排序---归并排序

1.  归并排序

归并排序（Merge sort），是创建在归并操作上的一种有效的排序算法，效率为O(nlogn)。该算法是采用分治法（Divide and Conquer）的一个非常典型的应用，且各层分治递归可以同时进行。【详情见维基百科】

归并排序

分类	排序算法
数据结构	数组
最坏时间复杂度
最优时间复杂度
平均时间复杂度
最坏空间复杂度

2. 归并排序（非递归版）C++ 实现

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

void MergeSort(vector<int> &array){
    int len = array.size();
    vector<int> temp(len);

    for(int seg = 1; seg <= len; seg = 2 * seg){
        // 将array中相邻长度为seg的子序列两两归并到temp
        for(int start = 0; start <= len; start = start + 2 * seg){
            // 确定归并范围 low, mid, high
            int low = start;
            int mid = min(len - 1, start + seg - 1);
            int high = min(len - 1, start + 2 * seg - 1);

            int start1 = low, end1 = mid;
            int start2 = mid+1, end2 = high;
            int idx = low;

            // 将array[low...mid]和array[mid+1...high]归并到temp[low...high]
            while(start1 <= end1 && start2 <= end2)
                temp[idx++] = array[start1] < array[start2]? array[start1++] : array[start2++];
            while(start1 <= end1)
                temp[idx++] = array[start1++];
            while(start2 <= end2)
                temp[idx++] = array[start2++];
        }
        // 将temp赋值给array，从新进行下一轮
        int i = 0;
        for(vector<int>::iterator it = temp.begin(); it != temp.end(); it++){
            array[i++] = *it;
        }
    }
}

bool Check(vector<int> arr){
    bool flag = true;
    for(int i=1; i<arr.size(); i++)
        flag = flag && (arr[i]-arr[i-1] >= 0);
    return flag;
}

int main(int argc, char const *argv[])
{
    vector<int> arr = {5, 9, 0, 1, 3, 6, 4, 8, 2, 7};

    MergeSort(arr);
    for(auto &it : arr)
        cout<<it<<' ';
    cout<<endl;

    // 判断返回结果的正确性
    bool isInOrder = Check(arr);
    if (isInOrder)
        cout<<"true"<<endl;
    else
        cout<<"false"<<endl;
    return 0;
}

3. 使用大量随机数据测试

#include<iostream>
#include<vector>
#include<stdlib.h>
#include<time.h>
using namespace std;

void MergeSort(vector<int> &array) {
    int len = array.size();
    vector<int> temp(len);

    for (int seg = 1; seg < len; seg = 2 * seg) {
        for (int start = 0; start < len; start += 2 * seg) {
            int low = start;
            int mid = min(start + seg - 1, len-1);
            int high = min(start + 2 * seg-1, len-1);

            int i = low, j = mid + 1;
            for(int k = low; k <= high; k++)
                temp[k] = array[k];

            for(int idx = low; idx <= high; idx++){
                if(i > mid)
                    array[idx] = temp[j++];
                else if(j > high)
                    array[idx] = temp[i++];
                else if(temp[i] < temp[j])
                    array[idx] = temp[i++];
                else
                    array[idx] = temp[j++];
            }
        }
    }
}

// 判断array是否有序
bool isOrder(vector<int> &array){
    for(int i = 1; i < array.size(); i++){
        if(array[i] < array[i-1])
            return false;
    }
    return true;
}

// 生成n个介于min，max之间的整型数
vector<int> RAND(int max, int min, int n) {
    vector<int> res;
    srand(time(NULL)); // 注释该行之后，每次生成的随机数都一样
    for(int i = 0; i < n; ++i) {
        int u = (double)rand() / (RAND_MAX + 1) * (max - min) + min;
        res.push_back(u);
    }
    return res;
}

// 使用20000000个介于1,10000之间的数据进行测试
int main(int argc, char const *argv[]) {
    vector<int> a = RAND(1, 10000, 20000000);

    clock_t start = clock();
    MergeSort(a);
    clock_t end   = clock();
    cout << "Time goes: " << (double)(end - start) / CLOCKS_PER_SEC << "sec" << endl;

    bool sorted = isOrder(a);
    cout<<sorted<<endl;
    return 0;
}

运行结果：对2千万随机数据排序耗时13.516sec

Time goes: 13.516sec
1
[Finished in 15.7s]

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