# 【LeetCode】486. Predict the Winner 解题报告（Python）

# 题目描述：

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. 1 <= length of the array <= 20.
2. Any scores in the given array are non-negative integers and will not exceed 10,000,000.
3. If the scores of both players are equal, then player 1 is still the winner.

# 解题方法

``````class Solution(object):
def PredictTheWinner(self, nums):
"""
:type nums: List[int]
:rtype: bool
"""
_sum = sum(nums)
self.f_map, self.s_map = dict(), dict()
player1 = self.f(nums, 0, len(nums)-1, self.f_map)
print(player1)
return player1 >= _sum / 2.0

def f(self, nums, start, end, f_map):
if start == end:
return nums[start]
if (start, end) not in f_map:
f_val = max(nums[start] + self.s(nums, start+1, end, self.s_map), nums[end] + self.s(nums, start, end-1, self.s_map))
f_map[(start, end)] = f_val
return f_map[(start, end)]

def s(self, nums, start, end, s_map):
if start == end:
return 0
if (start, end) not in s_map:
s_val = min(self.f(nums, start+1, end, self.f_map), self.f(nums, start, end-1, self.f_map))
s_map[(start, end)] = s_val
return s_map[(start, end)]
``````

``````class Solution(object):
def PredictTheWinner(self, nums):
"""
:type nums: List[int]
:rtype: bool
"""
_sum = sum(nums)
self.f_map, self.s_map = dict(), dict()
player1 = self.f(nums, 0, len(nums)-1)
return player1 >= _sum / 2.0

def f(self, nums, start, end):
if start == end:
return nums[start]
if (start, end) not in self.f_map:
f_val = max(nums[start] + self.s(nums, start+1, end), nums[end] + self.s(nums, start, end-1))
self.f_map[(start, end)] = f_val
return self.f_map[(start, end)]

def s(self, nums, start, end):
if start == end:
return 0
if (start, end) not in self.s_map:
s_val = min(self.f(nums, start+1, end), self.f(nums, start, end-1))
self.s_map[(start, end)] = s_val
return self.s_map[(start, end)]
``````

DP，未完待续。

# 日期

2018 年 9 月 8 日 ———— 美好的周末，从刷题开始