归并排序、逆序对

归并排序O(nlong)

#include<bits/stdc++.h>
#define N 100010
using namespace std;

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 k=0,i=l,j=mid+1;
    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() {
    cin>>n;
    for(int i=1; i<=n; i++) cin>>a[i];
    merge_sort(1,n);
    for(int i=1; i<=n; i++) cout<<a[i]<<" ";
    return 0;
}

 

归并求逆序对O(nlogn)

#include<bits/stdc++.h>
#define N 500010
using namespace std;

int n;
long long cnt;
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 k=0,i=l,j=mid+1;
    while(i<=mid&&j<=r) {
        if(a[i]<=a[j]) tmp[k++]=a[i++];
        else tmp[k++]=a[j++],cnt+=mid-i+1;
    }
    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() {
    while(cin>>n&&n) {
        cnt=0;
        for(int i=1; i<=n; i++) cin>>a[i];
        merge_sort(1,n);
        cout<<cnt<<endl;
    }

    return 0;
}

 

用途：冒泡排序、奇数码、

求逆序对的常用方法还有树状数组，