归并排序模板

代码模板

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 1e5 + 10;

int n; 
int a[N], tmp[N];

void merge_sort(int q[], int l, int r)
{
    if (l >= r) return;

    int mid = l + r >> 1;
    merge_sort(q, l, mid);
    merge_sort(q, mid + 1, r);

    int k = 0, i = l, j = mid + 1;
    while (i <= mid && j <= r)
        if (q[i] <= q[j]) tmp[k ++ ] = q[i ++ ];
        else tmp[k ++ ] = q[j ++ ];

    while (i <= mid) tmp[k ++ ] = q[i ++ ];
    while (j <= r) tmp[k ++ ] = q[j ++ ];

    for (i = l, j = 0; i <= r; i ++, j ++ ) q[i] = tmp[j];
}
int main()
{
    cin >> n;
    for (int i = 0; i < n; ++ i) cin >> a[i];

    merge_sort(a, 0, n - 1);

    for (int i = 0; i < n; ++ i) cout << a[i] << " ";

    return 0;
}

应用1-求逆序对

原理在于归并排序合并[l,mid]和[mid + 1, r]两个区间时会进行比较，每遇到一对前半段区间小于后半段区间的数就是一组逆序对

#include <iostream>
#include <algorithm>

using namespace std;

const int N = 1e5 + 10;

typedef long long LL;

int n;
int a[N], tmp[N];

LL merge_sort(int a[], int l, int r)
{
    if (l >= r) return 0;
    
    int mid = l + r >> 1;
    LL res = merge_sort(a, l, mid) + merge_sort(a, mid + 1, r);
    
    int k = 0, i = l, j = mid + 1;
    while (i <= mid && j <= r)
    {
        if (a[i] <= a[j]) tmp[k ++] = a[i ++];
        else 
        {
            res += mid - i + 1; // a[i] > a[j]，a[k](k > i) 一定 > a[j]，所以这里是i及之后关于a[j]的所有逆序对数量 这里采用res++的问题也是当a[i] > a[j]之后，i后面的数据就看不到a[j]了，后面对应的逆序对自然也就找不到了，这里需要全部加上
            tmp[k ++] = a[j ++];
        }
    }
    
    while (i <= mid) tmp[k ++] = a[i ++];
    while (j <= r) tmp[k ++] = a[j ++];
    
    for (int i = l, j = 0; j < k; ++ i, ++ j) a[i] = tmp[j];
    
    return res;
}
int main()
{
    cin >> n;
    for (int i = 0; i < n; ++ i) cin >> a[i];
    
    cout << merge_sort(a, 0, n - 1) << endl;
    
    return 0;
}