Question

I’m trying to write a program that will factor any trinomial of the form ax^2+bx+c, but I’m kind of stuck. I’ve got a sequence of 4 for loops that looks like this:

print "Factoring...\n"

for i in range(low_value, high_value):
    for j in range(low_value, high_value):
        for k in range(low_value, high_value):
            for l in range(low_value, high_value):
                print "testing\n"
                if i*k==a & j*l==c & (i*l)+(j*k)==b:
                    print "Your factored Equation is: (" + i + "x + " + j + ")(" + k + "x + " + l + ")"
                else:
                    print "No solution found.\n"
print "testing...\n"

Anyways I know the code is far from optimal but nothing inside the for loops are executing. The “testing…” message at the end is displayed but nothing is printed before that(by that I mean the “testing”, “Your factored equation is:”, or the “No solution found”). Is there some kind of limitation in Python where I can’t use so many for loops at once? Is there something wrong with my syntax that I just am unable to see? Any help would be greatly appreciated 🙂

Answer 1

Apart from the question stated, there are a few problems with the code: 🙂

• Given low_value of -1000 and high_value of 1000, “testing” and “no solution has been found” will be printed ~16 trillion times.
• Execution doesn’t stop when a solution is found.
• print as statement restricts the code to Python2, it is recommended to use the print(stuff) function instead.
• print automatically inserts a newline. \n is not needed.

Here’s a suggested rewrite:

def factor(a, b, c):
    low_value = min(a, b, c)
    high_value = max(a, b, c)
    for i in range(low_value, high_value):
        for j in range(low_value, high_value):
            for k in range(low_value, high_value):
                if i*k != a:
                    # check this clause earlier to improve speed a bit
                    continue
                for l in range(low_value, high_value):
                    if j*l != c:
                        continue
                    if (i*l) + (j*k) != b:
                        continue
                    return (i, j, k, l)
    return None

print("Factoring...")
solution = factor(1, 2, 4)
if solution:
    (i, j, k, l) = solution
    print("Your factored Equation is: (" + i + "x + " + j + ")" +
          "(" + k + "x + " + l + ")")
else:
    print("No solution can be found.")