Output For each graph, produce a line listing the weak vertices ordered from least to greatest. Sample Input 1 9 0 1 1 1 0 0 0 0 0 100000100 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 001100000 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 10 1 0 -1 Sample Output 1 18 0

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Engineers like to use triangles. It probably has something to do with how a triangle can provide a lot of structural strength. 

Output
For each graph, produce a line listing the weak vertices ordered from least to
greatest.
Sample Input 1
9
0 1 1 1 0 0 0 0 0
1 0 0 0 0 0 1 0 0
1 0 0 1 0 1 0 0 0
1 0 1 0 0 1 1 0 0
0 0 0 0 0 0 1 1 0
000000110
0 0 1 1 0 0 0 0 0
0 1 0 1 1 0 0 1 0
0 0 0 0 1 0 1 0 1
0 0 0 0 0 0 0 1 0
1
0
-1
Sample Output 1
18
0
↓
Transcribed Image Text:Output For each graph, produce a line listing the weak vertices ordered from least to greatest. Sample Input 1 9 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 000000110 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 -1 Sample Output 1 18 0 ↓
Problem A
Weak Vertices
<Hide
Engineers like to use triangles. It probably has something to do with how a
triangle can provide a lot of structural strength. We can describe the physical
structure of some designs using an undirected graph. We'll say vertex i is part of a
triangle if i has two different neighbors j and k such that j and k are neighbors of
each other. For this problem, find weak vertices in graphs - those vertices that is
not part of any triangle.
A
Figure 1: An illustration of the weak vertices (which are shaded) from the sample input graph.
Input
Input consists of up to 100 graphs. Each starts with an integer, 1 ≤ n ≤ 20,
giving the number of vertices in the graph. Next come n lines with n integers on
each line, which describe an n x n adjacency matrix for the graph. Vertices are
numbered from 0 to n - 1. If the adjacency matrix contains a one at row r,
column c (where 0 ≤r, c≤ n − 1), it means that there is an edge from vertex r
to vertex c. Since the graph is undirected, the adjacency matrix is symmetric. The
end of input is marked by a value of -1 for n.
Transcribed Image Text:Problem A Weak Vertices <Hide Engineers like to use triangles. It probably has something to do with how a triangle can provide a lot of structural strength. We can describe the physical structure of some designs using an undirected graph. We'll say vertex i is part of a triangle if i has two different neighbors j and k such that j and k are neighbors of each other. For this problem, find weak vertices in graphs - those vertices that is not part of any triangle. A Figure 1: An illustration of the weak vertices (which are shaded) from the sample input graph. Input Input consists of up to 100 graphs. Each starts with an integer, 1 ≤ n ≤ 20, giving the number of vertices in the graph. Next come n lines with n integers on each line, which describe an n x n adjacency matrix for the graph. Vertices are numbered from 0 to n - 1. If the adjacency matrix contains a one at row r, column c (where 0 ≤r, c≤ n − 1), it means that there is an edge from vertex r to vertex c. Since the graph is undirected, the adjacency matrix is symmetric. The end of input is marked by a value of -1 for n.
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