def test_prod_zero(self):
data = [0,4]
result = prod(data)
self.assertEqual(result, 0)
def test_prod_value_missing(self):
data = [3]
result = prod(data)
self.assertEqual(result, 3)
def test_prod_neg(self):
data = [-3,-20]
result = prod(data)
self.assertEqual(result, 60)
def test_prod_pos_neg(self):
data = [-3,20]
result = prod(data)
self.assertEqual(result, -60)
def test_prod_pos(self):
data = [3,20]
result = prod(data)
self.assertEqual(result, 60)
def test_prod_largenums(self):
data = [383821,494329]
result = prod(data)
self.assertEqual(result, 189733851109)
def test_prod_none(self):
data = []
result = prod(data)
self.assertEqual(result, 1)
def det(A, n):
"""
Using Gaussian elimination and gcd. For integers only!
>>> det( [ [ 4 , 1 ] , [ 1 , 2 ] ] , 2 )
7
>>> det( [ [ -2 , 2 , -3 ] , [ -1 , 1 , 3 ] , [ 2 , 0 , -1 ] ] , 3 )
18
>>> det( [ [ -1 , 1 , 3 ] , [ -2 , 2 , -3 ] , [ 2 , 0 , -1 ] ] , 3 )
-18
"""
d = 1
for i in range(n - 1):
# find first non zero row
if A[i][i] == 0:
j = i + 1
while j < n:
if A[j][i] != 0: break
j += 1
if j == n: return 0
# make it the ith row
A[i], A[j] = A[j], A[i]
d = -d
for j in range(i + 1, n):
a = A[i][i]
b = A[j][i]
c = gcd(a, b)
a //= c
b //= c
# we want to cancel A[j][i]
# assert a * A[j][i] == b * A[i][i]
A[j][i] = 0
# so we multiply both rows so that
#
# A[i][i] = A[j][i] = lcm( A[i][i] , A[j][i] )
#
# and we remove the ith row from the jth row
for k in range(i + 1, n):
A[j][k] = a * A[j][k] - b * A[i][k]
d *= a
return prod(A[i][i] for i in range(n)) // d
def det ( A , n ) : """ Using Gaussian elimination and gcd. For integers only! >>> det( [ [ 4 , 1 ] , [ 1 , 2 ] ] , 2 ) 7 >>> det( [ [ -2 , 2 , -3 ] , [ -1 , 1 , 3 ] , [ 2 , 0 , -1 ] ] , 3 ) 18 >>> det( [ [ -1 , 1 , 3 ] , [ -2 , 2 , -3 ] , [ 2 , 0 , -1 ] ] , 3 ) -18 """ d = 1 for i in range ( n - 1 ) : # find first non zero row if A[i][i] == 0 : j = i + 1 while j < n : if A[j][i] != 0 : break j += 1 if j == n : return 0 # make it the ith row A[i] , A[j] = A[j] , A[i] d = -d for j in range ( i + 1 , n ) : a = A[i][i] b = A[j][i] c = gcd( a , b ) a //= c b //= c # we want to cancel A[j][i] # assert a * A[j][i] == b * A[i][i] A[j][i] = 0 # so we multiply both rows so that # # A[i][i] = A[j][i] = lcm( A[i][i] , A[j][i] ) # # and we remove the ith row from the jth row for k in range ( i + 1 , n ) : A[j][k] = a * A[j][k] - b * A[i][k] d *= a return prod( A[i][i] for i in range( n ) ) // d