#822

Medium

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Card Flipping Game

The Card Flipping Game problem asks for the smallest integer that can be facing down but not up after flipping cards.

Problem Statement

You are given two arrays, fronts and backs, each containing n positive integers. The ith card has the integer fronts[i] on its front side and backs[i] on its back side. Initially, each card is placed with its front side up. You may flip any number of cards, and each card can either be flipped or left unchanged.

After flipping cards, an integer is considered good if it is facing down on some card but does not appear on any card's front side. Your task is to return the smallest good integer after any number of flips, or 0 if no such integer exists.

Examples

Example 1

Input: fronts = [1,2,4,4,7], backs = [1,3,4,1,3]

Output: 2

If we flip the second card, the face up numbers are [1,3,4,4,7] and the face down are [1,2,4,1,3]. 2 is the minimum good integer as it appears facing down but not facing up. It can be shown that 2 is the minimum possible good integer obtainable after flipping some cards.

Example 2

Input: fronts = [1], backs = [1]

Output: 0

There are no good integers no matter how we flip the cards, so we return 0.

Constraints

n == fronts.length == backs.length
1 <= n <= 1000
1 <= fronts[i], backs[i] <= 2000

Solution Approach

Iterate Through Cards with Hash Table

The solution involves scanning both the front and back arrays for each card. Use a hash table to store card numbers, checking for conflicts between front and back values. The goal is to find the smallest integer appearing only on the backs after flips.

Find the Minimum Good Integer

To find the minimum good integer, iterate over all integers from 1 to 2000. For each integer, check if it appears on the back side of any card but not on the front. Track the smallest such integer.

Efficient Lookup Using Hash Table

Using a hash table allows for efficient lookups and ensures the solution is optimal. The lookup checks whether a card's back value is unique, minimizing the number of flips and verifying if the integer appears exclusively on the back.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity depends on the number of unique values in the front and back arrays. With n cards, and checking each potential integer between 1 and 2000, the complexity is O(n + m), where n is the number of cards and m is the range of integers (2000). Space complexity is O(n) due to the storage of card values in the hash table.

What Interviewers Usually Probe

Understanding of hash table usage for efficient lookups
Ability to identify and minimize the good integer through array manipulation
Efficient solution approach with an optimal time complexity

Common Pitfalls or Variants

Common pitfalls

Incorrectly handling cases where an integer appears on both the front and back of a card
Overlooking edge cases where no integer is a good integer, leading to a wrong return of 0
Not efficiently managing the time complexity for larger input sizes, leading to performance issues

Follow-up variants

Generalization to handle different ranges of card values
Optimizing the algorithm for larger input sizes, such as n > 1000
Variation where flipping conditions are limited or have additional constraints

FAQ

What is the primary pattern in the Card Flipping Game problem?

The primary pattern involves array scanning combined with hash lookups to efficiently find the smallest good integer after flipping cards.

How can I optimize my solution for large inputs in Card Flipping Game?

By using a hash table to store card values and avoid redundant checks, you can keep the time complexity manageable, even for large inputs.

Why do we need to check for integers appearing on both the front and back in Card Flipping Game?

If an integer appears on both sides of a card, it cannot be considered a good integer, as it would always be facing up on at least one card after a flip.

What is the expected output if no good integer exists in the Card Flipping Game?

If no good integer exists, the expected output is 0, meaning there is no integer that satisfies the conditions after flipping cards.

What is the time complexity of solving the Card Flipping Game?

The time complexity is O(n + m), where n is the number of cards and m is the number of possible integers (2000), as it involves scanning the arrays and checking each integer for validity.

terminal

Solution

Solution 1: Hash Table

We observe that for position $i$, if $\textit{fronts}[i]$ is equal to $\textit{backs}[i]$, then it certainly does not satisfy the condition.

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class Solution:
    def flipgame(self, fronts: List[int], backs: List[int]) -> int:
        s = {a for a, b in zip(fronts, backs) if a == b}
        return min((x for x in chain(fronts, backs) if x not in s), default=0)

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