What is the time complexity of First Day Where You Have Been in All the Rooms?

The optimal solution has a time complexity of O(n).

What data structures are used to solve First Day Where You Have Been in All the Rooms?

This problem uses Array, Dynamic Programming. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving First Day Where You Have Been in All the Rooms?

Insight 1: The problem can be modeled as a dynamic programming problem where dp[i] represents the first day you visit room 'i'. Insight 2: The transition between rooms is governed by the 'nextVisit' array and the parity of the number of visits to a room.

Which companies ask LeetCode 1997. First Day Where You Have Been in All the Rooms in interviews?

This problem is frequently asked at ByteDance.

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First Day Where You Have Been in All the Rooms - LeetCode 1997 Solution

First Day Where You Have Been in All the Rooms - Complete Solution Guide

First Day Where You Have Been in All the Rooms is LeetCode problem 1997, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

There are n rooms you need to visit, labeled from 0 to n - 1 . Each day is labeled, starting from 0 . You will go in and visit one room a day. Initially on day 0 , you visit room 0 . The order you visit the rooms for the coming days is determined by the following rules and a given 0-indexed array nextVisit of length n : Assuming that on a day, you visit room i , if you have been in room i an odd number of times ( including the current visit), on the next day you will visit a room with a lower or

Detailed Explanation

The problem presents a scenario where you need to visit 'n' rooms in a specific order determined by the 'nextVisit' array. You start at room 0 on day 0. If you've visited room 'i' an odd number of times, you go to room 'nextVisit[i]' on the next day. If you've visited room 'i' an even number of times, you go to room '(i + 1) mod n' on the next day. The task is to find the first day when you have visited all 'n' rooms at least once. The final answer should be returned modulo 10^9 + 7.

Solution Approach

The solution uses dynamic programming. 'dp[i]' stores the first day you visit room 'i'. To calculate 'dp[i]', we consider the day we first visited room 'i-1' (dp[i-1]). On the subsequent day (dp[i-1] + 1), we move to room 'j = nextVisit[i-1]'. Then, to return to room 'i-1' to make an even number of visits, it takes 'dp[i-1] - dp[j]' days. Therefore, the total days required to reach room 'i' from the start is 'dp[i] = (dp[i-1] + 1) + (dp[i-1] - dp[j]) + 1 = 2 * dp[i-1] - dp[j] + 2'. The modulo operation is applied to keep the result within the required range.

Step-by-Step Algorithm

Step 1: Initialize a dynamic programming array 'dp' of size 'n' with all elements set to 0. 'dp[i]' will store the first day when room 'i' is visited.
Step 2: Iterate from 'i = 1' to 'n - 1'.
Step 3: For each 'i', get 'j = nextVisit[i - 1]', the room visited after the first visit to room 'i - 1'.
Step 4: Calculate 'dp[i]' using the recurrence relation: dp[i] = (2 * dp[i - 1] - dp[j] + 2) % MOD. Apply modulo arithmetic at each step to avoid overflow.
Step 5: Return 'dp[n - 1]' as the final answer (the first day all rooms have been visited), typecasted to int.

Key Insights

Insight 1: The problem can be modeled as a dynamic programming problem where dp[i] represents the first day you visit room 'i'.
Insight 2: The transition between rooms is governed by the 'nextVisit' array and the parity of the number of visits to a room.
Insight 3: Carefully handle modulo arithmetic to prevent integer overflows, especially when dealing with subtractions.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Dynamic Programming.

Companies

Asked at: ByteDance.

