What is the time complexity of Exclusive Time of Functions?

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

What data structures are used to solve Exclusive Time of Functions?

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

What are the key insights for solving Exclusive Time of Functions?

Insight 1: The problem can be solved efficiently using a stack to keep track of the currently executing function(s). The stack helps manage nested function calls and track execution time. Insight 2: When a 'start' event occurs, we need to check if another function is already running (i.e., the stack is not empty). If so, we add the time elapsed since the last event to the running function's exclusive time.

Which companies ask LeetCode 636. Exclusive Time of Functions in interviews?

This problem is frequently asked at IBM, LinkedIn, Snap, athenahealth.

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Exclusive Time of Functions - LeetCode 636 Solution

Exclusive Time of Functions - Complete Solution Guide

Exclusive Time of Functions is LeetCode problem 636, 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

On a single-threaded CPU, we execute a program containing n functions. Each function has a unique ID between 0 and n-1 . Function calls are stored in a call stack : when a function call starts, its ID is pushed onto the stack, and when a function call ends, its ID is popped off the stack. The function whose ID is at the top of the stack is the current function being executed . Each time a function starts or ends, we write a log with the ID, whether it started or ended, and the timestamp. You are

Detailed Explanation

The problem asks us to calculate the exclusive time of each function in a single-threaded program given a log of function calls. Each log entry indicates whether a function started or ended at a specific timestamp. The exclusive time for a function is the total time it spent actively executing (excluding time spent while another function was called recursively). We need to return an array where the i-th element represents the exclusive time of the function with ID i.

Solution Approach

The solution uses a stack to maintain the order of function calls. We iterate through the logs, parsing each log entry to determine the function ID, event type (start or end), and timestamp. If it's a 'start' event, we check if a function is already running. If so, we add the time elapsed to that function's exclusive time. Then, we push the current function ID onto the stack. If it's an 'end' event, we calculate the exclusive time of the function that just ended, pop it from the stack, and update the previous timestamp.

Step-by-Step Algorithm

Step 1: Initialize an array `exclusive_times` of size `n` with all elements set to 0. This array will store the exclusive time for each function.
Step 2: Initialize an empty stack `stack` to keep track of the currently executing function IDs.
Step 3: Initialize a variable `prev_time` to 0 to store the timestamp of the previous log entry.
Step 4: Iterate through the `logs` array.
Step 5: For each log entry, split the string by ':' to extract the function ID (`fid`), event type (`event`), and timestamp (`timestamp`). Convert `fid` and `timestamp` to integers.
Step 6: If the `event` is 'start':
Step 6a: If the `stack` is not empty, calculate the time elapsed since the previous event (`timestamp - prev_time`) and add it to the exclusive time of the function at the top of the `stack` (`exclusive_times[stack[-1]]`).
Step 6b: Push the current `fid` onto the `stack`.
Step 6c: Update `prev_time` to the current `timestamp`.
Step 7: If the `event` is 'end':
Step 7a: Calculate the exclusive time of the function that just ended (`timestamp - prev_time + 1`) and add it to its corresponding entry in `exclusive_times` (`exclusive_times[stack.pop()]`).
Step 7b: Pop the function ID from the `stack`.
Step 7c: Update `prev_time` to `timestamp + 1`.
Step 8: After iterating through all log entries, return the `exclusive_times` array.

Key Insights

Insight 1: The problem can be solved efficiently using a stack to keep track of the currently executing function(s). The stack helps manage nested function calls and track execution time.
Insight 2: When a 'start' event occurs, we need to check if another function is already running (i.e., the stack is not empty). If so, we add the time elapsed since the last event to the running function's exclusive time.
Insight 3: When an 'end' event occurs, we calculate the exclusive time of the function that just ended, taking into account the time elapsed and the inclusive nature of the 'end' timestamp. We also need to update the 'previous time' accordingly to account for the end event.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Stack.

Companies

Asked at: IBM, LinkedIn, Snap, athenahealth.

Exclusive Time of Functions | LeetCode 636

Medium

Array Stack

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

Solution Code

Available in:

import java.util.List;
import java.util.Stack;

class Solution {
    public int[] exclusiveTime(int n, List<String> logs) {
        int[] exclusive_times = new int[n];
        Stack<Integer> stack = new Stack<>();
        int prev_time = 0;

        for (String log : logs) {
            String[] parts = log.split(":");
            int fid = Integer.parseInt(parts[0]);
            String event = parts[1];
            int timestamp = Integer.parseInt(parts[2]);

            if (event.equals("start")) {
                if (!stack.isEmpty()) {
                    exclusive_times[stack.peek()] += timestamp - prev_time;
                }

                stack.push(fid);
                prev_time = timestamp;
            } else {
                // event == 'end'
                exclusive_times[stack.pop()] += timestamp - prev_time + 1;
                prev_time = timestamp + 1;
            }
        }

        return exclusive_times;
    }
}

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Problem Info

Description

Problem 636: Exclusive Time of Functions - Detailed explanation and solution approaches.

