I was doing this problem on Spoj. The solution of this problem is that first player always wins.
Can anyone give me proof of this?
№ | Пользователь | Рейтинг |
---|---|---|
1 | tourist | 4009 |
2 | jiangly | 3773 |
3 | Radewoosh | 3646 |
4 | ecnerwala | 3624 |
5 | jqdai0815 | 3620 |
5 | Benq | 3620 |
7 | orzdevinwang | 3612 |
8 | Geothermal | 3569 |
8 | cnnfls_csy | 3569 |
10 | Um_nik | 3396 |
Страны | Города | Организации | Всё → |
№ | Пользователь | Вклад |
---|---|---|
1 | Um_nik | 163 |
2 | cry | 161 |
3 | maomao90 | 160 |
4 | -is-this-fft- | 159 |
5 | awoo | 158 |
6 | atcoder_official | 157 |
7 | adamant | 155 |
7 | nor | 155 |
9 | maroonrk | 152 |
10 | Dominater069 | 148 |
Название |
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Proof by contradiction :
Say the initial state is always a losing state. This means regardless of the number the first player picks , the second player ends up with a winning state (if not , the initial state would have been a winning state). Say the first player picks 1 and the second player ends up with {2,3,4,.....,N} which is a winning state. Say the second player picks X now and provides the first player with state S (a losing state) , the first player could have just picked X and forced the second player to state S ( a losing state) which is a contradiction. Hence the first player always wins.
Thanks.. :))