Card Flipping Game

Problem Description

You are given two 0-indexed integer arrays fronts and backs of length n, where the ith card has the positive integer fronts[i] printed on the front and backs[i] printed on the back. Initially, each card is placed on a table such that the front number is facing up and the other is facing down. You may flip over any number of cards (possibly zero).

After flipping the cards, an integer is considered good if it is facing down on some card and not facing up on any card.

Return the minimum possible good integer after flipping the cards. If there are no good integers, return 0.

Key Insights

• The integers on the fronts that are visible after flipping should not appear on the backs that are facing down.
• We can track which integers are present on the fronts and backs of the cards.
• The minimum good integer is the smallest integer that is on the back of any card but not on the front of any card.
• We can use a set to efficiently check the existence of numbers on the fronts.

Space and Time Complexity

Time Complexity: O(n), where n is the number of cards. We iterate through the cards to build the sets and find the minimum good integer. Space Complexity: O(n), as we maintain sets to track the integers on the fronts and backs.

Solution

To solve the problem, we will:

1. Use a set to store all integers on the fronts.
2. Use another set to store all integers on the backs.
3. Iterate through the numbers from 1 to 2000 (the maximum possible value) and check which number is on the backs but not on the fronts.
4. Return the smallest such number or 0 if no number meets the criteria.

Code Solutions