Topics

Array Stack

Companies

IBMLinkedInSnapathenahealth

Stats

Difficulty:Medium

Languages:4

Companies:4

Problem #:636

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

14 steps

1
Step 1: Initialize an array `exclusive_times` of size `n` with all elements set to 0. This array will store the exclusive time for each function.
2
Step 2: Initialize an empty stack `stack` to keep track of the currently executing function IDs.
3
Step 3: Initialize a variable `prev_time` to 0 to store the timestamp of the previous log entry.
4
Step 4: Iterate through the `logs` array.
5
Step 5: For each log entry, split the string by ':' to extract the function ID (`fid`), event type (`event`), and timestamp (`timestamp`). Convert `fid` and `timestamp` to integers.
6
Step 6: If the `event` is 'start':
7
Step 6a: If the `stack` is not empty, calculate the time elapsed since the previous event (`timestamp - prev_time`) and add it to the exclusive time of the function at the top of the `stack` (`exclusive_times[stack[-1]]`).
8
Step 6b: Push the current `fid` onto the `stack`.
9
Step 6c: Update `prev_time` to the current `timestamp`.
10
Step 7: If the `event` is 'end':
11
Step 7a: Calculate the exclusive time of the function that just ended (`timestamp - prev_time + 1`) and add it to its corresponding entry in `exclusive_times` (`exclusive_times[stack.pop()]`).
12
Step 7b: Pop the function ID from the `stack`.
13
Step 7c: Update `prev_time` to `timestamp + 1`.
14
Step 8: After iterating through all log entries, return the `exclusive_times` array.

💡

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 time complexity is directly proportional to the number of logs because we process each log entry once. The space complexity is determined by the size of the stack, which in the worst case, can grow to be proportional to the number of logs if all entries are start events.

📖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

Without Stack (Less Efficient)

Instead of a stack, one could iterate through all logs for each function ID to compute the total time, which requires a nested loop and multiple passes through the data.

Time: O(n * m), where n is the number of functions and m is the number of logs.Space: O(1)

Trade-offs: This method trades space for time. It's simpler conceptually but less efficient for larger datasets, and it's generally not practical for problems with a significant number of logs or functions. The stack based approach offers a significant efficiency gain.

✨

Key Insights

1Insight 1: The problem can be solved efficiently using a stack to keep track of the currently executing function(s). The stack helps manage nested function calls and track execution time.
2Insight 2: When a 'start' event occurs, we need to check if another function is already running (i.e., the stack is not empty). If so, we add the time elapsed since the last event to the running function's exclusive time.
3Insight 3: When an 'end' event occurs, we calculate the exclusive time of the function that just ended, taking into account the time elapsed and the inclusive nature of the 'end' timestamp. We also need to update the 'previous time' accordingly to account for the end event.

📚

Key Terms Explained

For Students

Array

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

Stack

LIFO structure - Last In, First Out. Like a stack of plates!

Edge Cases

Edge case 1: Nested function calls. The stack ensures the correct function's time is updated when a nested function returns.
Edge case 2: Consecutive start events. The code correctly attributes time elapsed to the current function on the stack before pushing the new function ID.
Edge case 3: Correctly handling end events. The `timestamp - prev_time + 1` calculation handles the inclusive nature of the end timestamp.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not accounting for the inclusive nature of the 'end' timestamp. For example, forgetting to add 1 to the time calculation when an 'end' event occurs (timestamp - prev_time + 1).

✗Common mistake 2: Incorrectly updating `prev_time` after an 'end' event. It should be set to `timestamp + 1` to represent the beginning of the next time slot.

✗Common mistake 3: Not handling the case where a function is already running when a new 'start' event occurs. Failing to update the running function's time before pushing the new function onto the stack.

✅

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: Performance monitoring in a multi-threaded application. The logs can represent the execution time of different threads or processes, and the algorithm can be used to calculate the total CPU time consumed by each thread.

🏦Real-world scenario 2: Call stack analysis in debuggers. Debuggers use call stacks to track the sequence of function calls, and this algorithm can be used to measure the time spent in each function during a debugging session. This information can be useful for identifying performance bottlenecks or unexpected behavior.

💡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: September 5, 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 13

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

@InterviewProJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What problems are best solved with a stack?

Stacks excel at: matching problems (parentheses validation), next greater/smaller element, expression evaluation, backtracking, and undo operations. The key pattern is LIFO (Last In, First Out) - when you need to access the most recently added element.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Exclusive Time of Functions"?

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

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