1. 程式人生 > >2017 ccpc女生專場 1003 Coprime Sequence

2017 ccpc女生專場 1003 Coprime Sequence

style rst des 一個數 output sequence amp efi comm

前綴後綴gcd,其實自己中用的是種奇怪的方法A掉的,不過先把這個學上,自己的方法有時間再填。

題意

告訴你N個數,求刪除一個數可以求得最大GCD。

N可能是100000。

思路

這道題其實很簡單,但是想不到這點就很難。

簡單的說就是先預處理,得到每個數字左邊的GCD和右邊的GCD.

  1. befor(i)代表前i個數字的GCD, 復雜度 O(n*log(n))
  2. after(i)代表i之後的數字的GCD. 復雜度 O(n*log(n))
  3. ans = max(after(2), befor(1)+after(3), ..., befor(n-2)+after(n), befor(n-1)) ;

Coprime Sequence

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 250 Accepted Submission(s): 145


Problem Description Do you know what is called ``Coprime Sequence‘‘? That is a sequence consists of n positive integers, and the GCD (Greatest Common Divisor) of them is equal to 1.
``Coprime Sequence‘‘ is easy to find because of its restriction. But we can try to maximize the GCD of these integers by removing exactly one integer. Now given a sequence, please maximize the GCD of its elements.

Input The first line of the input contains an integer T(1T10), denoting the number of test cases.
In each test case, there is an integer n(3n100000) in the first line, denoting the number of integers in the sequence.
Then the following line consists of n integers a1,a2,...,an(1ai109), denoting the elements in the sequence.

Output For each test case, print a single line containing a single integer, denoting the maximum GCD.

Sample Input 3 3 1 1 1 5 2 2 2 3 2 4 1 2 4 8

Sample Output 1 2 2
 1 #include<iostream>
 2 #include<stdio.h>
 3 
 4 #define ff 1000000007
 5 
 6 using namespace std;
 7 
 8 int main()
 9 {
10     int t,n,k;
11     scanf("%d",&t);
12     while(t--)
13     {
14         scanf("%d%d",&n,&k);
15         long long ans=0,temp;
16         for(int i = 1; i <= n; i++)
17         {
18             temp=1;
19             for(int j = 1; j <= k; j++)
20             {
21                 temp=(temp*i)%ff;
22             }
23             ans=(ans+temp)%ff;
24         }
25         printf("%lld\n",ans%ff);
26     }
27     
28     return 0;
29 }

2017 ccpc女生專場 1003 Coprime Sequence