十大排序算法大总结

排序算法的分类：
1.插入：插入，折半插入，希尔
2.交换：冒泡，快速
3.选择：简单选择，堆
4.归并：归并（不只二路归并）
5.基数：基数 计数

这里提一下归并和快排的区别

归并排序，简单来说就是先将数组不断细分成最小的单位，然后每个单位分别排序，排序完毕后合并，重复以上过程最后就可以得到排序结果。

快速排序，简单来说就是先选定一个基准元素，然后以该基准元素划分数组，再在被划分的部分重复以上过程，最后可以得到排序结果。

两者都是用分治法的思想，不过最后归并排序的合并操作比快速排序的要繁琐。

1.插入排序

void insert_sort()
{
    for (int i = 1; i < n; i ++ )
    {
        int x = a[i];
        int j = i-1;

        while (j >= 0 && x < a[j])
        {
            a[j+1] = a[j];
            j -- ;
        }
        a[j+1] = x;
    }
}

2.选择排序

void select_sort()
{
    for (int i = 0; i < n; i ++ )
    {
        int k = i;
        for (int j = i+1; j < n; j ++ )
        {
            if (a[j] < a[k])
                k = j;
        }
        swap(a[i], a[k]);
    }

}

3.冒泡排序

void bubble_sort()
{
    for (int i = n-1; i >= 1; i -- )
    {
        bool flag = true;
        for (int j = 1; j <= i; j ++ )
            if (a[j-1] > a[j])
            {
                swap(a[j-1], a[j]);
                flag = false;
            }
        if (flag) return;
    }
}

4.希尔排序

void shell_sort()
{
    for (int gap = n >> 1; gap; gap >>= 1)
    {
        for (int i = gap; i < n; i ++ )
        {
            int x = a[i];
            int j;
            for (j = i; j >= gap && a[j-gap] > x; j -= gap)
                a[j] = a[j-gap];
            a[j] = x;
        }
    }
}

5.快速排序（最快）

void quick_sort(int l, int r)
{
    if (l >= r) return ;

    int x = a[l+r>>1], i = l-1, j = r+1;
    while (i < j)
    {
        while (a[++ i] < x);
        while (a[-- j] > x);
        if (i < j) swap(a[i], a[j]);
    }
    quick_sort(l, j),quick_sort(j+1, r);
}

6.归并排序

void merge_sort(int l, int r)
{
    if (l >= r) return;
    int temp[N];
    int mid = l+r>>1;
    merge_sort(l, mid), merge_sort(mid+1, r);
    int k = 0, i = l, j = mid+1;
    while (i <= mid && j <= r)
    {
        if (a[i] < a[j]) temp[k ++ ] = a[i ++ ];
        else temp[k ++ ] = a[j ++ ];

    }
    while (i <= mid) temp[k ++ ] = a[i ++ ];
    while (j <= r) temp[k ++ ] = a[j ++ ];
    for (int i = l, j = 0; i <= r; i ++ , j ++ ) a[i] = temp[j];
}

7.堆排序

（须知此排序为使用了模拟堆，为了使最后一个非叶子节点的编号为n/2，数组编号从1开始）
(https://www.cnblogs.com/wanglei5205/p/8733524.html)

void down(int u)
{
    int t = u;
    if (u<<1 <= n && h[u<<1] < h[t]) t = u<<1;
    if ((u<<1|1) <= n && h[u<<1|1] < h[t]) t = u<<1|1;
    if (u != t)
    {
        swap(h[u], h[t]);
        down(t);
    }
}

int main()
{
    for (int i = 1; i <= n; i ++ ) cin >> h[i];
    for (int i = n/2; i; i -- ) down(i);
    while (true)
    {
        if (!n) break;
        cout << h[1] << ' ';
        h[1] = h[n];
        n -- ;
        down(1);
    }
    return 0;
}

8.基数排序

int maxbit()
{
    int maxv = a[0];
    for (int i = 1; i < n; i ++ )
        if (maxv < a[i])
            maxv = a[i];
    int cnt = 1;
    while (maxv >= 10) maxv /= 10, cnt ++ ;

    return cnt;
}
void radixsort()
{
    int t = maxbit();
    int radix = 1;

    for (int i = 1; i <= t; i ++ )
    {
        for (int j = 0; j < 10; j ++ ) count[j] = 0;
        for (int j = 0; j < n; j ++ )
        {
            int k = (a[j] / radix) % 10;
            count[k] ++ ;
        }
        for (int j = 1; j < 10; j ++ ) count[j] += count[j-1];
        for (int j = n-1; j >= 0; j -- )
        {
            int k = (a[j] / radix) % 10;
            temp[count[k]-1] = a[j];
            count[k] -- ;
        }
        for (int j = 0; j < n; j ++ ) a[j] = temp[j];
        radix *= 10;
    }

}

9.计数排序

void counting_sort()
{
    int sorted[N];
    int maxv = a[0];
    for (int i = 1; i < n; i ++ )
        if (maxv < a[i])
            maxv = a[i];
    int count[maxv+1];
    for (int i = 0; i < n; i ++ ) count[a[i]] ++ ;
    for (int i = 1; i <= maxv; i ++ ) count[i] += count[i-1];
    for (int i = n-1; i >= 0; i -- )
    {
        sorted[count[a[i]]-1] = a[i];
        count[a[i]] -- ;
    }
    for (int i = 0; i < n; i ++ ) a[i] = sorted[i];
}

10.桶排序

（基数排序是桶排序的特例，优势是可以处理浮点数和负数，劣势是还要配合别的排序函数）

vector<int> bucketSort(vector<int>& nums) {
    int n = nums.size();
    int maxv = *max_element(nums.begin(), nums.end());
    int minv = *min_element(nums.begin(), nums.end());
    int bs = 1000;
    int m = (maxv-minv)/bs+1;
    vector<vector<int> > bucket(m);
    for (int i = 0; i < n; ++i) {
        bucket[(nums[i]-minv)/bs].push_back(nums[i]);
    }
    int idx = 0;
    for (int i = 0; i < m; ++i) {
        int sz = bucket[i].size();
        bucket[i] = quickSort(bucket[i]);
        for (int j = 0; j < sz; ++j) {
            nums[idx++] = bucket[i][j];
        }
    }
    return nums;
}