二分查找有序数组

　　昨天百度面试，问了这样一道题：

　　对于一个有序字符串数组，用二分法查找某一字符串是否存在于该字符串数组中。函数原型为：

bool BinarySearch(const vector<string>& array, const string& target)

　　注意这里的有序指的是字典序，如字符串数组 a, ab, ac, bc, cd, d 就是有序字符串数组，而 a, b, ab 及 a, ac, ab 都不是有序字符串数组。

　   对于这道题，一种很笨的做法是：

#include <iostream>
#include <vector>
#include <string>
#include <map>
#include <algorithm>
using namespace std;

bool BinarySearch(const vector<string>& array, const string& target);
int getUpperBound(const vector<string>& array, const string& target, int index, int low, int high);
int getLowerBound(const vector<string>& array, const string& target, int index, int low, int high);

int main() 
{
    vector<string> vec{ "ab", "abc", "abc", "abcd", "bcd", "bcde" };
    string target{ "abcd" };
    
    bool ret = BinarySearch(vec, target);

    return 0;
}

bool BinarySearch(const vector<string>& array, const string& target)
{
    if (array.size() == 0 && target.length() == 0)
        return false;
    else if (array.size() == 0 && target.length() != 0)
        return false;
    else if (array.size() != 0 && target.length() == 0)
    {
        if (array[0].empty())
            return true;
        else
            return false;
    }
    else
    {
        int len = target.length();
        int low = 0, high = array.size() - 1;
        for (int i = 0; i < len; i++)
        {
            int tmpLow = getLowerBound(array, target, i, low, high);
            int tmpHigh = getUpperBound(array, target, i, low, high);
            low = tmpLow;
            high = tmpHigh;
            if (low == high)
                break;
        }
    
        if (array[low] == target)
            return true;
    }

    return false;
}

int getUpperBound(const vector<string>& array, const string& target, int index, int low, int high)
{
    if (low >= high)
        return low;
    
    while (low < high)
    {
        int mid = (low + high) / 2 + 1;
        if ((index < array[mid].size() && array[mid][index] == target[index]) || index > array[mid].size())
            low = mid;
        else
            high = mid - 1;
    }

    return high;
}


int getLowerBound(const vector<string>& array, const string& target, int index, int low, int high)
{
    if (low >= high)
        return low;

    while (low < high)
    {
        int mid = (low + high) / 2;
        if (index < array[mid].size() && array[mid][index] == target[index])
            high = mid;
        else if (index > array[mid].size())
            low = mid + 1;
        else
            low = mid + 1;
    }
    
    return low;
}

　　而另一种方法则要简洁得多：

#include <iostream>
#include <vector>
#include <string>
using namespace std;

bool BinarySearch(const vector<string>& array, const string& target);

int main() 
{
    vector<string> vec{ "ab", "abc", "abcd", "bcd", "bcde" };
    string target{ "abcd" };
    
    bool ret = BinarySearch(vec, target);

    return 0;
}

bool BinarySearch(const vector<string>& array, const string& target)
{
    if (array.size() == 0 && target.length() == 0)
        return false;
    else if (array.size() == 0 && target.length() != 0)
        return false;
    else if (array.size() != 0 && target.length() == 0)    // array也是可能存在空字符串的，但该空字符串肯定存在于它的第一个元素
    {
        if (array[0].empty())
            return true;
        else
            return false;
    }
    else
    {
        int low = 0, high = array.size() - 1;
        while (low <= high)
        {
            int mid = low + (high - low) / 2;
            if (target.compare(array[mid]) == 0)
                return true;
            else if (target.compare(array[mid]) > 0)
                low = mid + 1;
            else
                high = mid - 1;
        }
    }

    return false;
}