What is the time complexity of Design a Stack With Increment Operation?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Design a Stack With Increment Operation?

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

What are the key insights for solving Design a Stack With Increment Operation?

Insight 1: The increment operation can be optimized by using an auxiliary array to store the increment values for each element, avoiding repeated updates to the stack itself. Insight 2: The stack and increment array sizes must be managed according to the maximum size limit to avoid exceeding allocated memory.

Which companies ask LeetCode 1381. Design a Stack With Increment Operation in interviews?

This problem is frequently asked at Cloudflare, IMC, Moloco, eBay.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Design a Stack With Increment Operation - LeetCode 1381 Solution

Design a Stack With Increment Operation - Complete Solution Guide

Design a Stack With Increment Operation is LeetCode problem 1381, 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

Design a stack that supports increment operations on its elements. Implement the CustomStack class: CustomStack(int maxSize) Initializes the object with maxSize which is the maximum number of elements in the stack. void push(int x) Adds x to the top of the stack if the stack has not reached the maxSize . int pop() Pops and returns the top of the stack or -1 if the stack is empty. void inc(int k, int val) Increments the bottom k elements of the stack by val . If there are less than k elements in

Detailed Explanation

The problem requires designing a custom stack data structure with a specific 'increment' operation in addition to the standard 'push' and 'pop' operations. The stack has a fixed maximum size. The 'push' operation adds an element to the top if the stack is not full. The 'pop' operation removes and returns the top element, returning -1 if the stack is empty. The 'increment' operation increases the bottom 'k' elements of the stack by a given value. If the stack contains less than 'k' elements, then all the elements in the stack are incremented.

Solution Approach

The solution uses two arrays: one to store the stack elements and another to store the increment values for each element. The 'push' operation adds a new element to the stack and initializes its increment value to 0. The 'pop' operation removes the top element, adds its increment value to the element below it (if one exists), and returns the sum of the element's value and its increment. The 'increment' operation adds the given value to the increment values of the bottom 'k' elements. The 'min' function is used to handle the case when 'k' is larger than the stack size.

Step-by-Step Algorithm

Step 1: Initialize the CustomStack with a maximum size and two arrays: 'stack' to store the stack elements and 'inc' to store the increments for each element.
Step 2: Implement the 'push' operation: If the stack is not full, add the element to the 'stack' array and initialize its corresponding 'inc' value to 0.
Step 3: Implement the 'pop' operation: If the stack is empty, return -1. Otherwise, get the increment value from the 'inc' array, get the element from the 'stack' array. If there is an element below the current one (not the base of the stack), add its increment to the increment below it. Return the sum of the stack value and increment value.
Step 4: Implement the 'increment' operation: Determine the minimum of 'k' and the stack size. Then, add the given 'val' to the increment values of the bottom 'k' elements in the 'inc' array.

Key Insights

Insight 1: The increment operation can be optimized by using an auxiliary array to store the increment values for each element, avoiding repeated updates to the stack itself.
Insight 2: The stack and increment array sizes must be managed according to the maximum size limit to avoid exceeding allocated memory.
Insight 3: When popping, the increment value for the popped element needs to be propagated to the element below it in the stack, if such an element exists.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(n)

Topics

This problem involves: Array, Stack, Design.

Companies

Asked at: Cloudflare, IMC, Moloco, eBay.

Design a Stack With Increment Operation | LeetCode 1381

Medium

Array Stack Design

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

Solution Code

Available in:

import java.util.ArrayList;
import java.util.List;

class CustomStack {

    private int maxSize;
    private List<Integer> stack;
    private List<Integer> inc;

    public CustomStack(int maxSize) {
        this.maxSize = maxSize;
        this.stack = new ArrayList<>();
        this.inc = new ArrayList<>();
    }
    
    public void push(int x) {
        if (stack.size() < maxSize) {
            stack.add(x);
            inc.add(0);
        }
    }
    
    public int pop() {
        if (stack.isEmpty()) {
            return -1;
        }
        
        int increment = inc.remove(inc.size() - 1);
        int val = stack.remove(stack.size() - 1);
        
        if (!inc.isEmpty()) {
            inc.set(inc.size() - 1, inc.get(inc.size() - 1) + increment);
        }
        
        return val + increment;
    }
    
    public void increment(int k, int val) {
        int limit = Math.min(k, stack.size());
        if (limit > 0) {
            inc.set(limit - 1, inc.get(limit - 1) + val);
        }
    }
}

