二分查找

一、普通的二分查找算法：

int BS(int a[], int k, int n)
{
    int low = 0;
    int high = n - 1;
    while (low <= high)
    {
        int mid = (high - low) / 2 + low;
        if (a[mid] == k)
            return mid;
        else
            if (a[mid] < k)
                low = mid + 1;
            else
                high = mid - 1;
    }
    return -1;
}
int main()
{
    int a[] = { 1,1, 3, 6, 8, 9, 9, 10 };
    cout << BS(a, 0, 8) << endl;
    system("pause");
    return 0;
}

二、查找关键元素在有序数组中的首次出现位置：

int lowerBoner(int a[], int k,int n)
{
    int low = 0;
    int high = n - 1;
    while (low < high)
    {
        int mid = (high - low) / 2 + low;
        if (a[mid] < k)
            low = mid+1;
        else
            high = mid;
    }
    if (low >= n || a[low] != k)
        return -1;
    else
        return low;
}
int main()
{
    int a[] = { 1,1, 3, 6, 8, 9, 9, 10 };
    cout << lowerBoner(a, 9, 7) << endl;
    system("pause");
    return 0;
}

三、查找关键元素在有序数组中的末次出现位置：

int upperbound(int a[], int k,int n){
    int low = 0;
    int high = n - 1;
    while (low < high){
        int mid = low + (high - low + 1) / 2;
        if (a[mid] > k){
            high = mid - 1;
        }
        else{
            low = mid;
        }
    }
    if (low >= n || a[low] != k){
        return -1;
    }
    else{
        return low;
    }
}

int main()
{
    int a[] = { 1,1, 3, 6, 8, 9, 9, 10 };
    cout << upperbound(a, 1, 8) << endl;
    system("pause");
    return 0;
}