《Cracking the Coding Interview》——第18章：难题——题目9

2014-04-29 04:18

题目：有一连串的数被读入，设计一个数据结构，能随时返回当前所有数的中位数。

解法：用一个大顶堆，一个小顶堆将数分成数量最接近的两份，就能轻松得到中位数了。

代码：

  1 // 18.9 A stream of integers are passed to you, you have to tell me the median as they keep coming in.

  2 #include <climits>

  3 #include <iostream>

  4 #include <vector>

  5 #include <queue>

  6 using namespace std;

  7 

  8 template <class T>

  9 struct LessFunctor

 10 {

 11     bool operator() (const T &x, const T &y)

 12     {

 13         return x < y;

 14     }

 15 };

 16 

 17 template <class T>

 18 struct GreaterFunctor

 19 {

 20     bool operator() (const T &x, const T &y)

 21     {

 22         return x > y;

 23     }

 24 };

 25 

 26 template <class T>

 27 class MedianArray {

 28 public:

 29     MedianArray() {

 30         n_small = 0;

 31         n_great = 0;

 32     };

 33     

 34     void push(const T& val) {

 35         if (n_great == 0) {

 36             greater_heap.push(val);

 37             ++n_great;

 38             return;

 39         }

 40         

 41         if (n_great > n_small) {

 42             smaller_heap.push(val);

 43             ++n_small;

 44         } else {

 45             greater_heap.push(val);

 46             ++n_great;

 47         }

 48         

 49         if (greater_heap.top() < smaller_heap.top()) {

 50             T tmp;

 51             

 52             tmp = greater_heap.top();

 53             greater_heap.pop();

 54             greater_heap.push(smaller_heap.top());

 55             smaller_heap.pop();

 56             smaller_heap.push(tmp);

 57         }

 58     };

 59     

 60     T median() {

 61         if (n_great == 0) {

 62             return INT_MIN;

 63         } else if (n_great > n_small) {

 64             return greater_heap.top();

 65         } else {

 66             return (smaller_heap.top() + greater_heap.top()) / 2;

 67         }

 68     };

 69     

 70     ~MedianArray() {

 71         n_small = 0;

 72         n_great = 0;

 73         while (!greater_heap.empty()) {

 74             greater_heap.pop();

 75         }

 76         while (!smaller_heap.empty()) {

 77             smaller_heap.pop();

 78         }

 79     };

 80 private:

 81     int n_small;

 82 

 83     // greater elements are stored in here.

 84     priority_queue<T, vector<T>, GreaterFunctor<T> > greater_heap;

 85 

 86     int n_great;

 87 

 88     // smaller elements are stored in here.

 89     priority_queue<T, vector<T>, LessFunctor<T> > smaller_heap;

 90 };

 91 

 92 int main()

 93 {

 94     MedianArray<int> ma;

 95     int val;

 96     

 97     while (cin >> val) {

 98         ma.push(val);

 99         cout << ma.median() << endl;

100     }

101     

102     return 0;

103 }