In the "100 game" two players take turns adding, to a running total, any integer from
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
true if the first player to move can force a win, otherwise, return
false. Assume both players play optimally.
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.
Input: maxChoosableInteger = 10, desiredTotal = 0 Output: true
Input: maxChoosableInteger = 10, desiredTotal = 1 Output: true
1 <= maxChoosableInteger <= 20
0 <= desiredTotal <= 300