First Day Where You Have Been in All the Rooms | LeetCode 1997

Medium

Array Dynamic Programming

Time: O(n)Space: O(n)

Solution Code

Available in:

class Solution {
    public int firstDayBeenInAllRooms(int[] nextVisit) {
        int n = nextVisit.length;
        int MOD = (int) 1e9 + 7;

        long[] dp = new long[n];

        for (int i = 1; i < n; i++) {
            // dp[i] is the first day we arrive at room i.
            // To get to room i, we must have come from room i-1.
            //
            // The day we first arrive at room i-1 is dp[i-1]. This is the 1st visit (odd).
            // On day dp[i-1] + 1, we go to room j = nextVisit[i-1].
            //
            // To get back from room j to room i-1, it takes (dp[i-1] - dp[j]) days.
            // So we arrive back at room i-1 for the 2nd time (even) on day:
            // (dp[i-1] + 1) + (dp[i-1] - dp[j])
            //
            // On the next day, we move to room i.
            // So, dp[i] = (dp[i-1] + 1) + (dp[i-1] - dp[j]) + 1
            // dp[i] = 2 * dp[i-1] - dp[j] + 2
            
            int j = nextVisit[i - 1];
            
            // Applying the recurrence relation with modulo arithmetic.
            dp[i] = (2 * dp[i - 1] - dp[j] + 2) % MOD;
            if (dp[i] < 0) {
                dp[i] += MOD;
            }
        }

        return (int) dp[n - 1];
    }
}

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Problem Info

Description

Problem 1997: First Day Where You Have Been in All the Rooms - Detailed explanation and solution approaches.

Topics

Array Dynamic Programming

Companies

ByteDance

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1997

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

5 steps

1
Step 1: Initialize a dynamic programming array 'dp' of size 'n' with all elements set to 0. 'dp[i]' will store the first day when room 'i' is visited.
2
Step 2: Iterate from 'i = 1' to 'n - 1'.
3
Step 3: For each 'i', get 'j = nextVisit[i - 1]', the room visited after the first visit to room 'i - 1'.
4
Step 4: Calculate 'dp[i]' using the recurrence relation: dp[i] = (2 * dp[i - 1] - dp[j] + 2) % MOD. Apply modulo arithmetic at each step to avoid overflow.
5
Step 5: Return 'dp[n - 1]' as the final answer (the first day all rooms have been visited), typecasted to int.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The algorithm iterates through the 'nextVisit' array once, which takes O(n) time. The 'dp' array of size 'n' stores the results. Therefore, the space complexity is O(n).

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Simulation

Simulate the process of visiting rooms day by day until all rooms have been visited. Keep track of the rooms visited and the current day.

Time: O(n * k), where k is the number of days it takes to visit all rooms. In the worst case, k could be very large.Space: O(n) to store the visited rooms.

Trade-offs: The simulation approach is conceptually simpler but can be much slower for larger inputs because it has a potentially very high time complexity. The dynamic programming approach provides a guaranteed O(n) time complexity.

✨

Key Insights

1Insight 1: The problem can be modeled as a dynamic programming problem where dp[i] represents the first day you visit room 'i'.
2Insight 2: The transition between rooms is governed by the 'nextVisit' array and the parity of the number of visits to a room.
3Insight 3: Carefully handle modulo arithmetic to prevent integer overflows, especially when dealing with subtractions.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Dynamic Programming

Breaking complex problems into smaller subproblems and storing results.

Edge Cases

Edge case 1: 'nextVisit[i]' can be 0. The solution correctly handles this case because the recurrence relation will work appropriately even when 'j = 0'.
Edge case 2: Large values of 'dp[i]' can cause integer overflow. The solution uses modulo arithmetic to prevent this issue.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not using modulo arithmetic, which can lead to integer overflow, resulting in incorrect answers, especially with larger inputs.

✗Common mistake 2: Incorrectly deriving the recurrence relation for the dynamic programming approach. The logic behind transitioning between rooms based on odd/even visits needs to be carefully considered.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Resource allocation where resources are accessed in a specific order based on certain conditions. For example, scheduling tasks in a system where the next task depends on the completion status of previous tasks.

🏦Real-world scenario 2: Game development where the player needs to visit certain locations in a particular sequence to unlock new areas. The 'nextVisit' array can represent the dependencies between locations.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 18, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

Should I use top-down (memoization) or bottom-up (tabulation)?

Start with top-down (recursion + memoization) as it directly maps to the recursive thinking and handles only needed subproblems. Convert to bottom-up for better space efficiency and to avoid stack overflow. Bottom-up is often faster due to no recursion overhead.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "First Day Where You Have Been in All the Rooms"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether dynamic programming techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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