What strategy ensures Alice can win in the Digit Game?

Alice can guarantee a win by selecting either all single-digit or all double-digit numbers if their total sum exceeds Bob's remaining sum.

How do I handle arrays where sums are equal?

If the sum of chosen numbers equals Bob's sum, Alice cannot win because the condition requires a strictly greater total.

Does the array length affect the solution approach?

No, the approach is linear in array length; you just separate numbers by digit count and sum them.

Can Alice mix single and double-digit numbers?

No, the rules only allow selecting all numbers of one digit type, making the decision straightforward with sums.

Which problem pattern does this exercise focus on?

This problem exemplifies the Array plus Math pattern, emphasizing sum calculations over subsets for decision-making.

#3232

Easy

auto_awesome数组·数学

LeetCode 题解工作台

判断是否可以赢得数字游戏

给你一个正整数数组 nums 。 Alice 和 Bob 正在玩游戏。在游戏中，Alice 可以从 nums 中选择所有个位数或所有两位数，剩余的数字归 Bob 所有。如果 Alice 所选数字之和严格大于 Bob 的数字之和，则 Alice 获胜。如果 Alice 能赢得这场游戏，返回…

数组数学

题目描述

给你一个 正整数 数组 nums。

Alice 和 Bob 正在玩游戏。在游戏中，Alice 可以从 nums 中选择所有个位数或所有两位数，剩余的数字归 Bob 所有。如果 Alice 所选数字之和 严格大于 Bob 的数字之和，则 Alice 获胜。

如果 Alice 能赢得这场游戏，返回 true；否则，返回 false。

示例 1：

输入：nums = [1,2,3,4,10]

输出：false

解释：

Alice 不管选个位数还是两位数都无法赢得比赛。

示例 2：

输入：nums = [1,2,3,4,5,14]

输出：true

解释：

Alice 选择个位数可以赢得比赛，所选数字之和为 15。

示例 3：

输入：nums = [5,5,5,25]

输出：true

解释：

Alice 选择两位数可以赢得比赛，所选数字之和为 25。

提示：

1 <= nums.length <= 100
1 <= nums[i] <= 99

lightbulb

解题思路

方法一：求和

根据题目描述，只要个位数之和不等于两位数之和，那么 Alice 一定可以选择一个较大的和来获胜。

时间复杂度 $O(n)$ ，其中 $n$ 是数组 $\textit{nums}$ 的长度。空间复杂度 $O(1)$ 。

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class Solution:
    def canAliceWin(self, nums: List[int]) -> bool:
        a = sum(x for x in nums if x < 10)
        b = sum(x for x in nums if x > 9)
        return a != b

speed

复杂度分析

指标	值
时间	complexity is O(n) since each number is inspected once to separate digits and compute sums. Space complexity is O(n) for storing single and double-digit groups, though it can be reduced to O(1) with running totals.
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Pay attention to array partitioning by single and double-digit numbers.
question_mark
Notice that summing all numbers of one type is faster than testing combinations.
question_mark
Check boundary cases like all numbers being single-digit or double-digit.

warning

常见陷阱

外企场景

error
Failing to correctly identify single versus double-digit numbers in the array.
error
Attempting unnecessary subset sums instead of total sums of each group.
error
Overlooking edge cases where sums are equal, which does not allow Alice to win.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Allow Alice to pick any numbers whose digit count is prime instead of single/double digits.
arrow_right_alt
Change the winning condition to sum difference >= k instead of strictly greater.
arrow_right_alt
Include negative numbers in nums to see how sum comparison logic adapts.

help

常见问题

外企场景

继续练习

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