/**
 * Your CustomStack object will be instantiated and called as such:
 * CustomStack obj = new CustomStack(maxSize);
 * obj.push(x);
 * int param_2 = obj.pop();
 * obj.increment(k,val);
 */

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 1381: Design a Stack With Increment Operation - Detailed explanation and solution approaches.

Topics

Array Stack Design

Companies

CloudflareIMCMolocoeBay

Stats

Difficulty:Medium

Languages:4

Companies:4

Problem #:1381

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

4 steps

1
Step 1: Initialize the CustomStack with a maximum size and two arrays: 'stack' to store the stack elements and 'inc' to store the increments for each element.
2
Step 2: Implement the 'push' operation: If the stack is not full, add the element to the 'stack' array and initialize its corresponding 'inc' value to 0.
3
Step 3: Implement the 'pop' operation: If the stack is empty, return -1. Otherwise, get the increment value from the 'inc' array, get the element from the 'stack' array. If there is an element below the current one (not the base of the stack), add its increment to the increment below it. Return the sum of the stack value and increment value.
4
Step 4: Implement the 'increment' operation: Determine the minimum of 'k' and the stack size. Then, add the given 'val' to the increment values of the bottom 'k' elements in the 'inc' 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(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is O(1) because array accesses take constant time. The space complexity is O(n) since we are using two lists, each with a maximum capacity equal to maxSize. The number of operations performed by each function does not scale with the size of the input.

📖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

Using a Single Array with Lazy Propagation

Instead of storing separate 'stack' and 'inc' arrays, we could use a single array. During push we add the element to the main array. During Increment, instead of directly modifying 'k' elements, we add the value to another 'inc' array. During Pop, we pop element from stack and decrement from increment array and add to result if element exists.

Time: O(1) for all operationsSpace: O(n)

Trade-offs: This reduces memory reads/writes slightly but doesn't change the overall complexity. The main advantage is reducing code complexity by dealing with a single array instead of two in some cases.

✨

Key Insights

1Insight 1: The increment operation can be optimized by using an auxiliary array to store the increment values for each element, avoiding repeated updates to the stack itself.
2Insight 2: The stack and increment array sizes must be managed according to the maximum size limit to avoid exceeding allocated memory.
3Insight 3: When popping, the increment value for the popped element needs to be propagated to the element below it in the stack, if such an element exists.

📚

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: Empty stack when 'pop' is called. The 'pop' operation returns -1 when the stack is empty.
Edge case 2: 'k' is larger than the stack size in the 'increment' operation. The code uses 'min(k, stack size)' to ensure that the increment operation does not access elements beyond the bounds of the array.
Edge case 3: Stack is already full, when push is called. No new element is added

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the case when the stack is empty during the 'pop' operation, resulting in an error.

✗Common mistake 2: Not correctly handling the 'increment' operation when 'k' is larger than the stack size, leading to out-of-bounds array access.

✗Common mistake 3: Forgetting to propagate the increment during the `pop` operation, leading to inaccurate results.

✗Common mistake 4: Not allocating memory for stack and inc in C implementation, leading to segmentation faults

✅

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: Implementing a buffered stream where increments represent the number of bytes consumed or produced.

🏦Real-world scenario 2: Designing a system for managing financial transactions, where the stack represents account balances and the increment operation represents adding interest or applying fees to multiple accounts.

💡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: September 30, 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

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

@CodeNinjaJun 29

❓

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.

What is a monotonic stack and when should I use it?

A monotonic stack maintains elements in sorted order (increasing or decreasing). Use it for "next greater element," "largest rectangle," or "stock span" problems. It achieves O(n) time by avoiding redundant comparisons through maintaining order invariants.

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 "Design a Stack With Increment Operation"?

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.

🤖 Need help with this problem?