First to Count to Target- Google Top Interview Questions


Problem Statement :


You are playing a game against a friend where in each round you pick a number from 1 to k to add to a shared running total that initially starts from 0. 
The first person to reach or exceed the running total to target wins.

Given that you go first, return whether you can force a win if everyone plays optimally.

Constraints

k ≤ 30

target ≤ 1,000

Example 1

Input

k = 5

target = 9

Output

True

Explanation

If we pick 3 first, then whether your friend picks 1, 2, ..., or 5 , we can always reach 9 by picking 5 next.



Example 2

Input

k = 3

target = 4

Output

False

Explanation

No mater what we pick your friend can pick 3 to reach 4.


Solution :



title-img 




                        Solution in C++ :

bool solve(int k, int target) {
    return target % (k + 1);
}
                    




                        Solution in Python : 
                            
class Solution:
    def solve(self, k, target):
        @functools.lru_cache(None)
        def f(total):
            win = False

            if k + total >= target:
                return True

            for i in range(1, k + 1):
                new_total = total + i
                win = win or not f(new_total)

            return win

        return f(0)


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