Ultra-QuickSort poj2299(树状数组+离散化)

Ultra-QuickSort
Time Limit: 7000MS Memory Limit: 65536K
Total Submissions: 80376 Accepted: 30098

Description

In this problem, you have to analyze a particular sorting algorithm. The algorithm processes a sequence of n distinct integers by swapping two adjacent sequence elements until the sequence is sorted in ascending order. For the input sequence
9 1 0 5 4 ,

Ultra-QuickSort produces the output
0 1 4 5 9 .

Your task is to determine how many swap operations Ultra-QuickSort needs to perform in order to sort a given input sequence.

Input

The input contains several test cases. Every test case begins with a line that contains a single integer n < 500,000 – the length of the input sequence. Each of the the following n lines contains a single integer 0 ≤ a[i] ≤ 999,999,999, the i-th input sequence element. Input is terminated by a sequence of length n = 0. This sequence must not be processed.

Output

For every input sequence, your program prints a single line containing an integer number op, the minimum number of swap operations necessary to sort the given input sequence.

Sample Input

5
9
1
0
5
4
3
1
2
3
0

Sample Output

6
0

题目大意：给我们一个长度为n的序列，采用某种快速排序（交换排序），问最小交换次数。
思路：一天下来就搞了两道题。。。唉。。。多半是废了。
首先因为是交换排序很容易想到用冒泡排序去模拟，果断mle了，这时需要考虑更高效的算法
最小交换次数就是这个序列的逆序数，这个百度有严格证明，我就不多说了，关键是怎么求出这个逆序数。有三种方法可以求逆序数，分别是归并排序，线段树（后续补上），今天写的是树状数组。
由于数据范围非常大，所以需要离散化一下。
然后依次入读每个点再询问，因为第i个点最有有i-1个逆序数，因为树状数组要计数，每次+1，所以我们假设第i个点有i个逆序数（多一个本身，这是我们自己抽象出来的，方便计算），然后第i个数的最多逆序数减去不是不是逆序数的数量，剩下的就是逆序数的数量，然后累加求和就行了。然后我们用树状数组sum[i]维护第i个数不是逆序数的数量，只有是在它之前出现的都不可能是它的逆序数，那么它不是逆序数++。
代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;

const int maxn=1e6+10;
typedef long long ll;
ll a[maxn],b[maxn];
ll sum[maxn];
ll k;
ll query(ll x){
	ll ans=0;
	for(;x;x-=(x&-x)){
		ans+=sum[x];
	}
	return ans;
}
void add(ll x,ll v){
	for(;x<=k;x+=(x&-x)){
		sum[x]+=v;
	}
}
/* 5 9 1 0 5 4 3 1 2 3 */
int main(){
	ll n;
	while(scanf("%lld",&n)&&n){
		memset(sum,0,sizeof(sum));
		for(ll i=0;i<n;i++){
			scanf("%lld",&a[i]);
			b[i]=a[i];
		}
		sort(b,b+n);
		k=unique(b,b+n)-b;
		ll ans=0;
		for(ll i=0;i<n;i++){
			ll x=lower_bound(b,b+k,a[i])-b;
			x++;
			add(x,1);
			ans+=(i+1-query(x));
		}
		printf("%lld\n",ans);
	}
}