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
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: [email protected]
> 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;
}