I've taken 1 course in Java and 1 in C++ and now I'm tinkering with Python (love it so far). My module I'm currently working on is designed to solve a certain puzzle. To understand the code you'll need to understand the puzzle:
There is an upside down triangle with n amount of numbers on the top row. For example, if n were 3 the triangle would look like this:
_ _ _
_ _
_
There are a total of 6 spaces in this example. The puzzle is to find all the possible solutions so that the difference between any 2 numbers above 1 number is equal to the number below. Below is an example of one particular solution. In this example, we can use the numbers 1 - 6 since there are 6 spaces. Note that we can say "3 - 2 = 1" and also "2 - 3 = 1" for this puzzle (just take the absolute value of the difference):
6 2 5
4 3
1
This is my solution. My code attempts to find all possible solutions, but I have hit a roadblock. I can't remember my Grade 12 statistics anymore and am having trouble testing all the possible combinations of the puzzle. I'm getting confused as to how to do this. For example, I understand that in this puzzle order matters, so I would say "6 choose 6" which is "6!" or 720 different combinations. I don't know how to systematically rotate through all of them. I'll post my code below. Any help is greatly appreciated.
"""Currently this module contains functions which solve
the upside down triangle puzzle thing."""
def triangle(toprow):
"""This function solves all possible answers for the
funny upside down triangle puzzle thing from calculus."""
print("You entered a puzzle with " + str(toprow) + " spaces on the top row.\n")
# Find the total number of numbers to be used in the puzzle
total = toprow
for i in range(0, toprow):
total = total + i
# State how many possibilities there are for the puzzle
if (toprow > 17):
print("There are A LOT of possibilities. Hopefully the program doesn't crash...\n")
elif (toprow > 4):
print("There are " + "%e" % npr(total) + " possibilities to test.\n")
else:
print("There are " + str(npr(total)) + " possibilities to test.\n")
# Apply the initial numbers to the triangle
tri = []
line = []
count = total
for k in range(0, toprow):
line = []
for l in range(0, (toprow - k)):
line.append(count)
count = count - 1
tri.append(line)
print("The initial triangle is: " + str(tri) + "\n")
# The array tri is correct up to here
# Ex. triangle(3) gives tri = [[6, 5, 4], [3, 2], [1]]
# Do all the possible arrangements of the numbers. Ugh.
# Currently this is not working. I need help here!
sols = []
for m in range(0, toprow):
for n in range(0, (toprow - m)):
for o in range(m, toprow):
for p in range(n, (toprow - o)):
print("Testing triangle " + str(tri) + "...")
if (test(tri)):
sols.append(tri)
print("The triangle " + str(tri) + " is a solution.")
temp = tri[o][n]
if (o == (toprow - 1)):
tri[o][n] = tri[m][n]
tri[m][n] = temp
elif (n == (toprow - o - 1)):
tri[o][n] = tri[(o + 1)][0]
tri[(o + 1)][0] = temp
else:
tri[o][n] = tri[o][(n + 1)]
tri[o][(n + 1)] = temp
return sols
def test(arr):
"""This complimentary function tests the array to see
if it is a solution."""
count = len(arr) - 1
# Test if the difference between two tops is equal to
# their corresponding bottom (directly below the pair)
for i in range(count):
for j in range(count - i):
if (((arr[i][j] - arr[i][(j + 1)]) != arr[(i + 1)][j]) and ((arr[i][(j + 1)] - arr[i][j]) != arr[(i + 1)][j])):
return 0
return 1
def npr(n):
"""This function determines how many possible arrangements
of the numbers there are (nPr from Math 12 statistics)."""
# Do n factorial (there is a math module function but ya)
for i in range(1, n):
n = n * i
return n
def triprint(arr):
"""This function prints the triangle."""
count = len(arr)
# Print the numbers
for i in range(0, count):
print(str(arr[i]))
