HDU 4034 Graph The 36th ACM/ICPC Asia Regional Chengdu Site —— Online Contest

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Graph

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65768/65768 K (Java/Others)
Total Submission(s): 26 Accepted Submission(s): 14

Problem Description

Everyone knows how to calculate the shortest path in a directed graph. In fact, the opposite problem is also easy. Given the length of shortest path between each pair of vertexes, can you find the original graph?

Input

The first line is the test case number T (T ≤ 100).
First line of each case is an integer N (1 ≤ N ≤ 100), the number of vertexes.
Following N lines each contains N integers. All these integers are less than 1000000.
The jth integer of ith line is the shortest path from vertex i to j.
The ith element of ith line is always 0. Other elements are all positive.

Output

For each case, you should output “Case k: ” first, where k indicates the case number and counts from one. Then one integer, the minimum possible edge number in original graph. Output “impossible” if such graph doesn't exist.

Sample Input

3
3
0 1 1
1 0 1
1 1 0
3
0 1 3
4 0 2
7 3 0
3
0 1 4
1 0 2
4 2 0

Sample Output

Case 1: 6
Case 2: 4
Case 3: impossible

Source

The 36th ACM/ICPC Asia Regional Chengdu Site —— Online Contest

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lcy

统计一下一条最短路由另外两条最短路构成的数量。

代码：

#include<cstdio>
#include<cstring>

int t,tt,n,a[105][105];
int solve()
{
	int i,j,k,m=0,f[105][105]={0};
	for(k=0;k<n;k++)
		for(i=0;i<n;i++)
			for(j=0;j<n;j++)
				if(i!=j&&i!=k&&k!=j)
				{
					if(a[i][j]==a[i][k]+a[k][j]&&!f[i][j])
					{
						f[i][j]=1;
						m++;
					}
					if(a[i][j]>a[i][k]+a[k][j])
						return -1;
				}
	return m;
}
int main()
{
	scanf("%d",&t);
	while(t--)
	{
		int i,j,k;
		scanf("%d",&n);
		for(i=0;i<n;i++)
			for(j=0;j<n;j++)
				scanf("%d",&a[i][j]);
		printf("Case %d: ",++tt);
		if((k=solve())==-1)
			puts("impossible");
		else
			printf("%d\n",n*(n-1)-k);
	}
}

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