You are given an array of positive integers nums.Alice and Bob are playing a game. In the game, Alice can choose either all single-digit numbers or all double-digit numbers from nums, and the rest of the numbers are given to Bob. Alice wins if the sum of her numbers is strictly greater than the sum of Bob's numbers.Return true if Alice can win this game, otherwise, return false. Example 1:Input: nums = [1,2,3,4,10]Output: falseExplanation:Alice cannot win by choosing either single-digit or double-digit numbers.Example 2:Input: nums = [1,2,3,4,5,14]Output: trueExplanation:Alice can win by choosing single-digit numbers which have a sum equal to 15.Example 3:Input: nums = [5,5,5,25]Output: trueExplanation:Alice can win by choosing double-digit numbers which have a sum equal to 25
Question
You are given an array of positive integers nums.Alice and Bob are playing a game. In the game, Alice can choose either all single-digit numbers or all double-digit numbers from nums, and the rest of the numbers are given to Bob. Alice wins if the sum of her numbers is strictly greater than the sum of Bob's numbers.Return true if Alice can win this game, otherwise, return false. Example 1:Input: nums = [1,2,3,4,10]Output: falseExplanation:Alice cannot win by choosing either single-digit or double-digit numbers.Example 2:Input: nums = [1,2,3,4,5,14]Output: trueExplanation:Alice can win by choosing single-digit numbers which have a sum equal to 15.Example 3:Input: nums = [5,5,5,25]Output: trueExplanation:Alice can win by choosing double-digit numbers which have a sum equal to 25
Solution
To solve this problem, we can follow these steps:
-
Initialize two variables,
singleDigitSumanddoubleDigitSum, to 0. These will hold the sum of all single-digit numbers and double-digit numbers in the array, respectively. -
Iterate over the array. For each number, check if it is a single-digit number (i.e., less than 10) or a double-digit number (i.e., greater than or equal to 10).
-
If it is a single-digit number, add it to
singleDigitSum. If it is a double-digit number, add it todoubleDigitSum. -
After iterating over the array, check if either
singleDigitSumordoubleDigitSumis greater than the sum of all numbers in the array divided by 2. If either is true, return true. Otherwise, return false.
Here is a Python solution following the above steps:
def canAliceWin(nums):
singleDigitSum = 0
doubleDigitSum = 0
totalSum = sum(nums)
for num in nums:
if num < 10:
singleDigitSum += num
else:
doubleDigitSum += num
return singleDigitSum > totalSum / 2 or doubleDigitSum > totalSum / 2
This function works by calculating the sum of all single-digit and double-digit numbers in the array, and then checking if either sum is greater than half of the total sum of all numbers in the array. If either sum is greater than half of the total sum, Alice can win the game by choosing those numbers.
Similar Questions
Alice and Bob came up with a rather strange game. They have an array of integers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛. Alice chooses a certain integer k𝑘 and tells it to Bob, then the following happens:Bob chooses two integers i𝑖 and j𝑗 (1≤i<j≤n1≤𝑖<𝑗≤𝑛), and then finds the maximum among the integers ai,ai+1,…,aj𝑎𝑖,𝑎𝑖+1,…,𝑎𝑗;If the obtained maximum is strictly greater than k𝑘, Alice wins, otherwise Bob wins.Help Alice find the maximum k𝑘 at which she is guaranteed to win.InputEach test consists of multiple test cases. The first line contains a single integer t𝑡 (1≤t≤1041≤𝑡≤104) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n𝑛 (2≤n≤5⋅1042≤𝑛≤5⋅104) — the number of elements in the array.The second line of each test case contains n𝑛 integers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛 (1≤ai≤1091≤𝑎𝑖≤109) — the elements of the array.It is guaranteed that the sum of n𝑛 over all test cases does not exceed 5⋅1045⋅104.OutputFor each test case, output one integer — the maximum integer k𝑘 at which Alice is guaranteed to win.ExampleinputCopy642 4 1 751 2 3 4 521 1337 8 16510 10 10 10 9103 12 9 5 2 3 2 9 8 2outputCopy3101592NoteIn the first test case, all possible subsegments that Bob can choose look as follows: [2,4],[2,4,1],[2,4,1,7],[4,1],[4,1,7],[1,7][2,4],[2,4,1],[2,4,1,7],[4,1],[4,1,7],[1,7]. The maximums on the subsegments are respectively equal to 4,4,7,4,7,74,4,7,4,7,7. It can be shown that 33 is the largest integer such that any of the maximums will be strictly greater than it.In the third test case, the only segment that Bob can choose is [1,1][1,1]. So the answer is 00.
Given an integer array nums, return true if you can partition the array into two subsets such that the sum of the elements in both subsets is equal or false otherwise. Example 1:Input: nums = [1,5,11,5]Output: trueExplanation: The array can be partitioned as [1, 5, 5] and [11].Example 2:Input: nums = [1,2,3,5]Output: falseExplanation: The array cannot be partitioned into equal sum subsets. Constraints:1 <= nums.length <= 2001 <= nums[i] <= 100
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Have the function ArrayChallenge(arr) take the array of numbers stored in arr and return the string true if any combination of numbers in the array (excluding the largest number) can be added up to equal the largest number in the array, otherwise return the string false. For example: if arr contains [4, 6, 23, 10, 1, 3] the output should return true because 4 + 6 + 10 + 3 = 23. The array will not be empty, will not contain all the same elements, and may contain negative numbers.
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