4. An x matrix that is filled wit tmbers 1,2,32 is a magic square if the sum of

Question

4. An x matrix that is filled wit tmbers 1,2,32 is a magic square if the sum of the elements in each row, in each column, and in the two diagonals is the same value. Write a program that reads in 16 values from a file containing each row of 4 values in each line, and tests whether they form a magic square when put into a 4 x 4 table as a list of lists. You need to test two features: (a) Does each of the numbers 1,2,... , 16 occur in the the file? (b) When the numbers are put into a square, are the sums of the rows, columns and diagonals equal to each other? 5. Create a python functions that rotates the elements of a list by one position Consider a function rotate(a list, direction) that takes as arguments the ist to rotate, and the direction (left or right) of rotation. Rotate the list in place.

Explanation / Answer

# first_question answer

fname = open('data.txt','r') #open file and read

line = fname.readline()

a=[]

diagonal1_sum=diagonal2_sum=0

i = 0

allow = True

x=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]

while(line != ""):

a.append(map(int,line.split()))

for j in xrange(4): # to check the numbers btwn 1 to 16

if a[i][j] not in x:

allow = False

break

i=i+1

line = fname.readline()

if(allow==False):

break

if(allow):

row_sum = 0

is_same = 1

for i in xrange(4): # row_sum

if(i==0):

row_sum = sum(a[i])

else:

if(row_sum != sum(a[i])):

is_same = 0

break

if(is_same):

col_sum = 0

is_col_same = 1

for i in xrange(4): #col_sum

sum1 = 0

if(is_col_same):

for j in xrange(4):

sum1+=a[j][i]

if(i==0):

col_sum = sum1

else:

if(col_sum!=sum1 and col_sum!=row_sum):

is_col_same = 0

break

else:

break

if(is_col_same):

diag_sum = 0

for i in xrange(4): #diag_sum

diag_sum+=a[i][i]

if(diag_sum == col_sum and col_sum == row_sum):

print "GIVEN MATRIX IS MAGIC SQUARE"

else:

print "GIVEN MATRIX IS NOT MAGIC SQUARE"

else:

print "GIVEN MATRIX IS NOT MAGIC SQUARE"

else:

print "GIVEN MATRIX IS NOT MAGIC SQUARE"

else:

print "GIVEN MATRIX VALUE IS NOT BETWEEN 1 TO 16"

#second_ques answer

# function to rotate list left or right by one position

def rotate(a,direction):

b=[]

if(direction == "right"): #right_position

print "rotate right"

for j in range(0,len(a)):

b.append(a[len(a)-1])

for i in range(0,len(a)-1):

b.append(a[i])

print b

a=b

b=[]

elif(direction == "left"): #left_position

print "rotate left"

for j in range(0,len(a)):

for i in range(1,len(a)):

b.append(a[i])

b.append(a[0])

print b

a=b

b=[]

else:

print "INvalid Direction"

a=map(int,raw_input().split())

rotate(a,'right')

rotate(a,'left')

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