What is the time complexity of Validate Stack Sequences?

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

What data structures are used to solve Validate Stack Sequences?

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

What are the key insights for solving Validate Stack Sequences?

Insight 1: The core idea is to simulate the push and pop operations using a stack data structure. The pushed array provides the order of insertions, and the popped array determines the expected order of removals. Insight 2: Maintaining a pointer (index) to the popped array helps track the expected order of pops. We continuously push elements from the pushed array onto the stack and then attempt to pop elements from the stack if they match the expected popped order.

Which companies ask LeetCode 946. Validate Stack Sequences in interviews?

This problem is frequently asked at Apollo.io.

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Validate Stack Sequences - LeetCode 946 Solution

Validate Stack Sequences - Complete Solution Guide

Validate Stack Sequences is LeetCode problem 946, 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

Given two integer arrays pushed and popped each with distinct values, return true if this could have been the result of a sequence of push and pop operations on an initially empty stack, or false otherwise. Example 1: Input: pushed = [1,2,3,4,5], popped = [4,5,3,2,1] Output: true Explanation: We might do the following sequence: push(1), push(2), push(3), push(4), pop() -> 4, push(5), pop() -> 5, pop() -> 3, pop() -> 2, pop() -> 1 Example 2: Input: pushed = [1,2,3,4,5], popped = [4,3,5,1,2] Outpu

Detailed Explanation

The problem asks us to determine whether a given `popped` array could have been the result of a sequence of push and pop operations on an initially empty stack, given an array `pushed` representing the sequence of elements being pushed onto the stack. Both arrays contain distinct values, `popped` is a permutation of `pushed`, and we must simulate stack operations to validate the `popped` sequence. The arrays represent push and pop operations on a stack, and the goal is to confirm if the `popped` array represents a valid pop sequence after pushing the elements from the `pushed` array.

Solution Approach

The provided solutions use a stack to simulate the push and pop operations. It iterates through the `pushed` array, pushing each element onto the stack. After each push, it checks if the top element of the stack matches the next element in the `popped` array. If they match, it pops the element from the stack and increments the `popped` array's index. This process continues until either the stack is empty or the top element doesn't match the next element in the `popped` array. After processing all the elements from `pushed`, if the stack is empty, it means all elements were popped in the correct sequence, and the function returns true. Otherwise, it returns false.

Step-by-Step Algorithm

Step 1: Initialize an empty stack to simulate the stack operations and a `pop_index` to 0 to track the current position in the `popped` array.
Step 2: Iterate through the `pushed` array. For each element in `pushed`, push it onto the stack.
Step 3: After each push operation, enter a `while` loop that continues as long as the stack is not empty, the `pop_index` is within the bounds of the `popped` array, and the top element of the stack matches the element at `popped[pop_index]`.
Step 4: Inside the `while` loop, pop the top element from the stack and increment the `pop_index` to move to the next element in the `popped` array.
Step 5: After the loop finishes, check if the stack is empty. If it's empty, it means all elements have been successfully pushed and popped according to the given sequences, so return `true`. Otherwise, return `false`.

Key Insights

Insight 1: The core idea is to simulate the push and pop operations using a stack data structure. The pushed array provides the order of insertions, and the popped array determines the expected order of removals.
Insight 2: Maintaining a pointer (index) to the popped array helps track the expected order of pops. We continuously push elements from the pushed array onto the stack and then attempt to pop elements from the stack if they match the expected popped order.
Insight 3: If, after processing all the push operations, the stack is empty, then the popped array represents a valid sequence; otherwise, it does not.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Stack, Simulation.

Companies

Asked at: Apollo.io.

Validate Stack Sequences | LeetCode 946

Medium

Array Stack Simulation

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

Solution Code

Available in:

import java.util.Stack;

class Solution {
    public boolean validateStackSequences(int[] pushed, int[] popped) {
        Stack<Integer> stack = new Stack<>();
        int pop_index = 0;
        for (int num : pushed) {
            stack.push(num);
            while (!stack.isEmpty() && pop_index < popped.length && stack.peek() == popped[pop_index]) {
                stack.pop();
                pop_index++;
            }
        }
        return stack.isEmpty();
    }
}

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Problem Info

Description

Problem 946: Validate Stack Sequences - Detailed explanation and solution approaches.

