POJ 2299 Ultra-QuickSort 逆序数 树状数组 归并排序 线段树

题目链接：http://poj.org/problem?id=2299

求逆序数的经典题，求逆序数可用树状数组，归并排序，线段树求解，本文给出树状数组，归并排序，线段树的解法。

归并排序：

#include<cstdio>
#include<iostream>
using namespace std;
#define max 500002
int arr[max],b[max];//b[]为临时序列，arr[]为待排序数列，结果在arr[]中
int tp[max];
long long cnt=;//总逆序数
void Merge(int a[],int start,int mid,int end){
    int i =start,j=mid+,k=start;
    while(i<=mid&&j<=end){
        if(a[i]<=a[j]){
            cnt+=j-mid-;
            b[k++]=a[i++];
        }else{
            cnt+=j-k;
            b[k++]=a[j++];
        }
    }
    while(i<=mid){
        cnt+=end-mid;
        b[k++]=a[i++];
    }
    while(j<=end){
        b[k++]=a[j++];
    }
    for(int i=start;i<=end;i++){
        a[i]=b[i];
    }
}
void MergeSort(int a[], int start,int end){
    if(start<end){
        int mid=(start+end)/;
        MergeSort(a,start,mid);
        MergeSort(a,mid+,end);
        Merge(a,start,mid,end);
    }
}
int main(){
    int n;
    while(~scanf("%d",&n)&&n){
        for(int i=;i<n;i++){
            scanf("%d",&arr[i]);
        }
        cnt=;
        MergeSort(arr,,n-);
        printf("%I64d\n",cnt/);
    }
    return ;
}

　　

树状数组：

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define lowbit(x) (x&(-x))
using namespace std;
const int MAX = ;
struct data{
    int id,val;
}num[MAX];
int n, C[MAX];
bool cmp(data a, data b){
    return a.val>b.val;
}
void add(int i){
    while(i<=n){
        C[i]+=;
        i+=lowbit(i);
    }
}
long long sum(int i){
    long long ans = ;
    while(i>){
        ans+=C[i];
        i-=lowbit(i);
    }
    return ans;
}

int main(){
    while(scanf("%d",&n)&&n){
        memset(C,,sizeof(C));
        for(int i=;i<n;i++){
            num[i].id=i+;
            scanf("%d",&num[i].val);
        }
        sort(num,num+n,cmp);//离散化，将数组按降序排序，再求下标的逆序数，下标的逆序数与值逆序数相等
        long long ans = ;
        for(int i=;i<n;i++){
            ans+=sum(num[i].id-);//求在i前面比第i个数大的数的个数
            add(num[i].id);
        }
        printf("%I64d\n", ans);
    }
    return ;
}

 线段树( 以HDU1394 Minimum Inversion Number为例)：

#include<iostream>
#include<cstdio>
#include<cstdlib>#include<algorithm>
const int INF = 0x3F3F3F3F;
using namespace std;
#define lson l, m, rt<<1
#define rson m+1, r, rt<<1|1
#define N 5008
int sum[N<<], a[N];
inline void pushUp(int rt){
    sum[rt] = sum[rt << ] + sum[rt <<  | ];
}

int query(int a, int b, int l, int r, int rt){
    if(a <= l && b >= r){
        return sum[rt];
    }
    int m=(l + r) >> ;
    int ret=;
    if(a <= m){
        ret += query(a, b, lson);
    }
    if(b > m){
      ret += query(a, b, rson);
    }
    return ret;
}
void update(int x, int val, int l, int r, int rt){
    if(l == r){
        sum[rt] = val;
    }else{
    int m = (l + r)/;
    if(x <= m){
        update(x, val, lson);
    }else{
        update(x, val, rson);
    }
    pushUp(rt);
    }
}

int main(){
    int n;
    while(~scanf("%d", &n)){
        memset(sum, , sizeof(sum));
        int ans = ;
        for(int i =  ; i < n; i++){
            scanf("%d", &a[i]);
            a[i]++;
            ans += query(a[i] + , n, , n , );
            update(a[i], , , n, );
        }
        int tp = ans;
        for(int i =  ; i < n - ; i++){
            tp += n -  * a[i] + ;
            ans = min(ans , tp);
        }
        printf("%d\n",ans);
    }
}