ABC172E

https://gyazo.com/a43c39f8615db563d14106992866b62e

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Lately, I've been circling back around and thinking, "Why not just write plainly first?" I'm starting to think that it's a good idea. I can quickly notice when I'm misreading a problem statement, and since I've TLE'd, I can have test code generated when writing complex algorithms.

code:python

def blute(N, M):

"""

>> blute(2, 2)

2

>> blute(2, 3)

18

"""

from itertools import permutations

nums = range(M)

count = 0

for a in permutations(nums, N):

for b in permutations(nums, N):

count += 1

print(count)

code:python

for M in range(1, 10):

for N in range(1, M + 1):

print("N, M, f = ", N, M, blute(N, M))

code::

N, M, f = 1 1 0

N, M, f = 1 2 2

N, M, f = 2 2 2

N, M, f = 1 3 6

N, M, f = 2 3 18

N, M, f = 3 3 12

N, M, f = 1 4 12

N, M, f = 2 4 84

N, M, f = 3 4 264

N, M, f = 4 4 216

N, M, f = 1 5 20

N, M, f = 2 5 260

N, M, f = 3 5 1920

N, M, f = 4 5 6360

N, M, f = 5 5 5280

N, M, f = 1 6 30

N, M, f = 2 6 630

N, M, f = 3 6 8520

N, M, f = 4 6 65160

N, M, f = 5 6 222480

N, M, f = 6 6 190800

N, M, f = 1 7 42

N, M, f = 2 7 1302

N, M, f = 3 7 28140

N, M, f = 4 7 390600

N, M, f = 5 7 3059280

f(N, M)

f(1, M) = M * (M - 1)

code:python

for M in range(2, 100):

r1 = blute(1, M)

r2 = blute(2, M)

r3 = blute(3, M)

debug("r2/r1, r3/r2, r3/r1", r2/r1, r3/r2, r3/r1)

code::

r2/r1, r3/r2, r3/r1 1.0 0.0 0.0

r2/r1, r3/r2, r3/r1 3.0 0.6666666666666666 2.0

r2/r1, r3/r2, r3/r1 7.0 3.142857142857143 22.0

r2/r1, r3/r2, r3/r1 13.0 7.384615384615385 96.0

r2/r1, r3/r2, r3/r1 21.0 13.523809523809524 284.0

r2/r1, r3/r2, r3/r1 31.0 21.612903225806452 670.0

r2/r1, r3/r2, r3/r1 43.0 31.674418604651162 1362.0

r2/r1, r3/r2, r3/r1 57.0 43.719298245614034 2492.0

r2/r1, r3/r2, r3/r1 73.0 57.75342465753425 4216.0

r2/r1, r3/r2, r3/r1 91.0 73.78021978021978 6714.0

r2/r1, r3/r2, r3/r1 111.0 91.8018018018018 10190.0

code::

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