POJ Ultra-2299 QuickSort 【离散化+树状数组】

Time Limit: 7000MS		Memory Limit: 65536K
Total Submissions: 55716		Accepted: 20578

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

Sample Output

6
0

Source

Waterloo local 2005.02.05

思路：
这道题问的是给你一个数列，求将数列进行升序排要操作多少次。
首先分析怎么求操作的次数。
例如9 1 0 5 4
先进行第一次排序 0 9 1 5 4 交换了2次，等于0的逆序数。
再进行排序 0 1 9 5 4 交换了1次，等于1的逆序数。
在进行排序 0 1 4 9 5 交换了2次，等于4的逆序数。
在进行排序 0 1 4 5 9 交换了1次，等于1的逆序数。
这样操作的次数为2 + 1 + 2 + 1 = 6，正好等于数列的逆序数和。
每次都要把数列中相对小的数向前移动，因为每次移动都是把小的放到大的前面，有几个大的就要移动几次，这正好是这个数的逆序数。所以，接下来就就是求逆序数了。
可以用两层循环求每一个数的逆序数，但是500,000*500,000会TLE。
主要是解决一个数他前面比他大的个数有几个。
转换一下求前面有多少个数比他小，用树状数组，我们用这个数作为树状数组的下标，每次向下标中放上1，统计他前面共有多少个数，这样就完美的解决了时间复杂度和逆序数的问题。
但是，另外一个问题出现了。如果这个数要是做下标，那么他的范围可是0 <= a[i] <= 999,999,999,所以在进行离散就ok了。

#include <cstdio>
#include <set>
#include <map>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>
#define space " "
using namespace std;
const int MAXN = 500000 + 10;
int n, ar[MAXN], b[MAXN], num[MAXN];
int sum(int x) {
    int s = 0;
    while (x >= 1) {
        s += num[x];
        x -= x&-x;
    }
    return s;
}
void add(int x, int y) {
    while (x <= n) {
        num[x] += y;
        x += x&-x;
    }
}
int main() {
    while (scanf("%d", &n), n) {
        for (int i = 1; i <= n; i++) {
            scanf("%d", &ar[i]);
            b[i] = ar[i];
        }
        memset(num, 0, sizeof(num));
        sort(b + 1, b + 1 + n); long long ans = 0;
        for (int i = 1; i <= n; i++) {
            ar[i] = lower_bound(b + 1, b + 1 + n, ar[i]) - b;
        }
     //   for (int i = 1; i <= n; i++) printf("%d %d
", i, ar[i]);
        for (int i = 1; i <= n; i++) {
            add(ar[i], 1);
            ans += i - sum(ar[i]);
        }
        printf("%lld
", ans);
    }
    return 0;
}