ListSet_对半搜索的递归算法

对半搜索是一种二分搜索, 将表划分为长度几乎相等的两个子表.

共有函数Search()调用私有函数BSearch(). 而后递归调用BSearch()函数实现对有序表的对半搜索.

mid, left, right均为元素下标, 如果当前表不为空, 则令x与l[mid]比较. 若两者相等, 则搜索成功. 若前者小于后者, 则继续查找左半部分, 否

则查找右半部分. 下标范围分别为[left, mid - 1], [mid + 1, right]. 如果当前搜索表为空表, 搜索失败返回NotPresent.

实现代码:

#include "iostream"
#include "cstdio"
#include "cstring"
#include "algorithm"
#include "assert.h"
using namespace std;
const int MAXN = 9999;

enum ResultCode
{
    Underflow, Overflow, Success, Duplicate, NotPresent
};
template <class T>
class DynamicSet
{
public:
	virtual ResultCode Search(T &x) const = 0; // 表中搜索与x关键字相同的元素, 若存在则赋值给x并且返回Success, 否则返回NotPresent
	virtual ResultCode Insert(T &x) = 0; // 表中搜索与x关键字相同的元素, 若存在该元素, 赋值给x返回Duplicate, 若表已满返回Overflow, 若表未满返回Success
	virtual ResultCode Remove(T &x) = 0; // 表中搜索与x关键字相同的元素, 若存在该元素, 赋值给x返回Success, 否则返回NotPresent
	virtual bool IsEmpty() const = 0; // 集合为空返回true
	virtual bool IsFull() const = 0; // 集合为满返回true
	/* data */
};

template <class T>
class ListSet: public DynamicSet<T>
{
public:
	ListSet( int mSize );
	~ListSet() { delete []l; }
	bool IsEmpty() const { return n == 0; }
	bool IsFull() const { return n == maxSize; }
	ResultCode Search(T &x) const;
	ResultCode Insert(T &x);
	ResultCode Remove(T &x);
	void Print();
private:
	T *l;
	int maxSize, n;
	int BSearch(T &x, int left, int right) const;
	/* data */
};

template <class T>
void ListSet<T>::Print()
{
	for(int i = 0; i < n; ++i)
		cout << l[i] << "\t";
	cout << endl;
}

template <class T>
ListSet<T>::ListSet(int mSize)
{
	maxSize = mSize;
	l = new T[maxSize];
	n = 0;
}

template <class T>
ResultCode ListSet<T>::Insert(T &x)
{
	assert(!IsFull());
	l[n++] = x;
	l[n] = MAXN;
	return Success;
}

template <class T>
ResultCode ListSet<T>::Remove(T &x)
{

}

template <class T>
ResultCode ListSet<T>::Search(T &x) const
{
	int i = BSearch(x, 0, n - 1);
	if(i == -1) return NotPresent;
	x = l[i];
	return Success;
}

template <class T>
int ListSet<T>::BSearch(T &x, int left, int right) const
{
	if(left <= right) {
		int mid = (left + right) / 2;
		if(x < l[mid]) return BSearch(x, left, mid - 1);
		else if(x > l[mid]) return BSearch(x, mid + 1, right);
		else return mid;
	}
	return -1;
}

int main(int argc, char const *argv[])
{
	ListSet<int> ls(20);
	int x = 21; ls.Insert(x);
	x = 30; ls.Insert(x);
 	x = 36; ls.Insert(x);
	x = 41; ls.Insert(x);
 	x = 52; ls.Insert(x);
	x = 54; ls.Insert(x);
	x = 66; ls.Insert(x);
	x = 72; ls.Insert(x);
	x = 83; ls.Insert(x);
	x = 97; ls.Insert(x);
	ls.Print();
	x = 66;
	if(ls.Search(x) == Success) cout << "Found " << x << endl;
	else cout << "Not Found " << x << endl;
	return 0;
}

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