What is the time complexity of Find Triangular Sum of an Array?

The optimal solution has a time complexity of O(n^2).

What data structures are used to solve Find Triangular Sum of an Array?

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

What are the key insights for solving Find Triangular Sum of an Array?

Insight 1: The problem can be solved by directly simulating the described process. Insight 2: The modulo operator (%) is crucial to keep the values within the range of 0-9.

Which companies ask LeetCode 2221. Find Triangular Sum of an Array in interviews?

This problem is frequently asked at Zoho.

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Find Triangular Sum of an Array - LeetCode 2221 Solution

Q: How to solve Find Triangular Sum of an Array?

The provided code directly implements the algorithm described in the problem statement. It uses a `while` loop to continue the process until the array size reduces to 1. Inside the `while` loop, a `for` loop iterates through the array and updates each element with the sum of it and the next element modulo 10. After each iteration of the `while` loop, the effective size of the array decreases by 1 because the last element is 'removed' in terms of the algorithm's process. This process continues until only one element remains, which is then returned.

Find Triangular Sum of an Array - Complete Solution Guide

Find Triangular Sum of an Array is LeetCode problem 2221, 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

You are given a 0-indexed integer array nums , where nums[i] is a digit between 0 and 9 ( inclusive ). The triangular sum of nums is the value of the only element present in nums after the following process terminates: Let nums comprise of n elements. If n == 1 , end the process. Otherwise, create a new 0-indexed integer array newNums of length n - 1 . For each index i , where 0 <= i < n - 1 , assign the value of newNums[i] as (nums[i] + nums[i+1]) % 10 , where % denotes modulo operator. Replace

Detailed Explanation

The problem requires you to calculate the 'triangular sum' of an integer array. The array initially contains digits between 0 and 9. The triangular sum is computed iteratively. In each iteration, a new array is created where each element is the sum (modulo 10) of adjacent elements in the previous array. This process continues until only one element remains in the array, which is the triangular sum.

Solution Approach

The provided code directly implements the algorithm described in the problem statement. It uses a `while` loop to continue the process until the array size reduces to 1. Inside the `while` loop, a `for` loop iterates through the array and updates each element with the sum of it and the next element modulo 10. After each iteration of the `while` loop, the effective size of the array decreases by 1 because the last element is 'removed' in terms of the algorithm's process. This process continues until only one element remains, which is then returned.

Step-by-Step Algorithm

Step 1: Determine the size of the input array `nums` and store it in the variable `n`.
Step 2: Start a `while` loop that continues as long as `n` is greater than 1. This ensures the algorithm continues until the array size reduces to 1.
Step 3: Inside the `while` loop, iterate through the array using a `for` loop from index `i = 0` to `n - 2`.
Step 4: Within the `for` loop, update the element at index `i` with the sum of the element at `i` and the element at `i + 1`, taken modulo 10: `nums[i] = (nums[i] + nums[i + 1]) % 10`.
Step 5: After the inner `for` loop finishes, decrement `n` by 1 to reflect the reduction in the effective array size.
Step 6: After the `while` loop terminates (when `n` becomes 1), return the element at index 0 of the array `nums`, as this is the triangular sum.

Key Insights

Insight 1: The problem can be solved by directly simulating the described process.
Insight 2: The modulo operator (%) is crucial to keep the values within the range of 0-9.
Insight 3: The in-place modification of the input array helps reduce space complexity.

Complexity Analysis

Time Complexity: O(n^2)

Space Complexity: O(1)

Topics

This problem involves: Array, Math, Simulation, Combinatorics.

Companies

Asked at: Zoho.

Find Triangular Sum of an Array | LeetCode 2221

Medium

Array Math Simulation Combinatorics

Time: O(n^2)Space: O(1)

Solution Code

Available in:

class Solution {
    public int triangularSum(int[] nums) {
        int n = nums.length;
        while (n > 1) {
            for (int i = 0; i < n - 1; i++) {
                nums[i] = (nums[i] + nums[i+1]) % 10;
            }
            n -= 1;
        }
        return nums[0];
    }
}

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Problem Info

Description

Problem 2221: Find Triangular Sum of an Array - Detailed explanation and solution approaches.

Topics

Array Math Simulation Combinatorics

Companies

Zoho

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2221

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

6 steps

1
Step 1: Determine the size of the input array `nums` and store it in the variable `n`.
2
Step 2: Start a `while` loop that continues as long as `n` is greater than 1. This ensures the algorithm continues until the array size reduces to 1.
3
Step 3: Inside the `while` loop, iterate through the array using a `for` loop from index `i = 0` to `n - 2`.
4
Step 4: Within the `for` loop, update the element at index `i` with the sum of the element at `i` and the element at `i + 1`, taken modulo 10: `nums[i] = (nums[i] + nums[i + 1]) % 10`.
5
Step 5: After the inner `for` loop finishes, decrement `n` by 1 to reflect the reduction in the effective array size.
6
Step 6: After the `while` loop terminates (when `n` becomes 1), return the element at index 0 of the array `nums`, as this is the triangular sum.

💡

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^2)

🐢 Quadratic - Gets slow with large inputs. Consider optimization!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is determined by the nested loops. The space complexity is constant because the modification is done in place.

📖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

Combinatorial Approach

The triangular sum can be calculated directly using combinatorial coefficients. The final sum is a weighted sum of the original elements, where the weights are binomial coefficients modulo 10. This approach avoids the iterative process.

Time: O(n), where n is the length of the input array. This is because we only need to calculate the binomial coefficients once and then perform a linear pass to calculate the weighted sum.Space: O(n) or O(1) depending on how binomial coefficients are calculated. O(n) if we precompute factorial and inverse factorial arrays, O(1) if binomial coefficients are calculated on demand using formula.

Trade-offs: The combinatorial approach has better time complexity but may be more complex to implement and understand, especially considering the modulo arithmetic involved in computing binomial coefficients modulo 10. The iterative approach is simpler to implement and easier to understand, although it has a higher time complexity.

✨

Key Insights

1Insight 1: The problem can be solved by directly simulating the described process.
2Insight 2: The modulo operator (%) is crucial to keep the values within the range of 0-9.
3Insight 3: The in-place modification of the input array helps reduce space complexity.

📚

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: Input array with a single element. The algorithm correctly handles this case because the `while` loop is skipped, and the single element is returned.
Edge case 2: Input array containing only zeros. The algorithm correctly calculates the triangular sum as zero, since the sum of zeros modulo 10 will always be zero.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting the modulo operator. Without the modulo operator, the values in the array can exceed 9, leading to an incorrect result.

✗Common mistake 2: Incorrect loop termination condition. Using the wrong condition for the `while` loop or `for` loop can cause an out-of-bounds error or premature termination of the algorithm.

✅

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: Data compression algorithms. Techniques similar to triangular sums can be used to reduce redundancy in data, where each element represents the difference or sum of neighboring elements.

🏦Real-world scenario 2: Image processing. Smoothing filters can be implemented using concepts similar to calculating the triangular sum, where each pixel is updated based on the values of its neighboring pixels.

💡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: August 1, 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 "Find Triangular Sum of an Array"?

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

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