.vs/ directory, matrix_multiplication_addition file and binary tree directory (#894)

* Added print function into matrix_multiplication_addition.py and removed blank space in data_structures/binary tree directory

* Removed .vs/ folder per #893

* Rename matrix_multiplication_addition.py to matrix_operation.py

matrix/matrix_operation.py

@@ -0,0 +1,76 @@
+from __future__ import print_function
+
+def add(matrix_a, matrix_b):
+    rows = len(matrix_a)
+    columns = len(matrix_a[0])
+    matrix_c = []
+    for i in range(rows):
+        list_1 = []
+        for j in range(columns):
+            val = matrix_a[i][j] + matrix_b[i][j]
+            list_1.append(val)
+        matrix_c.append(list_1)
+    return matrix_c
+
+def scalarMultiply(matrix , n):
+    return [[x * n for x in row] for row in matrix]
+
+def multiply(matrix_a, matrix_b):
+    matrix_c = []
+    n = len(matrix_a)
+    for i in range(n):
+        list_1 = []
+        for j in range(n):
+            val = 0
+            for k in range(n):
+                val = val + matrix_a[i][k] * matrix_b[k][j]
+            list_1.append(val)
+        matrix_c.append(list_1)
+    return matrix_c
+
+def identity(n):
+    return [[int(row == column) for column in range(n)] for row in range(n)] 
+
+def transpose(matrix):
+    return map(list , zip(*matrix))
+
+def minor(matrix, row, column):
+    minor = matrix[:row] + matrix[row + 1:]
+    minor = [row[:column] + row[column + 1:] for row in minor]
+    return minor
+
+def determinant(matrix):
+    if len(matrix) == 1: return matrix[0][0]
+    
+    res = 0
+    for x in range(len(matrix)):
+        res += matrix[0][x] * determinant(minor(matrix , 0 , x)) * (-1) ** x
+    return res
+
+def inverse(matrix):
+    det = determinant(matrix)
+    if det == 0: return None
+
+    matrixMinor = [[] for _ in range(len(matrix))]
+    for i in range(len(matrix)):
+        for j in range(len(matrix)):
+            matrixMinor[i].append(determinant(minor(matrix , i , j)))
+    
+    cofactors = [[x * (-1) ** (row + col) for col, x in enumerate(matrixMinor[row])] for row in range(len(matrix))]
+    adjugate = transpose(cofactors)
+    return scalarMultiply(adjugate , 1/det)
+
+def main():
+    matrix_a = [[12, 10], [3, 9]]
+    matrix_b = [[3, 4], [7, 4]]
+    matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
+    matrix_d = [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
+    print('Add Operation, %s + %s = %s \n' %(matrix_a, matrix_b, (add(matrix_a, matrix_b))))
+    print('Multiply Operation, %s * %s = %s \n' %(matrix_a, matrix_b, multiply(matrix_a, matrix_b)))
+    print('Identity:  %s \n' %identity(5))
+    print('Minor of %s = %s \n' %(matrix_c, minor(matrix_c , 1 , 2)))
+    print('Determinant of %s = %s \n' %(matrix_b, determinant(matrix_b)))
+    print('Inverse of %s = %s\n'%(matrix_d, inverse(matrix_d)))
+
+if __name__ == '__main__':
+    main()