문제 설명
데이터 스트림에서 정수를 읽는다고 가정합니다. 효율적인 방법으로 읽은 요소의 중앙값 찾기
스트림의 첫 번째 요소를 읽은 후 - 10 -> 중앙값 - 10
스트림의 두 번째 요소를 읽은 후 - 10, 20 -> 중앙값 - 15
스트림의 세 번째 요소 - 10, 20, 30 -> 중앙값 - 20 등을 읽은 후...
알고리즘
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
예
#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;
} 출력
위 프로그램을 컴파일하고 실행할 때. 다음 출력을 생성합니다 -
Result: 10 15 20