POJ-2299 Ultra-QuickSort

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Ultra-QuickSort

Time Limit: 7000MS		Memory Limit: 65536K
Total Submissions: 68838		Accepted: 25801

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：就是求逆序数

思路：①归并排序    ②树状数组

归并排序思想：可以从two pointers里体现出来（把A数组和B数组合并成递增的C数组）---A和B都是递增的数列

int merge(int A[], int B[], int C[], int n, int m) {
	int i = 0, j = 0, index = 0;//i 指向 A[0] j指向B[0]
	while(i < n && j < m) {//其中一个到最后，就结束了 
		if(A[i] < B[j])// 谁小谁放入C数组，并后移1位 
			C[index++] = A[i++];
		else
			C[index++] = B[j++]; 
	} //把另一个没有到最后的 直接放进去 （A和B都是递增的数组） 
	while(i < n) C[index++] = A[i++];
	while(j < n) C[index++] = B[j++]; 
}

归并排序就是这样的思想，下面的代码有所改动，可以比较着理解一下。

归并排序AC代码:

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int MAX = 500010;

int a[MAX], temp[MAX];//temp临时合并的数组 
long long cnt; // 会爆int 
int n;

void merge(int l, int m, int r) {//l到r  合并   
	int i = l;
	int j = m + 1;
	int k = l;//这个重要 
	while(i <= m && j <= r) {//two pointers思想 
		if(a[i] > a[j]) {
			cnt += j - k;  //逆序数 
			temp[k++] = a[j++]; 
		} else temp[k++] = a[i++];
	}
	while(i <= m) temp[k++] = a[i++];
	while(j <= r) temp[k++] = a[j++];
	for(int i = l; i <= r; i++) { //把temp 赋值给 a数组（排完了） 
		a[i] = temp[i];
	}
}

void mergesort(int l, int r) {//分治 
	if(l < r) {
		int m = (l+r) / 2;
		mergesort(l, m);
		mergesort(m+1, r);
		merge(l, m, r);
	}
}

int main() {
	while(~scanf("%d", &n)) {
		if(n == 0)	
			break;
		for(int i = 0; i < n; i++) 
			scanf("%d", &a[i]);
		cnt = 0;
		mergesort(0, n-1);//0~n-1  
		printf("%lld
", cnt);	
	}
}

②树状数组AC代码：

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

struct node{
	int pos;
	int zhi;
}stu[500010];//离散化处理 

int n, x; 

bool cmp(node a, node b) {
	return a.zhi < b.zhi;
}
//存数组 
int sum[500010];
int b[500010];

//树状数组操作 
void update(int pos, int val) { 
	while(pos <= n) {
		sum[pos] += val;
		pos += (pos & (-pos));
	}
}

int query(int pos) {
	int rec = 0;
	while(pos > 0) {
		rec += sum[pos];
		pos -= (pos & (-pos));
	}
	return rec;
}

int main() {
	while(~scanf("%d", &n)) {
		if(n == 0)
			break;
		for(int i = 1; i <= n; i++) {//离散化处理 
			scanf("%d", &stu[i].zhi);
			stu[i].pos = i;
		}
		sort(stu+1, stu+n+1, cmp);
		for(int i = 1; i <= n; i++) {
			b[stu[i].pos] = i;
		}
		memset(sum, 0, sizeof(sum));
		long long nxs = 0;
		for(int i = 1; i <= n; i++) {//操作 
			update(b[i], 1);//该位置加1 
			int temp = query(b[i]);//前缀和 
			nxs += (i - temp);//前面有几个空位（0）
		}
		printf("%lld
", nxs);
	}	
}