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法律研究C++ 中连续整数流中的中位数（连续的整数）
问题陈述
假设从数据流中读取整数。以有效方式查找迄今为止读取的元素中位数
在读取流的第 1 个元素 - 10 -> 中位数 - 10
在读取流的第 2 个元素 - 10, 20 -> 中位数 - 15
在读取流的第 3 个元素 - 10, 20, 30 -> 中位数 - 20，依此类推...
算法
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
范例
#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;
}输出
当你编译并执行上述程序时它会生成以下输出 −
Result: 10 15 20
更新于：10-Feb-2020
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