486 Predict the Winner.py

#!/usr/bin/python3
"""
Given an array of scores that are non-negative integers. Player 1 picks one of
the numbers from either end of the array followed by the player 2 and then
player 1 and so on. Each time a player picks a number, that number will not be
available for the next player. This continues until all the scores have been
chosen. The player with the maximum score wins.

Given an array of scores, predict whether player 1 is the winner. You can assume
each player plays to maximize his score.

Example 1:
Input: [1, 5, 2]
Output: False
Explanation: Initially, player 1 can choose between 1 and 2.
If he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player
2 chooses 5, then player 1 will be left with 1 (or 2).
So, final score of player 1 is 1 + 2 = 3, and player 2 is 5.
Hence, player 1 will never be the winner and you need to return False.
Example 2:
Input: [1, 5, 233, 7]
Output: True
Explanation: Player 1 first chooses 1. Then player 2 have to choose between 5
and 7. No matter which number player 2 choose, player 1 can choose 233.
Finally, player 1 has more score (234) than player 2 (12), so you need to return
True representing player1 can win.
Note:
1 <= length of the array <= 20.
Any scores in the given array are non-negative integers and will not exceed
10,000,000.
If the scores of both players are equal, then player 1 is still the winner.
Author: Rajeev Ranjan

"""
from collections import defaultdict


class Solution:
    def PredictTheWinner(self, nums):
        """
        Let F[i][j] be the max score choose from A[i:j]. The player has two
        options
        F[i][j] = max(
            A[i] + sum(A[i+1:j]) - F[i+1][j],
            A[j-1] + sum(A[i:j-1]) - F[i][j-1]
        )
        Compare F[0][n] and sum(A) - F[0][n] t0 determine the winner

        :type nums: List[int]
        :rtype: bool
        """
        l = len(nums)
        gross = [0]  # sum [0:i]
        for e in nums:
            gross.append(gross[-1] + e)

        F = defaultdict(lambda: defaultdict(int))
        for i in range(l-1, -1, -1):
            for j in range(i+1, l+1):
                F[i][j] = max(
                    gross[j] - gross[i] - F[i+1][j],
                    gross[j] - gross[i] - F[i][j-1]
                )
        return F[0][l] >= (gross[-1] - F[0][l])


if __name__ == "__main__":
    assert Solution().PredictTheWinner([1, 5, 2]) == False
    assert Solution().PredictTheWinner([1, 5, 233, 7]) == True