How to Solve Can I Win Problem
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Can I Win
In the "100 game" two players take turns adding, to a running total, any integer from 1 to 10. The player who first causes the running total to reach or exceed 100 wins. What if we change the game so ...
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Understanding the Can I Win Problem
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Problem Statement
In the "100 game" two players take turns adding, to a running total, any integer from 1 to 10. The player who first causes the running total to reach or exceed 100 wins. What if we change the game so that players cannot re-use integers? For example, two players might take turns drawing from a common pool of numbers from 1 to 15 without replacement until they reach a total >= 100. Given two integers maxChoosableInteger and desiredTotal, return true if the first player to move can force a win, otherwise, return false. Assume both players play optimally.
Can I Win
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Examples
maxChoosableInteger = 10, desiredTotal = 11
false
No matter which integer the first player choose, the first player will lose. The first player can choose an integer from 1 up to 10. If the first player choose 1, the second player can only choose integers from 2 up to 10. The second player will win by choosing 10 and get a total = 11, which is >= desiredTotal. Same with other integers chosen by the first player, the second player will always win.
maxChoosableInteger = 10, desiredTotal = 0
true
maxChoosableInteger = 10, desiredTotal = 1
true
Constraints
1 <= maxChoosableInteger <= 20
0 <= desiredTotal <= 300
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