查找算法四：二分查找（折半查找）

1.原理简介

要求线性表必须采用顺序存储结构，而且表中元素按关键字有序排列。最坏情况下，关键词比较次数为 log(n+1) ，时间复杂度：O(logn)

2.C++代码实现

（1）版本1

int BinarySearch1(int a[], int value, int n) //二分查找（折半查找），

{

    int low, high, mid;

    low = 0;

    high = n-1;

    while(low<=high)

    {

        mid = (low+high)/2;

        if(a[mid]==value)

            return mid;

        if(a[mid]>value)

            high = mid-1;

        if(a[mid]<value)

            low = mid+1;

    }

    return -1;

}

（2）递归版本

int BinarySearch2(int a[], int value, int low, int high) //二分查找，

{

    int mid = low+(high-low)/2;

    if(a[mid]==value)

        return mid;

    if(a[mid]>value)

        return BinarySearch2(a, value, low, mid-1);

    if(a[mid]<value)

        return BinarySearch2(a, value, mid+1, high);

}

（3）建立顺序变查找

#define MAXLEN 50

typedef struct

{

      int data[MAXLEN];

      int len;

}Seqlist;

int main()

{

      int i, n, x，low, high, mid;

      Seqlist *L;

      x = 3;

      L = (Seqlist*)malloc(sizeof(Seqlist));

      L->len = 0;

      cout << "Input length of List:";

      cin >> n;

      low = 1;high = n;L->len = n;

      cout << "Input element of List:" << endl;

      for (i = 1; i <= L->len; i++)

           cin >> L->data[i];

      for (i = 1; i <= L->len; i++)

           cout << L->data[i] << "  ";

      cout << endl;

      while (low <= high)

      {

           mid = (low + high) / 2;

           if (L->data[mid] == x)

           {

                 cout << mid;

                 return mid;

           }

           else

           {

                 if (L->data[mid] > x)

                      high = mid - 1;

                 if (L->data[mid] < x)

                      low = mid + 1;

           }

      }

      return -1;

}