8_21_2013_Problem B: SUME_太水

Problem B: SUME

Time Limit: 1 Sec   Memory Limit: 32 MB
Submit: 6   Solved: 5
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Description

Once upon a time, there existed a sequence A  consisting of N positive integers. You don't know the 
sequence itself, but you do know the sum of every two elements of the sequence. Find the sequence A!

Input

The first line of input contains the positive integer N (2 ≤ N ≤ 1000). 
Each of the following N lines contains N positive integers smaller than or equal to 100 000, forming 
the table S. The following relations hold: S(i, j) = A [i] + A [j] for i ≠ j, and S(i, j) = 0 for i = j. Here S(i, 
j) denotes the number in the ith  row and jth column of the table, and A [i] denotes the ith element of the

sequence A.

It is guaranteed that for any input data set there exists a unique sequence of positive integers A with 
the given properties.

Output

The   first   and   only   line   of   output   must   contain   the   required   sequence  A (in   the   form   of  N  space- 
separated positive integers).

Sample Input

2 

0 2

 2 0 

4

0 3 6 7 

3 0 5 6 

6 5 0 9 

7 6 9 0

Sample Output

1 1 

2 1 4 5

#include  <iostream>
using namespace std;
int 
main()
{
	freopen("sume.data.in", "r", stdin);
	freopen("test.out", "w", stdout);
	int s, n, a[1010], ans[1010];
	long long int ssum, sa;//注意越界问题
	while(cin>>n){
		sa=0;
		ssum=0;
		for(int i=1; i<=n; i++){
			for(int j=1; j<=n; j++){
				cin>>s;
				ssum+=s;
				if(i==1){
					a[j]=s;
					sa+=s;
				}
			}
		}
		ssum=(ssum/2)/(n-1);
		if(sa==2){
			ans[1]=1;
		}
		else{
			ans[1]=(sa-ssum)/(n-2);
		}
		
		for(int i=2; i<=n; i++){
			ans[i]=a[i]-ans[1];
		}
		for(int i=1; i<=n; i++){
			cout<<ans[i];
			if(i!=n){
				cout<<" ";
			}
		}
		cout<<endl;
	}
	return 0;
}