What is the time complexity of Average Waiting Time?

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

What data structures are used to solve Average Waiting Time?

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

What are the key insights for solving Average Waiting Time?

Insight 1: The chef starts working on a customer's order as soon as the chef is idle or the customer arrives, whichever is later. Insight 2: To calculate the waiting time for each customer, we need to keep track of the current time the chef is available.

Which companies ask LeetCode 1701. Average Waiting Time in interviews?

This problem is frequently asked at DE Shaw, Instacart.

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Average Waiting Time - LeetCode 1701 Solution

Average Waiting Time - Complete Solution Guide

Average Waiting Time is LeetCode problem 1701, 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 is a restaurant with a single chef. You are given an array customers , where customers[i] = [arrival i , time i ]: arrival i is the arrival time of the i th customer. The arrival times are sorted in non-decreasing order. time i is the time needed to prepare the order of the i th customer. When a customer arrives, he gives the chef his order, and the chef starts preparing it once he is idle. The customer waits till the chef finishes preparing his order. The chef does not prepare food for mo

Detailed Explanation

The problem asks us to calculate the average waiting time for customers at a restaurant with a single chef. We are given a list of customers, where each customer is represented by their arrival time and the time it takes to prepare their order. The chef serves customers in the order they arrive, and the chef can only work on one order at a time. The waiting time for a customer is the time they spend waiting between arriving and receiving their completed order. The input `customers` is sorted by arrival time in non-decreasing order. We need to compute the average of all customers' waiting times.

Solution Approach

The solution uses a simulation approach. We iterate through the `customers` array, maintaining a variable `current_time` that represents the time the chef is available to start a new order. For each customer, we update `current_time` to be the maximum of the customer's arrival time and the chef's current available time. We then add the customer's preparation time to `current_time`. The waiting time for that customer is calculated by subtracting the arrival time from `current_time`. We sum up the waiting times for all customers and then divide by the number of customers to get the average waiting time.

Step-by-Step Algorithm

Step 1: Initialize `total_wait_time` to 0 and `current_time` to 0.
Step 2: Iterate through the `customers` array.
Step 3: For each customer, extract the arrival time (`arrival`) and preparation time (`prep_time`).
Step 4: Update `current_time` to `max(arrival, current_time) + prep_time`. This represents the time the chef finishes preparing the customer's order.
Step 5: Calculate the waiting time for the current customer as `current_time - arrival`.
Step 6: Add the waiting time to `total_wait_time`.
Step 7: After iterating through all customers, calculate the average waiting time by dividing `total_wait_time` by the number of customers.
Step 8: Return the average waiting time.

Key Insights

Insight 1: The chef starts working on a customer's order as soon as the chef is idle or the customer arrives, whichever is later.
Insight 2: To calculate the waiting time for each customer, we need to keep track of the current time the chef is available.
Insight 3: Since the customer arrival times are sorted, we can iterate through the customers array in order to simulate the chef's workflow and maintain the current time.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Simulation.

Companies

Asked at: DE Shaw, Instacart.

Average Waiting Time | LeetCode 1701

Medium

Array Simulation

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public double averageWaitingTime(int[][] customers) {
        double total_wait_time = 0;
        double current_time = 0;
        
        for (int[] customer : customers) {
            int arrival = customer[0];
            int prep_time = customer[1];
            
            current_time = Math.max(arrival, current_time) + prep_time;
            total_wait_time += current_time - arrival;
        }
        
        return total_wait_time / customers.length;
    }
}

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Problem Info

Description

Problem 1701: Average Waiting Time - Detailed explanation and solution approaches.

Topics

Array Simulation

Companies

DE ShawInstacart

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:1701

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

8 steps

1
Step 1: Initialize `total_wait_time` to 0 and `current_time` to 0.
2
Step 2: Iterate through the `customers` array.
3
Step 3: For each customer, extract the arrival time (`arrival`) and preparation time (`prep_time`).
4
Step 4: Update `current_time` to `max(arrival, current_time) + prep_time`. This represents the time the chef finishes preparing the customer's order.
5
Step 5: Calculate the waiting time for the current customer as `current_time - arrival`.
6
Step 6: Add the waiting time to `total_wait_time`.
7
Step 7: After iterating through all customers, calculate the average waiting time by dividing `total_wait_time` by the number of customers.
8
Step 8: Return the average waiting time.

💡

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(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is linear because we process each customer in the input array exactly once. The space complexity is constant because we are not using any additional data structures that scale with the input size.

📖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

Priority Queue

If the customer arrival times weren't sorted, one could use a priority queue to keep track of customers waiting to be served. The priority queue would be ordered by arrival time. This would allow us to process customers in the correct order even if they weren't given in sorted order.

Time: O(n log n) due to the heap operations of adding and removing from the priority queue.Space: O(n) to store all the customers in the priority queue.

Trade-offs: This approach is not necessary in this problem since the arrival times are sorted. But if the input isn't sorted, then this could be used. The tradeoff is between an O(n log n) vs O(n) time complexity, and O(n) vs O(1) space complexity. The simulation approach is better for sorted inputs.

✨

Key Insights

1Insight 1: The chef starts working on a customer's order as soon as the chef is idle or the customer arrives, whichever is later.
2Insight 2: To calculate the waiting time for each customer, we need to keep track of the current time the chef is available.
3Insight 3: Since the customer arrival times are sorted, we can iterate through the customers array in order to simulate the chef's workflow and maintain the current time.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: The first customer arrives at time 0. The solution correctly handles this case because `current_time` is initialized to 0, and `max(arrival, current_time)` will correctly calculate the start time for the chef.
Edge case 2: Consecutive customers arrive before the chef finishes the previous order. The solution handles this by ensuring that `current_time` is always updated to the later of the arrival time or the chef's availability, ensuring that the next customer's order isn't started before it's possible.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to take the maximum of the arrival time and the current time. This leads to incorrect calculation of when the chef starts the order, and an inaccurate waiting time.

✗Common mistake 2: Integer division when calculating the average. Ensure `total_wait_time` and the number of customers are treated as floats to get an accurate average.

✅

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: Simulating a queue in a bank or call center to optimize the number of tellers or operators needed to minimize customer waiting times.

🏦Real-world scenario 2: Optimizing task scheduling in a multi-core processor to minimize the average completion time of tasks.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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: August 21, 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

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

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

@InterviewProJul 7

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

@CodeNinjaJun 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.

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 "Average Waiting Time"?

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 simulation techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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