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Problem StatementHemanth is assigned the task of identifying a prominent figure within a group of individuals who have certain connections.There is a group of people, each of whom knows some of the others. This knowledge is represented as a matrix where each row and column corresponds to a person in the group. The value in the matrix cell (i, j) indicates whether person i knows person j. This matrix is guaranteed to be symmetric.A prominent figure is someone who is well-connected within the group. More specifically, a person is considered prominent if they are known by more people in the group than they know others.Write a program to help Hemanth that takes the number of people in the group and their connections as input. The program should determine if there is a prominent figure within the group using Warshall's Algorithm.If such a person exists, the program should identify their index (position) within the list of people. If there is no prominent figure in the group, print the message accordingly.Input format :The first line of input consists of an integer N, representing the number of individuals in the group.The following N lines will contain N space-separated integers, representing the connections of a person with others.Output format :If a prominent figure is found, print "A prominent figure is present at index X." where X is the index of the prominent figure (0-based).Otherwise, print "There is no prominent figure in the group."Refer to the sample output for the formatting specifications.Code constraints :The test cases will fall under the following constraints:1 ≤ N ≤ 10Each element of the adjacency matrix is either 0 or 1.Sample test cases :Input 1 :40 1 1 00 0 1 00 0 0 00 0 1 0Output 1 :A prominent figure is present at index 2.Input 2 :50 1 1 0 00 0 0 0 00 0 0 1 00 0 0 0 10 0 0 0 0Output 2 :There is no prominent figure in the group.Input 3 :30 1 10 0 00 1 0Output 3 :A prominent figure is present at index 1.Note :

Question

Problem StatementHemanth is assigned the task of identifying a prominent figure within a group of individuals who have certain connections.There is a group of people, each of whom knows some of the others. This knowledge is represented as a matrix where each row and column corresponds to a person in the group. The value in the matrix cell (i, j) indicates whether person i knows person j. This matrix is guaranteed to be symmetric.A prominent figure is someone who is well-connected within the group. More specifically, a person is considered prominent if they are known by more people in the group than they know others.Write a program to help Hemanth that takes the number of people in the group and their connections as input. The program should determine if there is a prominent figure within the group using Warshall's Algorithm.If such a person exists, the program should identify their index (position) within the list of people. If there is no prominent figure in the group, print the message accordingly.Input format :The first line of input consists of an integer N, representing the number of individuals in the group.The following N lines will contain N space-separated integers, representing the connections of a person with others.Output format :If a prominent figure is found, print "A prominent figure is present at index X." where X is the index of the prominent figure (0-based).Otherwise, print "There is no prominent figure in the group."Refer to the sample output for the formatting specifications.Code constraints :The test cases will fall under the following constraints:1 ≤ N ≤ 10Each element of the adjacency matrix is either 0 or 1.Sample test cases :Input 1 :40 1 1 00 0 1 00 0 0 00 0 1 0Output 1 :A prominent figure is present at index 2.Input 2 :50 1 1 0 00 0 0 0 00 0 0 1 00 0 0 0 10 0 0 0 0Output 2 :There is no prominent figure in the group.Input 3 :30 1 10 0 00 1 0Output 3 :A prominent figure is present at index 1.Note :

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Solution

To solve this problem, we can use Warshall's Algorithm, which is used to find the shortest path in a graph. However, in this case, we will use it to find a prominent figure in a group. Here are the steps to solve this problem:

  1. First, we need to read the number of individuals in the group from the input. This will be the size of our matrix.

  2. Next, we need to read the connections of each person. This will be represented as a matrix where each row and column corresponds to a person in the group. The value in the matrix cell (i, j) indicates whether person i knows person j.

  3. We will then apply Warshall's Algorithm on this matrix. The algorithm works by comparing each element in the matrix with the sum of its row and column. If the element is greater than the sum, it means that the person knows more people than they are known by, and therefore, they are not a prominent figure.

  4. We will keep track of the index of the person who is known by more people than they know others. This person is considered as a prominent figure.

  5. If such a person exists, we will print their index. If there is no such person, we will print a message saying that there is no prominent figure in the group.

Here is a Python code snippet that implements the above steps:

N = int(input())
matrix = [list(map(int, input().split())) for _ in range(N)]

for k in range(N):
    for i in range(N):
        for j in range(N):
            matrix[i][j] = matrix[i][j] or (matrix[i][k] and matrix[k][j])

prominent = -1
for i in range(N):
    if matrix[i].count(1) < matrix.count([1 if j == i else 0 for j in range(N)]):
        prominent = i
        break

if prominent != -1:
    print(f"A prominent figure is present at index {prominent}.")
else:
    print("There is no prominent figure in the group.")

This code reads the number of individuals and their connections from the input, applies Warshall's Algorithm to find a prominent figure, and prints the result.

This problem has been solved

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