排序算法

快速排序，O($nlogn$)

#include <cstdio>
#include <algorithm>
using namespace std;

const int N = 1e5 + 10;
int vals[N], n;

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

int main()
{
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i)
        scanf("%d", &vals[i]);
    quick_sort(1, n);
    for(int i = 1; i <= n; ++i)
        printf("%d ", vals[i]);
    return 0;
}

快速选择算法，O(n)

#include <cstdio>
#include <algorithm>
using namespace std;

const int N = 1e5 + 10;
int vals[N];

int quick_select(int l, int r, int k)
{
    if(l == r) return vals[l];
    int i = l - 1, j = r + 1, mid = vals[i + j >> 1];
    while(i < j)
    {
        do ++i; while(vals[i] < mid);
        do --j; while(vals[j] > mid);
        if(i < j) swap(vals[i], vals[j]);
    }
    int len = j - l + 1;
    if(len >= k) return quick_select(l, j, k);
    return quick_select(j + 1, r, k - len);
}

int main()
{
    int n, k;
    scanf("%d%d", &n, &k);
    for(int i = 1; i <= n; ++i)
        scanf("%d", &vals[i]);
    printf("%d", quick_select(1, n, k));
    return 0;
}

归并排序，O($nlogn$)，需要额外O(n)的空间

#include <cstdio>
using namespace std;

const int N = 1e5 + 10;
int vals[N], temp[N];

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

int main()
{
    int n;
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i)
        scanf("%d", &vals[i]);
    merge_sort(1, n);
    for(int i = 1; i <= n; ++i)
        printf("%d ", vals[i]);
    return 0;
}