HDU-1394 Minimum Inversion Number 线段树+逆序对

仍旧在练习线段树中。。这道题一开始没有完全理解搞了一上午，感到了自己的shabi。。

Minimum Inversion Number

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 15527 Accepted Submission(s): 9471

Problem Description

The inversion number of a given number sequence a1, a2, …, an is the number of pairs (ai, aj) that satisfy i < j and ai > aj.

For a given sequence of numbers a1, a2, …, an, if we move the first m >= 0 numbers to the end of the seqence, we will obtain another sequence. There are totally n such sequences as the following:

a1, a2, …, an-1, an (where m = 0 - the initial seqence)

a2, a3, …, an, a1 (where m = 1)

a3, a4, …, an, a1, a2 (where m = 2)

…

an, a1, a2, …, an-1 (where m = n-1)

You are asked to write a program to find the minimum inversion number out of the above sequences.

Input

The input consists of a number of test cases. Each case consists of two lines: the first line contains a positive integer n (n <= 5000); the next line contains a permutation of the n integers from 0 to n-1.

Output

For each case, output the minimum inversion number on a single line.

Sample Input

10

1 3 6 9 0 8 5 7 4 2

Sample Output

16

题目大意：

给出一个n，和0-n的一个数列，求这个数列的最小逆序对数，最小逆序对表示，给定数列每次都将第一个数放到最后一个位置，如此变化n次至变换回原状，在这n种不同的数列中，逆序对数的最小值即为所求（N<=5000）每组样例多组数据

明白题意后想到求逆序对的三种方法，第一种暴力法，第二种归并，第三种树状数组和线段树，由于在学习线段树于是果断练习用线段树编写
此处线段树的作用是求出原数列的逆序对
对于每次变换，我们发现，第一个数移到最后一位，只需要在上一步里求出的逆序对减去上一步第一位的数，并加上比上一步第一位要大的数即可

下面是代码：

#include <cstdio>
#include <algorithm>
using namespace std;
#define maxn 5005
int sum[maxn<<2];
int a[maxn];

void updata(int now)
{
    sum[now]=sum[now<<1]+sum[now<<1|1];
}

void build(int l,int r,int now)
{
    sum[now]=0;
    if(l==r) return;
    int mid=(l+r)>>1;
    build(l,mid,now<<1);
    build(mid+1,r,now<<1|1);
}

int query(int L,int R,int l,int r,int now)
{
    if(L<=l && r<=R)
        return sum[now];
    int mid=(l+r)>>1;
    int total=0;
    if(L<=mid) total+=query(L,R,l,mid,now<<1);
    if(R>mid) total+=query(L,R,mid+1,r,now<<1|1);
    return total;
}

void point_change(int loc,int l,int r,int now)
{
    if(l==r)
    {
        sum[now]++;
        return;
    }
    int mid=(l+r)>>1;
    if(loc<=mid)
        point_change(loc,l,mid,now<<1);
    else
        point_change(loc,mid+1,r,now<<1|1);
    updata(now);
}

int main()
{
    int n;
    while(~scanf("%d",&n))
    {
        build(0,n-1,1);
        int number=0;
        for(int i=0;i<n;i++)
        {
            scanf("%d",&a[i]);
            number+=query(a[i],n-1,0,n-1,1);
            point_change(a[i],0,n-1,1);
        }
        int ans=number;
        for(int i=0;i<n;i++)
        {
            number+=n-a[i]-a[i]-1;
            ans=min(ans,number);
        }
        printf("%d\n",ans);
    }
    return 0;
}