归并排序模板

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
const int N = 100010;
int q[N],t[N]; //q是原数组和最终数组，t是中间暂存数组
void merge_sort(int q[],int l,int r)
{
    if(l>=r) return;  //递归的终点，即数组中没有数或者只有1个数了停止
    int mid=l+r>>1;
    merge_sort(q,l,mid),merge_sort(q,mid+1,r);
    int k=0;
    int i=l,j=mid+1;
    while (i<=mid&&j<=r) //双指针
    {
        if (q[i]<=q[j]) t[k++]=q[i++];
        else t[k++]=q[j++];
    }
    while (i<=mid) t[k++]=q[i++];
    while (j<=r) t[k++]=q[j++];
    for (int i=l,j=0;i<=r;i++,j++)  //将暂存数组的数据赋值到原数组中
        q[i]=t[j];

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

归并排序的重要应用（逆序对个数求解）

788.逆序对的数量

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
const int N = 100010;
int q[N],t[N]; 
long long merge_sort(int l,int r)
{
    if (l>=r) return 0;
    int mid=l+r>>1;
    long long ans=merge_sort(l,mid)+merge_sort(mid+1,r);
    int k=0;
    int i=l,j=mid+1;
    while (i<=mid&&j<=r)
    {
        if (q[i]<=q[j]) t[k++]=q[i++];
        else  //此时q[i]>q[j],即i~mid的所有数字都比q[j]大，因此可构成mid-i+1个逆序对
        {
            t[k++]=q[j++];
            ans+=mid-i+1;
        }
    }
    while (i<=mid) t[k++]=q[i++];
    while (j<=r) t[k++]=q[j++];
    for (int i=l,j=0;i<=r;i++,j++)
        q[i]=t[j];
    return ans;
}
int main()
{
    int n;
    cin>>n;
    for (int i=0;i<n;i++)
        cin>>q[i];
    cout<<merge_sort(0,n-1)<<endl;
    return 0;
}