二分查找

数字在排序数组中出现的次数

统计一个数字在排序数组中出现的次数，例如输入排序数组{0, 1, 2, 3, 4, 4, 4, 4, 5}和数字4，由于4在这个数组中出现了4次，因此输出4。（出自：剑指offer）

既然输入的数组是排序的，那么很自然地就能想到用二分查找算法。

#include <iostream>

int getFirstK( int *data, int length, int k, int start, int end )
{
    if ( start > end )
    {
        return -1;
    }
    int midIndex = ( end + start ) / 2;
    int midValue = data[ midIndex ];
    if ( midValue == k )
    {
        if ( ( midIndex > 0 && data[ midIndex - 1 ] != k ) || midIndex == 0 )
        {
            return midIndex;
        }
        else
        {
            end = midIndex - 1;
        }
    }
    else if ( midValue > k )
    {
        end = midIndex - 1;
    }
    else
    {
        start = midIndex + 1;
    }
    return getFirstK( data, length, k, start, end );
}

int getLastK( int *data, int length, int k, int start, int end )
{
    if ( start > end )
    {
        return -1;
    }
    int midIndex = ( end + start ) / 2;
    int midValue = data[ midIndex ];
    if ( midValue == k )
    {
        if ( ( midIndex > 0 && data[ midIndex + 1 ] != k ) || midIndex == length - 1 )
        {
            return midIndex;
        }
        else
        {
            start = midIndex + 1;
        }
    }
    else if ( midValue > k )
    {
        end = midIndex - 1;
    }
    else
    {
        start = midIndex + 1;
    }
    return getLastK( data, length, k, start, end );
}

int getNumbersOfK( int *data, int length, int k )
{
    int num = 0;
    if ( data != NULL || length > 0 )
    {
        int first = getFirstK( data, length, k, 0, length - 1 );
        int last = getLastK( data, length, k, 0, length - 1 );
        if ( first > -1 && last > -1 )
        {
            num = last - first + 1;
        }
    }
    return num;
}

int main()
{
    int data[] = {0, 1, 2, 3, 4, 4, 4, 4, 5};
    int ret4 = getNumbersOfK( data, 9, 4);
    std::cout << "4 appear " << ret4 << " times in data." << std::endl;
    int ret6 = getNumbersOfK( data, 9, 6 );
    std::cout << "6 appear " << ret6 << " times in data." << std::endl;

    return 0;
}