Day 22 part 2: we're done!
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225
2019/day22.py
225
2019/day22.py
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@ -1,168 +1,83 @@
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EX1 = [
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"deal with increment 7",
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"deal into new stack",
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"deal into new stack",
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]
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EX2 = [
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"cut 6",
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"deal with increment 7",
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"deal into new stack",
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]
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EX3 = [
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"deal with increment 7",
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"deal with increment 9",
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"cut -2",
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]
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EX4 = [
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"deal into new stack",
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"cut -2",
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"deal with increment 7",
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"cut 8",
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"cut -4",
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"deal with increment 7",
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"cut 3",
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"deal with increment 9",
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"deal with increment 3",
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"cut -1",
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]
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"""
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Disclaimer: I could not solve part 2 on my own and had to look at some tips
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abour modular arithmetic. Gotta gid gud at discrete maths... What I've
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understood to get it to work in just a few milliseconds is commented below.
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Dumb part 1 is somewhere in Git history.
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"""
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def main():
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with open("day22.txt") as input_file:
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lines = [l.rstrip() for l in input_file.readlines()]
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# Part 1
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deck = list(range(10))
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# deck = list(range(10007))
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deck = part1(deck, EX3)
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print(deck)
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# deck = part1(deck, lines)
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# print(f"Position of card 2019: {deck.index(2019)}.")
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deck_len = 10007
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o, i = shuffle(deck_len, lines)
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print(o, i)
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for n in range(deck_len):
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if (o + i * n) % deck_len == 2019:
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break
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print(f"Position of card 2019: {n}.")
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# Part 2
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part2(10, 1, EX3, pos=0); input()
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part2(10, 1, EX3, pos=1); input()
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part2(10, 1, EX3, pos=2); input()
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part2(10, 1, EX3, pos=3); input()
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part2(10, 1, EX3, pos=4); input()
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part2(10, 1, EX3, pos=5); input()
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part2(10, 1, EX3, pos=6); input()
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part2(10, 1, EX3, pos=7); input()
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part2(10, 1, EX3, pos=8); input()
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part2(10, 1, EX3, pos=9); input()
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# part2(10007, 1, lines, pos=8191)
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# part2(119315717514047, 101741582076661, lines)
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# print(f"2020th card: {deck[2020]}.")
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deck_len = 119315717514047
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num_shuf = 101741582076661
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o, i = shuffle(deck_len, lines)
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# Each shuffle makes increment a multiple of its previous value % deck_len,
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# and new offset is the old offset incremented by this value.
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#
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# Using the offset and increment of the first shuffle (O1, I1), we can write
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# a function for n shuffles as they will use those same values:
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# On = On-1 + (In * O1) % deck_len
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# In = In-1 * I1 % deck_len
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#
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# We observe that the increment for n shuffles is I1^n-1 % deck_len.
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#
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# We observe that the offset is dependent of each previous increment value:
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# O0 = 0
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# O1 = k
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# O2 = k + I2*k (or: O1 + I2*O1)
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# O3 = k + I2*O1 + I3*O2 (or: O2 + I3*O2)
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# and this can be factorised as:
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# On = k * (1 + I1 + I2 + ... + In-1) % deck_len
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# This expression corresponds to a geometric series, which has a formula to
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# calculate its n-point value, here for our offset function:
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# On = O1 (1 - I1^n) (1 - I1)^n
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inc_n = pow(i, num_shuf, deck_len)
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ofs_n_op1 = 1 - pow(i, num_shuf, deck_len)
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ofs_n_op2 = pow(1 - i, deck_len - 2, deck_len)
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ofs_n = (o * ofs_n_op1 * ofs_n_op2) % deck_len
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print(f"Card at pos 2020: {(ofs_n + inc_n * 2020) % deck_len}")
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def part1(deck, commands):
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for command in commands:
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# Deal into new stack.
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if command.endswith("k"):
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deck.reverse()
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def shuffle(deck_len, raw_commands):
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commands = parse_commands(raw_commands)
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offset, inc = 0, 1
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for c, a in commands:
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if c == "dins":
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inc = -inc
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offset += inc
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elif c == "cut":
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offset += inc * a
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elif c == "dwi":
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inc *= pow(a, deck_len - 2, deck_len) # Fermat's lil theorem.
