Out of Sorts II 树状数组

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本文探讨了牛Bessie通过修改冒泡排序算法以提高排序效率的方法，并利用树状数组来预测排序过程中特定操作的执行次数。

6347: Out of Sorts II

时间限制: 1 Sec 内存限制: 128 MB
提交: 441 解决: 80
[提交] [状态] [讨论版] [命题人:admin]

题目描述

Keeping an eye on long term career possibilities beyond the farm, Bessie the cow has started learning algorithms from various on-line coding websites.
Her favorite algorithm thus far is "bubble sort". Here is Bessie's initial implementation, in cow-code, for sorting an array A of length N.

sorted = false
while (not sorted):
sorted = true
moo
for i = 0 to N-2:
if A[i+1] < A[i]:
swap A[i], A[i+1]
sorted = false
Apparently, the "moo" command in cow-code does nothing more than print out "moo". Strangely, Bessie seems to insist on including it at various points in her code.

After testing her code on several arrays, Bessie learns an interesting observation: while large elements can be pulled to the end of the array very quickly, it can take small elements a very long time to "bubble" to the front of the array (she suspects this is how the algorithm gets its name). In order to try and alleviate this problem, Bessie tries to modify her code so that it scans forward and then backward in each iteration of the main loop, so that both large and small elements have a chance to be pulled long distances in each iteration of the main loop. Her code now looks like this:

sorted = false
while (not sorted):
sorted = true
moo
for i = 0 to N-2:
if A[i+1] < A[i]:
swap A[i], A[i+1]
for i = N-2 downto 0:
if A[i+1] < A[i]:
swap A[i], A[i+1]
for i = 0 to N-2:
if A[i+1] < A[i]:
sorted = false
Given an input array, please predict how many times "moo" will be printed by Bessie's modified code.

输入

The first line of input contains N (1≤N≤100,000). The next N lines describe A[0]…A[N−1], each being an integer in the range 0…109. Input elements are not guaranteed to be distinct.

输出

Print the number of times "moo" is printed.

样例输入

样例输出

来源/分类

USACO 2018 US Open Contest, Gold

[提交] [状态]

求一列数用两次冒泡排序（正向+反向）的方法总共需要几次循环

第一遍循环将大数向右移，第二遍循环将小数向左移，即将大数向右移

所以要求每个数左边比他大的数的个数

用树状数组求

代码：

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxx=1e6+10;
const int INF=1e9;
const int MOD=1e9+7;
struct node
{
    int a,p;
}s[maxx];
bool cmp(node x,node y)
{
    return x.a<y.a;
}
int sum[maxx];
void add(int x)
{
    while(x<maxx){
        sum[x]++;
        x+= x&(-x);
    }
}
int ask(int x)
{
    int ret=0;
    for(int i=x; i>0; i-= i&(-i)){
        ret+=sum[i];
    }
    return ret;
}
int main()
{
    int n;
    cin>>n;
    for(int i=1; i<=n; i++){
        cin>>s[i].a;
        s[i].p=i;
    }
    sort(s+1,s+n+1,cmp);
    int ans=-1;
    for(int i=1; i<=n; i++){
        add(s[i].p);
        ans=max(ans,i-ask(i));
    }
    cout<<max(ans,1)<<endl;
    return 0;
}