Python Program to find out the determinant of a given special matrix

Suppose, we have a tree with n vertices, where each vertex is labeled from 1 to n. The root of the tree has the label 1, and each vertex weights wi. Now a nxn matrix A is formed where A(x,y) = Wf(x, y) where f(x, y) is the least common predecessor of vertex x and y. We have to find out the determinant of matrix A. The edges of the matrix, weights, and the total number of vertices are given to us as input.

So, if the input is like input_array = [[1, 2], [1, 3], [1, 4], [1, 5]], weights = [1, 2, 3, 4, 5], vertices = 5, then the output will be 24.

The matrix A is given as =

the determinant of this matrix is 24.

To solve this, we will follow these steps −

• w := an empty list
• for i in range 0 to vertices, do
  • add weights[i] and a new list to w
• for each i, item in enumerate(input_array), do
  • p := item[0]
  • q := item[1]
  • insert q - 1 at the end of w[p - 1, 1]
  • insert p - 1 at the end of w[q - 1, 1]
• det := 1
• stack := a stack containing a tuple (0, 0)
• while stack is not empty, do
  • i, weights := delete top element from stack
  • det := (det * (w[i, 0] - weights)) mod (10^9 + 7)
  • for t in w[i][1], do
    • add tuple containing (t,w[i,0]) to the stack
    • for each t in w[i][1], do
      • delete i from w[t,1]
• return det

Example

Let us see the following implementation to get better understanding −

 Live Demo

def solve(input_array, weights, vertices):
   w = [[weights[i],[]] for i in range(vertices)]
   for i, item in enumerate(input_array):
      p,q = item[0], item[1]
      w[p - 1][1].append(q - 1)
      w[q - 1][1].append(p - 1)
   det = 1
   stack = [(0,0)]
   while stack:
      i, weights = stack.pop()
      det = (det * (w[i][0] - weights)) % (10**9 + 7)
      stack += [(t,w[i][0]) for t in w[i][1]]
      for t in w[i][1]:
         w[t][1].remove(i)
   return det
print(solve([[1, 2], [1, 3], [1, 4], [1, 5]], [1, 2, 3, 4, 5], 5))

Input

[[1, 2], [1, 3], [1, 4], [1, 5]], [1, 2, 3, 4, 5], 5

Output

24

Arnab Chakraborty

Updated on 18-May-2021 06:14:42

• Related Questions & Answers
• Program to find out the number of special numbers in a given range in Python
• Program to find out special types of subgraphs in a given graph in Python
• C++ code to find out the sum of the special matrix elements
• C++ Program to Compute Determinant of a Matrix
• Determinant of a Matrix in C++ Program
• Program to Find Out the Special Nodes in a Tree in Python
• Program to find out the value of a given equation in Python
• Program to find number of special positions in a binary matrix using Python
• Program to find the transpose of given matrix in Python
• Determinant of a Matrix in C++?
• Program to find out the greatest subarray of a given length in python
• C++ Program to find out if a palindromic matrix can be made from a given matrix
• Python Program to find out the number of sets greater than a given value
• Program to Find Out the Occurrence of a Digit from a Given Range in Python
• Python Program to find the transpose of a matrix