CF——A. Ehab Fails to Be Thanos(第一场cf爆零之战)

本文解析了一场Codeforces比赛中的题目A.EhabFailstoBeThanos,介绍了如何判断并输出一个2n长度序列的任意排列,使得前n项和与后n项和不相等的方法。

A. Ehab Fails to Be Thanos

You’re given an array a of length 2n. Is it possible to reorder it in such way so that the sum of the first n elements isn’t equal to the sum of the last n elements?

Input
The first line contains an integer n (1≤n≤1000), where 2n is the number of elements in the array a.

The second line contains 2n space-separated integers a1, a2, …, a2n (1≤ai≤106) — the elements of the array a.

Output
If there’s no solution, print “-1” (without quotes). Otherwise, print a single line containing 2n space-separated integers. They must form a reordering of a. You are allowed to not change the order.
Examples
input
3
1 2 2 1 3 1
output
2 1 3 1 1 2
input
1
1 1
output
-1
Note
In the first example, the first n elements have sum 2+1+3=6 while the last n elements have sum 1+1+2=4. The sums aren’t equal.

In the second example, there’s no solution.
ps:打的第一场cf,由于这道题始终没搞懂题目意思,不懂怎样输出,所以爆零了。最后看了别人代码才才知道,还有这种输出的格式,长知识了。题意就是给一个2n的序列,任意交换位置,使前n位之和与后n位的和不等,如果满足情况,则输出任意一列情况 就可以了,否则输出-1。哎,菜是原罪,请原谅我孤陋寡闻

#include<bits/stdc++.h>
using namespace std;
int arr[10005];
int main(){
    int n;
    cin>>n;
    for(int i=0;i<2*n;i++){
        cin>>arr[i];
    }
    sort(arr,arr+2*n);
    int suma=0,sumb=0;
    for(int i=0;i<n;i++){
        suma+=arr[i];
    }
    for(int i=n;i<2*n;i++){
        sumb+=arr[i];
    }
    if(suma==sumb){
        cout<<"-1"<<endl;
    }else{
        for(int i=0;i<2*n;i++){
            cout<<arr[i]<<" ";
        }
        cout<<endl;
    }
    return 0;
}
This time Baby Ehab will only cut and not stick. He starts with a piece of paper with an array a a of length n n written on it, and then he does the following: he picks a range ( l , r ) (l,r) and cuts the subsegment a l , a l + 1 , … , a r a l ​ ,a l+1 ​ ,…,a r ​ out, removing the rest of the array. he then cuts this range into multiple subranges. to add a number theory spice to it, he requires that the elements of every subrange must have their product equal to their least common multiple (LCM). Formally, he partitions the elements of a l , a l + 1 , … , a r a l ​ ,a l+1 ​ ,…,a r ​ into contiguous subarrays such that the product of every subarray is equal to its LCM. Now, for q q independent ranges ( l , r ) (l,r), tell Baby Ehab the minimum number of subarrays he needs. Input The first line contains 2 2 integers n n and q q ( 1 ≤ n , q ≤ 10 5 1≤n,q≤10 5 ) — the length of the array a a and the number of queries. The next line contains n n integers a 1 a 1 ​ , a 2 a 2 ​ , … …, a n a n ​ ( 1 ≤ a i ≤ 10 5 1≤a i ​ ≤10 5 ) — the elements of the array a a. Each of the next q q lines contains 2 2 integers l l and r r ( 1 ≤ l ≤ r ≤ n 1≤l≤r≤n) — the endpoints of this query's interval. Output For each query, print its answer on a new line. Examples Inputcopy Outputcopy 6 3 2 3 10 7 5 14 1 6 2 4 3 5 3 1 2 Note The first query asks about the whole array. You can partition it into [ 2 ] [2], [ 3 , 10 , 7 ] [3,10,7], and [ 5 , 14 ] [5,14]. The first subrange has product and LCM equal to 2 2. The second has product and LCM equal to 210 210. And the third has product and LCM equal to 70 70. Another possible partitioning is [ 2 , 3 ] [2,3], [ 10 , 7 ] [10,7], and [ 5 , 14 ] [5,14]. The second query asks about the range ( 2 , 4 ) (2,4). Its product is equal to its LCM, so you don't need to partition it further. The last query asks about the range ( 3 , 5 ) (3,5). You can partition it into [ 10 , 7 ] [10,7] and [ 5 ] [5]. 解法:条件就是两两互质,预处理质因⼦集,找出每个数下⼀个不互质的位置。 i 进⼀步的,可以找出每个 作为左端点,可⾏的右端点最⼤是多⼤(区间 min)。 2j 因此每次划分极⻓就可以了,令 f(i, j) 然后枚举答案的⼆进制下每⼀位即可。 。 求C++代码.
06-10
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