Week 2.py

Shuffle Program: O(n)

Trailing os program: O(n)

def MultiplyingMatrices(matrix1,matrix2,finalMatrix):
  for i in range(len(matrix1)): #iterating through the rows
    for j in range(len(matrix1)): #iterating through elements in each row
      for k in range(len(matrix1)): #iterating through the columns
        counter = matrix1[i][k] * matrix2[k][j] #product of the two number in matrix
        finalMatrix[i][j] = counter + finalMatrix[i][j] #adding the product to the value in the final matrix
        

  return(finalMatrix)

def MultiplyingMatrix(matrix1,B):

  for i in range(len(matrix1)): #iterating through the rows
    for j in range(len(matrix1)): #iterating through elements in each row
      matrix1[i][j] = matrix1[i][j]*B
      
     

  return(matrix1)

def AddingMatrices(matrix1,matrix2):

  for i in range (len(matrix1)): #iterating through the rows
    for j in range(len(matrix1)): #iterating through elements in each row
      matrix1[i][j] = matrix1[i][j] + matrix2[i][j]
      

  return(matrix1)

def SubtractingMatrices(matrix1,matrix2):

  for i in range (len(matrix1)): #iterating through the rows
    for j in range(len(matrix1)): #iterating through elements in each row
      matrix1[i][j] = matrix1[i][j] - matrix2[i][j]

  return(matrix1)


#Computing A = B*C - 2(B+C)

B = [[3,1],[2,4]]
C = [[2,10],[4,3]]
matrix = [[0,0],[0,0]]

x = MultiplyingMatrices(B,C,matrix)
y = AddingMatrices(B,C)
z = MultiplyingMatrix(y,2)

print("A = " + str(SubtractingMatrices(x,z)))

def HighestPerfectSquare(x):
    """Given a positive integer this function will return the highest perfect square that is either equal or less than the number"""

    n = 1 #number to test 
    perfectSquare = 1 #current highest perfect square
        
    while n**2 <= x :
        perfectSquare = n**2
        n = n+1
        
        
    return("The Highest perfect square is >> " + str(perfectSquare))
    
    Pseudocode for finding the highest perfect square given a number

HighestPerfectSquare(x)
	
	n <- 1
	perfectSquare <- 1

	WHILE n*n <= x
		perfectSquare <- n*n
		n <- n+1
	RETURN(perfcetSquare)
  
  Task 2:
Shuffle Algorithm: O(n)
Factoral Algorithm: O(n)

Task 3:

Pseudocode for functions that add, subtract and multiple matrices.

These functions work by accepting two matrices which are arrays where each row in the matrix is an array within the array. 
example:
matrix = [[1,2,3],
	  [4,5,6],
	  [7,8,9]]

AddingMatrices(matrix1,matrix2)

	for i <- 0 to length[matrix1]
		for j <- 0 length[matrix1]
			matrix1[i][j] <- matrix1[i][j] + matrix2[i][j]

	RETURN(matrix1)

Big O notation for this algorithm = O(n^2)

SubtractingMatrices(matrix1,matrix2)

	for i <- 0 to length[matrix1]
		for j <- 0 length[matrix1]
			matrix1[i][j] <- matrix1[i][j] - matrix2[i][j]

	RETURN(matrix1)
Big O notation for this algorithm = O(n^2)

when you want to multiply a matrix by and integer or a float

MultiplyingMatrix(matrix,x)

	for i <- 0 to length[matrix]
		for j <- 0 to length[matrix]
			matrix[i][j] <- matrix[i][j] * x


	RETURN(matrix)

Big O notation for this algorithm = O(n^2)


when you want to multiply a matrix by another matrix
This fuction only works if you provide a Final matrix full of 0s
for example
[[1,2],[3,4]] * [[3,5],[2,4]]
The resulting matrix would be a 2 by 2 matrix so the final matrix would be entered as [[0,0],[0,0]]

MultiplyingMatrices(matrix1,matrix2,finalMatrix)

	for i <- 0 to length[matrix1]
		for j <- 0 to length[matrix1]
			for k <- 0 to length[matrix1]
				counter <- matrix1[i][k] * matrix2[k][j] 
				finalMatrix[i][j] <- counter + finalMatrix[i][j]


	RETURN(finalMatrix)

Big O notation for this algorithm = O(n^3)


Method of caculating A = B*C - 2*(B+C)

x <- MultiplyingMatrix(B,C,finalMatrix)
y <- AddingMatrices(B.C)
z <- MultiplyingMatrix(y,2)

finalResult <- SubtractingMatrices(x,z)