(A, size);
return 0;
} आउटपुट
जब आप उपरोक्त प्रोग्राम को संकलित और निष्पादित करते हैं। यह निम्न आउटपुट उत्पन्न करता है -
Result: 10 15 20