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offset %= deck_len
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inc %= deck_len
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return offset, inc
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def parse_commands(raw_commands):
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commands = []
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for rc in raw_commands:
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if rc.endswith("k"):
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commands.append(("dins", 0))
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continue
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arg = int(command[command.rfind(" "):])
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# Deal with increment.
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if command[0] == "d":
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new_deck = [None] * len(deck)
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for i in range(len(deck)):
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new_deck[(i * arg) % len(new_deck)] = deck[i]
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deck = new_deck
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# Cut.
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elif command[0] == "c":
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cut, deck = deck[:arg], deck[arg:]
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deck += cut
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return deck
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def part2(deck_len, num_shuf, commands, pos=2020):
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required = find_required(deck_len, commands, pos)
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for c, r in zip(commands, required):
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print(f"- Command '{c}' requires knowing value at {r[0]} for {r[1]}.")
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print(f"Which gives us value at {pos}.")
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deck = {i: i for r in required for i in r}
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print(required)
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print("Shuffling...")
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shuffle(deck, required)
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print(f"Card at {pos}: {deck[pos]}.")
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def find_required(deck_len, commands, pos):
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required = []
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for command in reversed(commands):
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dest = pos
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if command.endswith("k"):
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pos = req_dins(pos, deck_len)
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required.append((pos, dest))
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continue
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arg = int(command[command.rfind(" "):])
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if command[0] == "d":
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print(f"What's req for {pos} in deal with increment {arg}?")
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pos = req_dwi(pos, deck_len, arg)
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print(f"- answer: {pos}.")
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elif command[0] == "c":
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pos = req_cut(pos, deck_len, arg)
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required.append((pos, dest))
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required.reverse()
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return required
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def req_dins(pos, deck_len):
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return deck_len - 1 - pos
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def req_cut(pos, deck_len, n):
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return (pos + n) % deck_len
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def req_dwi(pos, deck_len, inc):
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# Straight is (i * arg) % deck_len = j
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# (i * arg) = modinv(j, deck_len)
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# i = modinv(j, deck_len) / arg
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# damn idk
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return (pos * inc - deck_len) % deck_len
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def shuffle(deck, required):
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for required_pair in required:
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from_pos, to_pos = required_pair
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deck[to_pos] = deck[from_pos]
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def dins(parameter_list):
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pass
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def cut(parameter_list):
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pass
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def dwi(parameter_list):
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pass
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arg = int(rc[rc.rfind(" "):])
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if rc[0] == "d":
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commands.append(("dwi", arg))
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elif rc[0] == "c":
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commands.append(("cut", arg))
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return commands
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if __name__ == "__main__":
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# main()
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assert req_cut(0, 10, 3) == 3
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assert req_cut(1, 10, 3) == 4
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assert req_cut(2, 10, 3) == 5
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assert req_cut(5, 10, 3) == 8
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assert req_cut(8, 10, 3) == 1
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assert req_cut(0, 10, -4) == 6
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assert req_cut(0, 10, -4) == 6
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assert req_cut(1, 10, -4) == 7
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assert req_cut(2, 10, -4) == 8
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assert req_cut(3, 10, -4) == 9
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assert req_cut(4, 10, -4) == 0
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assert req_cut(5, 10, -4) == 1
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assert req_cut(6, 10, -4) == 2
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assert req_cut(7, 10, -4) == 3
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assert req_cut(8, 10, -4) == 4
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assert req_cut(9, 10, -4) == 5
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assert req_dins(0, 10) == 9
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assert req_dins(1, 10) == 8
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assert req_dins(2, 10) == 7
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assert req_dins(8, 10) == 1
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assert req_dins(9, 10) == 0
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assert req_dwi(0, 10, 3) == 0
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assert req_dwi(1, 10, 3) == 7
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assert req_dwi(2, 10, 3) == 4
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assert req_dwi(3, 10, 3) == 1
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assert req_dwi(4, 10, 3) == 8
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assert req_dwi(5, 10, 3) == 5
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assert req_dwi(6, 10, 3) == 2
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assert req_dwi(7, 10, 3) == 9
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assert req_dwi(8, 10, 3) == 6
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assert req_dwi(9, 10, 3) == 3
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main()
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