Metric Matrice
时间限制：1000 ms | 内存限制：65535 KB
难度：1
描述
Given as input a square distance matrix, where a[i][j] is the distance between point i and point j, determine if the distance matrix is "a metric" or not.
A distance matrix a[i][j] is a metric if and only if
1. a[i][i] = 0
2, a[i][j]> 0 if i != j
3. a[i][j] = a[j][i]
4. a[i][j] + a[j][k] >= a[i][k] i ¹ j ¹ k
输入
The first line of input gives a single integer, 1 ≤ N ≤ 5, the number of test cases. Then follow, for each test case,
* Line 1: One integer, N, the rows and number of columns, 2 <= N <= 30
* Line 2..N+1: N lines, each with N space-separated integers
(-32000 <=each integer <= 32000).
输出
Output for each test case , a single line with a single digit, which is the lowest digit of the possible facts on this list:
* 0: The matrix is a metric
* 1: The matrix is not a metric, it violates rule 1 above
* 2: The matrix is not a metric, it violates rule 2 above
* 3: The matrix is not a metric, it violates rule 3 above
* 4: The matrix is not a metric, it violates rule 4 above
样例输入
2
4
0 1 2 3
1 0 1 2
2 1 0 1
3 2 1 0
2
0 3
2 0
样例输出
0
3
#include<stdio.h>
#include<string.h>
int x[35][35];
void slove(int n)
{
for(int i=0;i<n;++i)
{
if(x[i][i]!=0)
{
printf("1
");
return;
}
}
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{
if(i!=j&&x[i][j]<=0)
{
printf("2
");
return;
}
}
}
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{
if(i!=j&&x[i][j]!=x[j][i])
{
printf("3
");
return;
}
}
}
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{
for(int k=0;k<n;++k)
{
if(i!=j&&j!=k&&i!=k&&x[i][j]+x[j][k]<x[i][k])
{
printf("4
");
return ;
}
}
}
}
printf("0
");
}
int main()
{
int t,n;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
for(int i=0;i<n;++i)
{
for(int j=0;j<n;++j)
{
scanf("%d",&x[i][j]);
}
}
slove(n);
}
return 0;
}