Topics

Array Stack Simulation

Companies

Apollo.io

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:946

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 an empty stack to simulate the stack operations and a `pop_index` to 0 to track the current position in the `popped` array.
2
Step 2: Iterate through the `pushed` array. For each element in `pushed`, push it onto the stack.
3
Step 3: After each push operation, enter a `while` loop that continues as long as the stack is not empty, the `pop_index` is within the bounds of the `popped` array, and the top element of the stack matches the element at `popped[pop_index]`.
4
Step 4: Inside the `while` loop, pop the top element from the stack and increment the `pop_index` to move to the next element in the `popped` array.
5
Step 5: After the loop finishes, check if the stack is empty. If it's empty, it means all elements have been successfully pushed and popped according to the given sequences, so return `true`. Otherwise, return `false`.

💡

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 linear because each element in both arrays is processed at most a constant number of times. The space complexity is linear because, in the worst-case scenario, the stack could potentially hold all the elements of the `pushed` array.

📖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

No stack approach (difficult and impractical)

Attempting to solve this problem without using an explicit stack would be exceptionally complicated. It would involve trying to discern a pattern within the `pushed` and `popped` arrays to directly determine if a valid push/pop sequence exists without simulating the operations. This approach is not recommended due to its complexity and lack of clarity.

Time: Difficult to achieve O(n) without a stack, likely much worseSpace: O(1) potentially, but the code would be much more complex

Trade-offs: The tradeoff would be avoiding the extra space for the stack, but with a significant increase in code complexity and likely higher constant factors in execution time. This approach is generally not practical or recommended.

✨

Key Insights

1Insight 1: The core idea is to simulate the push and pop operations using a stack data structure. The pushed array provides the order of insertions, and the popped array determines the expected order of removals.
2Insight 2: Maintaining a pointer (index) to the popped array helps track the expected order of pops. We continuously push elements from the pushed array onto the stack and then attempt to pop elements from the stack if they match the expected popped order.
3Insight 3: If, after processing all the push operations, the stack is empty, then the popped array represents a valid sequence; otherwise, it does not.

📚

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: `pushed` and `popped` are both empty arrays. The solution will correctly handle this, as the loop won't execute, and the stack will remain empty, resulting in a `true` return.
Edge case 2: `pushed` is non-empty, but `popped` is empty. The loop will execute, pushing all elements onto the stack, and the stack will not be empty at the end, resulting in a `false` return.
Edge case 3: `pushed` and `popped` contain a single element, and they match. The algorithm pushes the element onto the stack, pops it immediately, and finds an empty stack, leading to a `true` result.
Edge case 4: `pushed` and `popped` contain a single element, but they do not match. The algorithm pushes the element from `pushed` onto the stack. The `while` condition becomes false immediately, and the stack is left with the pushed element. Returns `false`.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly assuming that `pushed` and `popped` always start with matching elements. This leads to prematurely returning `false` when a valid sequence is still possible later.

✗Common mistake 2: Failing to check the bounds of the `popped` array while incrementing `pop_index`. This can cause an `IndexOutOfBoundsException` or similar error. The solution code correctly checks `pop_index < popped.length`.

✗Common mistake 3: Not understanding the problem and trying to sort arrays or perform other unrelated operations. It's crucial to realize that this is a simulation problem, and a stack is the most natural data structure to use.

✅

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: Undo/Redo functionality in software applications relies on stack data structures to manage the sequence of actions. Validating undo/redo sequences is similar to this problem.

🏦Real-world scenario 2: Compiler design and parsing of programming languages use stacks to handle function calls, expressions, and code blocks. Validating the order of operations is related to this problem.

🎮Real-world scenario 3: Web browser history tracking utilizes stacks to keep track of visited web pages. This problem's logic can be applied in ensuring the forward and backward navigation is consistent.

💡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

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ 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: July 17, 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 "Validate Stack Sequences"?

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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