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数据结构基础(2) --顺序查找 & 二分查找

顺序查找

适用范围:

没有进行排序的数据序列

缺点:

速度非常慢, 效率为O(N)

//实现
template <typename Type>
Type *sequenceSearch(Type *begin, Type *end, const Type &searchValue)
throw(std::range_error)
{
    if ((begin == end) || (begin == NULL) || (end == NULL))
        throw std::range_error("pointer unavailable");

    for (Type *index = begin; index < end; ++index)
    {
        if (*index == searchValue)
            return index;
    }

    return end;
}

template <typename Type>
Type *sequenceSearch(Type *array, int length, const Type &searchValue)
throw(std::range_error)
{
    return sequenceSearch(array, array+length, searchValue);
}

迭代二分查找

应用范围:

数据必须首先排序,才能应用二分查找;效率为(logN)

算法思想:

譬如数组{1, 2, 3, 4, 5, 6, 7, 8, 9},查找元素6,用二分查找的算法执行的话,其顺序为:

    1.第一步查找中间元素,即5,由于5<6,则6必然在5之后的数组元素中,那么就在{6, 7, 8, 9}中查找,

    2.寻找{6, 7, 8, 9}的中位数,为7,7>6,则6应该在7左边的数组元素中,那么只剩下6,即找到了。

    二分查找算法就是不断将数组进行对半分割,每次拿中间元素和目标元素进行比较

//实现:迭代二分
template <typename Type>
Type *binarySearch(Type *begin, Type *end, const Type &searchValue)
throw(std::range_error)
{
    if ((begin == end) || (begin == NULL) || (end == NULL))
        throw std::range_error("pointer unavailable");

    /**注意:此处high为end-1,并不是end
        因为在后续的查找过程中,可能会如下操作 (*high), 或等价的操作
        此时应该访问的是最后一个元素, 必须注意不能对数组进行越界访问!
    */
    Type *low = begin, *high = end-1;
    while (low <= high)
    {
        //计算中间元素
        Type *mid = low + (high-low)/2;
        //如果中间元素的值==要找的数值, 则直接返回
        if (*mid == searchValue)
            return mid;
        //如果要找的数比中间元素大, 则在数组的后半部分查找
        else if (searchValue > *mid)
            low = mid + 1;
        //如果要找的数比中间元素小, 则在数组的前半部分查找
        else
            high = mid - 1;
    }

    return end;
}

template <typename Type>
Type *binarySearch(Type *array, int length, const Type &searchValue)
throw(std::range_error)
{
    return binarySearch(array, array+length, searchValue);
}

递归简介

递归就是递归...(自己调用自己),递归的是神,迭代的是人;

 

递归与非递归的比较

//递归求解斐波那契数列
unsigned long ficonacciRecursion(int n)
{
    if (n == 1 || n == 2)
        return 1;
    else
        return ficonacciRecursion(n-1) + ficonacciRecursion(n-2);
}
//非递归求解斐波那契数列
unsigned long ficonacciLoop(int n)
{
    if (n == 1 || n == 2)
        return 1;

    unsigned long  first = 1, second = 1;
    unsigned long  ans = first + second;
    for (int i = 3; i <= n; ++i)
    {
        ans = first + second;
        first = second;
        second = ans;
    }

    return ans;
}

递归二分查找

算法思想如同迭代二分查找;

//实现
template <typename Type>
Type *binarySearchByRecursion(Type *front, Type *last, const Type &searchValue)
throw(std::range_error)
{
    if ((front == NULL) || (last == NULL))
        throw std::range_error("pointer unavailable");

    if (front <= last)
    {
        Type *mid = front + (last-front)/2;
        if (*mid == searchValue)
            return mid;
        else if (searchValue > *mid)
            return binarySearchByRecursion(mid+1, last, searchValue);
        else
            return binarySearchByRecursion(front, mid-1, searchValue);
    }

    return NULL;
}

template <typename Type>
int binarySearchByRecursion(Type *array, int left, int right, const Type &searchValue)
throw (std::range_error)
{
    if (array == NULL)
        throw std::range_error("pointer unavailable");

    if (left <= right)
    {
        int mid = left + (right-left)/2;
        if (array[mid] == searchValue)
            return mid;
        else if (searchValue < array[mid])
            return binarySearchByRecursion(array, left, mid-1, searchValue);
        else
            return binarySearchByRecursion(array, mid+1, right, searchValue);
    }

    return -1;
}

小结:

其实C++ 的STL已经实现好了std::binary_search(),在用的时候我们只需调用即可, 但是二分算法的思想还是非常重要的, 在求解一些较为复杂的问题时, 我们时常能够看到二分的身影.

数据结构基础(2) --顺序查找 & 二分查找