 Wrong constraints in Cook-a-Code (MODME)

Both the codes will output the same value for any input for the given constraints.

The only difference is:

if n <= m:
print('A')
continue

Which is supposed to work absolutely fine as if N ≤ M, player A can choose N from the range 1 to M.

This will only fail in the case N ≤ 0 but constraints clearly say 1 ≤ N ≤ 10^{18}.

My friend @sarthakmanna submitted this and got NZEC.

What he did is pretty simple: 7 / 0 will raise ZeroDivisionError and will only be called if n == 0 2 Likes

Already discussed here, though I haven’t seen any plans for dealing with the fallout from it 3 Likes

I see 2 Likes

I’m unable to understand first test case with N =4, M=2.
Lets say, A will start the game with 0, now he can add any number from 1 to M. Lets say A added 2 to 0, shouts 2 and pass 2 to B.
B can add any number from 1 to M. B adds 2 to 2, resulting it in 4. He shouts 4 which is actually N. So, B must be the winner ?
And many other scenario is possible.

The starting value is 0.

If N = 1, the first player can add 1 and win the game.
If N = 2, the first player can add 2 and win the game.

If N = 3, the first player can add 1 or 2:

If N = 4, the first player will add 1

The second player can add 1 or 2:

Therefore, the first player will always win

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This is called game theory.

For N = 10 and M = 5

Player A can win for 1, 2, 3, 4.

For 5 though, no matter what player A does, player B can capture 5.

But for 6, player A can go to 1. Now, if we calculate all possibilities of player B, it’ll be in the range 2 to 5. Now, A can add 6 minus the value B selected.

For 7, A will start at 2, then B's range would be from 3 to 6. A can add 7 minus the value B selected.

Same for 8, 9.

But for 10, B will win as B will just capture 5 after what A plays. Then A has to select a value from 6 to 9. B will just add 10 minus what A selects.

Same for all other values.

If N % (M + 1) = 0, B wins. Else A.

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If N=4, the first player will add 1

Here, why first player can’t add 2 ? Since it’s written he will add any number from 1 to M, and M being 2. The first 3 case is clear to me.

If the first player adds 2, then the second player will also add 2, winning the game.

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Ok, thanks, got it! Point here was A is always trying to win the game and starting first, A has an advantage. I was simply lost in case where why B can’t be a winner, neglecting the normal human behavior of winning if possible. The problem also mentions “If both players play optimally”

1 Like