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文章目录

• 快速排序
• 归并排序
• 整数二分
• 浮点数二分

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一、快速排序

#include<iostream>

using namespace std;

const int N = 1e6 + 10;

int n;
int q[N];

void quick_sort(int q[], int l, int r)
{
	//此时区间只有一个数或者没有数不需要排序了
	if (l >= r) return;

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

}
int main()
{
	//关于快速排序：第一点就是确定分界点：q[l],q[(l+r)/2],q[r]为分界点都是可以
	//调整范围： 将区间分为左右两侧，左边的小于等于分界点，右边的大于等于分界点
	//最后再递归左右区间即可
	scanf("%d", &n);
	for (int i = 0; i < n; i++) scanf("%d", &q[i]);

	quick_sort(q, 0, n - 1);

	for (int i = 0; i < n; i++) printf("%d ", q[i]);

	return 0;

}

二、归并排序

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 1e5 + 10;
int a[N], tmp[N];

void Merge_sort(int a[], int l, int r)
{
    if (l >= r) return;
    int mid = (l + r) >> 1;
    //先分后合
    Merge_sort(a, l, mid);
    Merge_sort(a, mid + 1, r);
    int i = l, j = mid + 1, k = 0;
    //归并
    while (i <= mid && j <= r)
    {
        if (a[i] <= a[j]) tmp[k++] = a[i++];
        else tmp[k++] = a[j++];
    }
    //续尾
    while (i <= mid) tmp[k++] = a[i++];
    while (j <= r) tmp[k++] = a[j++];
    for (i = l, j = 0; i <= r;)
        a[i++] = tmp[j++];
}
int main()
{
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i++) scanf("%d", &a[i]);
    Merge_sort(a, 0, n - 1);
    for (int i = 0; i < n; i++) printf("%d ", a[i]);
    return 0;
}

三、整数二分

#include<iostream>
#include<cstring>
#include<algorithm>

using namespace std;

const int N = 1e5 + 10;

int n;
int q[N];

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);

	int x;
	cin >> n>>x;

	for (int i = 0; i < n; i++)
		cin >> q[i];

	//第一种二分模板
	//int l = 0, r = n - 1;
	//while (l < r) {
	//	int mid = l + r >> 1;
	//	if (q[mid] >= x) r = mid;
	//	else
	//		l = mid + 1;
	//}

	//第二种模板
	int l = 0, r = n - 1;
	while (l < r) {
		int mid = (l + r + 1) >> 1;
		if (q[mid] <= x) l = mid ;
		else
			r = mid-1;
	}

	cout << l << endl;
	return 0;
}

四、浮点数二分

#include<iostream>
#include<cstring>
#include<algorithm>

using namespace std;

int main()
{
	double x;
	cin >> x;

	double l = 0, r = x;
	while (r - l > 1e-8){
		double mid = (l + r) /2;
		if (mid * mid >= x) r = mid;
		else
			l = mid;
	}

	cout << l << endl;
	return 0;
}