Can I Win
In the "100 game" two players take turns adding, to a running total, any integer from 1 to 10.
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.
Example 1
Input: maxChoosableInteger = 10, desiredTotal = 11
Output: false
Explanation: 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.
Example 2
Input: maxChoosableInteger = 10, desiredTotal = 0
Output: true
Example 3
Input: maxChoosableInteger = 10, desiredTotal = 1
Output: true
Constraints
- 1 <= maxChoosableInteger <= 20
- 0 <= desiredTotal <= 300
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