【codeforces 727 C】【交互题 求原数组】【告诉你有一个长度为n序列，你可以问n个问题，每个问题为ai+aj等于多少，最后输出这个序列】

传送门：C. Guess the Array

描述：

C. Guess the Array

time limit per test
1 second

memory limit per test
256 megabytes

input
standard input

output
standard output

This is an interactive problem. You should use flush operation after each printed line.
For example, in C++ you should usefflush(stdout), in Java you should use System.out.flush(),
and in Pascal — flush(output).

In this problem you should guess an array a which is unknown for you. The only information you have initially is the length n of
the arraya.

The only allowed action is to ask the sum of two elements by their indices. Formally, you can print two indices i and j (the
indices should be distinct). Then your program should read the response: the single integer equals to ai + aj.

It is easy to prove that it is always possible to guess the array using at most n requests.

Write a program that will guess the array a by making at most n requests.

Interaction

In each test your program should guess a single array.

The input starts with a line containing integer n (3 ≤ n ≤ 5000) —
the length of the array. Your program should read it at first.

After that your program should print to the standard output the requests about the sum of two elements or inform that the array is guessed.
In case your program is making a request to ask the sum of two elements, it should print line in the format "?
i j" (i and j are distinct integers
between 1 and n), where i and j are
indices in the array a.
In case your program informs that the array is guessed, it should print line in the format "! a1 a2 ... an"
(it is guaranteed that all ai are
positive integers not exceeding 105), where ai is
the i-th element of the array a.

The response on a request is a single integer equal to ai + aj,
printed on a separate line.

Your program can do at most n requests. Note that the final line «! a1 a2 ... an»
is not counted as a request.

Do not forget about flush operation after each printed line.

After you program prints the guessed array, it should terminate normally.

Example

input

5
 
9
 
7
 
9
 
11
 
6
 

output

 
? 1 5
 
? 2 3
 
? 4 1
 
? 5 2
 
? 3 4
 
! 4 6 1 5 5

Note

The format of a test to make a hack is:
The first line contains an integer number n (3 ≤ n ≤ 5000) —
the length of the array.
The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 105) —
the elements of the array to guess.

题意：

给你一个序列，长度为n，你事先不知道这个序列是什么，你可以问n个问题，每个问题为ai+aj等于多少，最后输出这个序列

思路：

 先问3个问题算出前3个，后面直接推就好了，然后就是注意交互题的格式

代码：

#include <bits/stdc++.h>
#define rep(i,k,n) for(int i=k;i<=n;i++)
using  namespace  std;

const int N=5010;

int a
, n;

int ask(int i, int j){
int res;
cout<<"? "<<i<<' '<<j<<endl;
fflush(stdout);
cin>>res;
return res;
}

int  main(){
cin>>n;
int x = ask(1, 2);
int y = ask(1, 3);
int z = ask(2, 3);
a[1] = (x + y - z) / 2;
a[2] = x - a[1];
a[3] = y - a[1];
rep(i, 3, n-1){
int res = ask(i, i+1);
a[i + 1] = res - a[i];
}
cout<<"! ";
rep(i, 1, n){
cout<<a[i]<<' ';
}
cout<<endl;
return 0;
}

/*5
10
5
7
6
10*/