bc #43(hdu 5265) pog loves szh II （单调性优化）

pog loves szh II

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 2115    Accepted Submission(s): 609

Problem Description

Pog and Szh are playing games.There is a sequence with n numbers, Pog will choose a number A from the sequence. Szh will choose an another number named B from the rest in the sequence. Then the score will be (A+B) mod p.They hope to get the largest score.And what is the largest score?

 

Input

Several groups of data (no more than 5 groups,n≥1000).

For each case: 

The following line contains two integers,n(2≤n≤100000)，p(1≤p≤231−1)。

The following line contains n integers ai(0≤ai≤231−1)。

 

Output

For each case,output an integer means the largest score.

 

Sample Input

4 4 1 2 3 0 4 4 0 0 2 2

 

Sample Output

3 2

 

Source

BestCoder Round #43

 

Recommend

hujie   |   We have carefully selected several similar problems for you:  5338 5337 5336 5335 5334 

对于读入的a[i] mod p后

对于任意 0=<i,j<=n-1  a[i]+a[j] 大于等于0小于等于2p-2

所以a[i]+a[j]的结果只有两种情况，一种是 <p,直接就是答案，另一种是 >=p  <=2p-2   a[i]+a[j]-p 是答案

把a[i]升序排列，如果存在a[i]+a[j]>=p ,那么最大的一定是a[n-1]+a[n-2]

对于a[i]+a[j]小于p的，我们枚举i，找到最大的j，使得a[i]+a[j]<p，这是对于i最大的答案。

如果直接枚举O(N2)会超时

由于a[i]数组已经是有序的了

我们可以利用a[i]的单调性，从两边往中间找。

这样复杂度就是O(N)了

这个优化前几天刚遇到过。。。。

 

/*************************************************************************
    > File Name: code/bc/#43/B.cpp
    > Author: 111qqz
    > Email: rkz2013@126.com 
    > Created Time: 2015年07月31日 星期五 16时38分13秒
 ************************************************************************/

#include<iostream>
#include<iomanip>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<string>
#include<map>
#include<set>
#include<queue>
#include<vector>
#include<stack>
#define y0 abc111qqz
#define y1 hust111qqz
#define yn hez111qqz
#define j1 cute111qqz
#define tm crazy111qqz
#define lr dying111qqz
using namespace std;
#define REP(i, n) for (int i=0;i<int(n);++i)  
typedef long long LL;
typedef unsigned long long ULL;
const int inf = 0x7fffffff;
const int N=1E5+7;
LL a[N];
int n,p;

int main()
{
    while (scanf("%d %d",&n,&p)!=EOF)
    {
    LL ans = -1;
    for ( int i = 0 ; i < n;  i++ )
    {
        scanf("%lld",&a[i]);
        a[i]=a[i]%p;
    }
    sort(a,a+n);
    ans = (a[n-1]+a[n-2])%p;
    int j = n-1;
    for ( int i = 0 ; i  < n-2 ; i++ )
    {
        while (i<j&&a[i]+a[j]>=p) j--;
        ans = max(ans,(a[i]+a[j])%p);
    }
    cout<<ans<<endl;

    }
  
    return 0;
}