Problem Statement:

You are given an array of positive integers nums and want to maximize your score by playing a game.

On each turn, you can either:

Pick two numbers x and y from nums. Multiply x and y together to get a new number z. Replace nums with the result of replacing x and y with z in nums. For example, if nums = [1,2,3,4], you can:

Pick x=2 and y=4, which makes nums = [1,8,3]. Pick x=1 and y=3, which makes nums = [3,8]. Pick x=3 and y=8, which makes nums = [24]. The game ends when there is only one element left in nums.

Return the largest possible score you can achieve.

Solution:

The problem statement is asking us to maximize the score by playing the game. We can simply start by understanding the problem constraints and approaches to find out the possible solutions.

There are a total of three operations that we can perform in this game, as given below:

• Pick two numbers from nums
• Multiply x and y to get the new number z
• Replace nums by replacing x and y with z in nums

As per the problem statement, we need to play the game until only one element is left in nums. To maximize the score, we need to pick the two highest numbers in nums and multiply them with each other. Once we have the new number z, we replace the two original numbers with z in nums.

We can repeat this process until we have only one element left in nums. This way, we can maximize the score of the game.

Let's take an example to understand this. Suppose nums = [1,2,3,4]. We need to perform the following steps:

Step 1: Pick x=3 and y=4, which makes nums = [1,2,12]. Step 2: Pick x=2 and y=12, which makes nums = [1,24]. Step 3: Pick x=1 and y=24, which makes nums = [24*1 = 24].

Now, we have only one element in nums, and the score of the game is 24.

To implement this solution, we can first sort the nums array in descending order. Then, we can pick the two highest numbers from nums and multiply them with each other. Once we have the new number z, we can replace the two original numbers with z in nums.

We can repeat this process until we have only one element left in nums. Finally, we return the last remaining element as the score of the game.

Here's the code to implement the above solution:

def canIWin(nums): nums.sort(reverse=True)

while len(nums) > 1:
    x = nums[0]
    y = nums[1]
    z = x * y
    nums = [z] + nums[2:]
    
return nums[0]

Testing the function

print(canIWin([1, 2, 3, 4])) # Output: 24 print(canIWin([5, 4, 3, 2, 1])) # Output: 120

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