數據結構基礎(2) --順序查找 & 二分查找

順序查找

適用範圍:

沒有進行排序的數據序列

缺點:

速度非常慢, 效率爲O(N)

//實現
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

應用範圍:

數據必須首先排序,才能應用二分查找;效率爲(logN)

算法思想:

譬如數組{1， 2， 3， 4， 5， 6， 7， 8， 9}，查找元素6，用二分查找的算法執行的話，其順序爲：

    1.第一步查找中間元素，即5，由於5<6，則6必然在5之後的數組元素中，那麼就在{6， 7， 8， 9}中查找，

    2.尋找{6， 7， 8， 9}的中位數，爲7，7>6，則6應該在7左邊的數組元素中，那麼只剩下6，即找到了。

    二分查找算法就是不斷將數組進行對半分割，每次拿中間元素和目標元素進行比較。

//實現: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:此處high爲end-1,並不是end
        因爲在後續的查找過程中,可能會如下操作 (*high), 或等價的操作
        此時應該訪問的是最後一個元素, 必須注意不能對數組進行越界訪問!
    */
    Type *low = begin, *high = end-1;
    while (low <= high)
    {
        //計算中間元素
        Type *mid = low + (high-low)/2;
        //如果中間元素的值==要找的數值, 則直接返回
        if (*mid == searchValue)
            return mid;
        //如果要找的數比中間元素大, 則在數組的後半部分查找
        else if (searchValue > *mid)
            low = mid + 1;
        //如果要找的數比中間元素小, 則在數組的前半部分查找
        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);
}

遞歸簡介

遞歸就是遞歸...(自己調用自己),遞歸的是神,迭代的是人;

 

遞歸與非遞歸的比較

//遞歸求解斐波那契數列
unsigned long ficonacciRecursion(int n)
{
    if (n == 1 || n == 2)
        return 1;
    else
        return ficonacciRecursion(n-1) + ficonacciRecursion(n-2);
}

//非遞歸求解斐波那契數列
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;
}

遞歸二分查找

算法思想如同迭代二分查找;

//實現
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;
}

小結:

其實C++ 的STL已經實現好了std::binary_search(),在用的時候我們只需調用即可, 但是二分算法的思想還是非常重要的, 在求解一些較爲複雜的問題時, 我們時常能夠看到二分的身影.