[Sorting Algorithm Encyclopedia] Template Level

Sorting efficiency comparison chart

1 Insertion sort

1.1 Simple insertion sort

#include <iostream>
using namespace std;
const int N = 100010;
int n;
int q[N];

// 直接插入排序 
void insert_sort()
{
    
    
	for (int i = 1; i < n; i ++)
	{
    
    
		// 取出当前元素赋值给t，j从当前位置开始往前看 
		int t = q[i], j = i;
		while (j && q[j - 1] > t)
		{
    
    
			q[j] = q[j - 1];
			j --;
		}
		q[j] = t; // 把t放到正确的位置上
	}
}
int main()
{
    
    
	cin >> n;
	for (int i = 0; i < n; i ++) cin >> q[i];
	insert_sort();
	for (int i = 0; i < n; i ++) cout << q[i] << ' ';
	return 0;
}

1.2 Binary insertion sort

void binsert_sort()
{
    
    
	for (int i = 1; i < n; i ++)
	{
    
    
		if (q[i - 1] <= q[i]) continue;
		int t = q[i];
		// 二分出第一个大于t的位置
		int l = 0, r = i - 1;
		while (l < r)
		{
    
    
			int mid = l + r >> 1;
			if (q[mid] > t) r = mid;
			else l = mid + 1;
		}
		// 从r开始到i - 1的位置的数往后移动一位 
		for (int j = i - 1; j >= r; j --)
			q[j + 1] = q[j];
			
		q[r] = t; // 把t放到正确的位置上
	}
}

1.3 Hill sort

void shell_sort()
{
    
    
	// 枚举增量 
	for (int d = n / 3; d; d = d == 2 ? 1 : d / 3)
	{
    
    
		// 枚举起点 
		for (int start = 0; start < d; start ++)
		{
    
    
			// 做插入排序 
			for (int i = start + d; i < n; i += d)
			{
    
    
				int t = q[i], j = i;
				while (j > start && q[j - d] > t)
				{
    
    
					q[j] = q[j - d];
					j -= d;
				}
				q[j] = t;
			}
		}
	}
}

2 swap sort

2.1 Bubble sort

void bubble_sort()
{
    
    
	// 迭代n - 1次
	for (int i = 0; i < n - 1; i ++)
	{
    
    
		bool has_sawp = false; // 优化 
		for (int j = n - 1; j > i; j --)
			if (q[j] < q[j - 1])
			{
    
    
				swap(q[j], q[j - 1]); 
				has_sawp = true;
			}
		if (!has_sawp) break;
	}
}

2.2 Quick Sort

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

3 selection sort

3.1 Simple Selection Sort

void select_sort()
{
    
    
	// 迭代n - 1次
	for (int i = 0; i < n - 1; i ++)
	{
    
    
		int k = i;
		for (int j = i + 1; j < n; j ++)
			if (q[j] < q[k])
				k = j;
		swap(q[i], q[k]);
	}
}

3.2 Heap sort

#include <iostream>
using namespace std;
const int N = 100010;
int n; 
int h[N], sz;

// 调整为大根堆
void down(int u)
{
    
    
	int tmax = u;
	if (u * 2 <= sz && h[u * 2] > h[tmax]) tmax = u * 2;
	if (u * 2 + 1 <= sz && h[u * 2 + 1] > h[tmax]) tmax = u * 2 + 1;
	if (u != tmax)
	{
    
    
		swap(h[u], h[tmax]);
		down(tmax);
	}
}

void heap_sort()
{
    
    
	sz = n;
	for (int i = n / 2; i; i --) down(i);
	
	for (int i = 0; i < n - 1; i ++)
	{
    
    
		swap(h[1], h[sz]);
		sz --;
		down(1);
	}
}

int main()
{
    
    
	cin >> n;
	for (int i = 1; i <= n; i ++) cin >> h[i];
	heap_sort();
	for (int i = 1; i <= n; i ++) cout << h[i] << ' ';
	return 0;
} 

4 Merge sort

#include <iostream>
#include <algorithm>
using namespace std;
const int N = 100010;
int n;
int a[N], tmp[N];

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

    while (i <= mid) tmp[k ++] = a[i ++];
    while (j <= r) tmp[k ++] = a[j ++];
    
    for (int i = l, j = 0; i <= r; i ++, j ++) a[i] = tmp[j];
}
int main()
{
    
    
    scanf("%d", &n);
    for (int i = 0; i < n; i ++) scanf("%d", &a[i]);
    merge_sort(0, n - 1);
    for (int i = 0; i < n; i ++) printf("%d ", a[i]);
    return 0;
}