What is the time complexity of Find Pivot Index?

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

What data structures are used to solve Find Pivot Index?

This problem uses Array, Prefix Sum. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Find Pivot Index?

Insight 1: The problem can be efficiently solved using the concept of prefix sum, by calculating the total sum of the array in advance. Insight 2: Instead of calculating left and right sums repeatedly, we can maintain a running left sum and deduce the right sum by subtracting the left sum and the current element from the total sum.

Which companies ask LeetCode 724. Find Pivot Index in interviews?

This problem is frequently asked at Agoda, Attentive, Citigroup, Coupang, Nvidia and 2 more companies.

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Find Pivot Index - LeetCode 724 Solution

Find Pivot Index - Complete Solution Guide

Find Pivot Index is LeetCode problem 724, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Given an array of integers nums , calculate the pivot index of this array. The pivot index is the index where the sum of all the numbers strictly to the left of the index is equal to the sum of all the numbers strictly to the index's right. If the index is on the left edge of the array, then the left sum is 0 because there are no elements to the left. This also applies to the right edge of the array. Return the leftmost pivot index . If no such index exists, return -1 . Example 1: Input: nums =

Detailed Explanation

The problem requires finding the 'pivot index' in a given array of integers. The pivot index is an index where the sum of elements to the left of the index is equal to the sum of elements to the right of the index. If there's no pivot index, the function should return -1. If multiple pivot indices exist, the function should return the leftmost one. An important consideration is that the sum of elements to the left of the first element (index 0) and to the right of the last element is considered to be 0.

Solution Approach

The provided solutions utilize a prefix sum approach. First, the total sum of the array is calculated. Then, the code iterates through the array, maintaining a 'left sum' that represents the sum of elements to the left of the current index. For each index, it calculates the 'right sum' by subtracting the 'left sum' and the current element's value from the 'total sum'. If the 'left sum' equals the 'right sum', the current index is the pivot index, and it is returned. If no such index is found after iterating through the entire array, the function returns -1.

Step-by-Step Algorithm

Step 1: Calculate the total sum of all elements in the input array `nums`.
Step 2: Initialize `left_sum` to 0.
Step 3: Iterate through the `nums` array using a loop with index `i` and element `num`.
Step 4: Inside the loop, calculate the `right_sum` as `total_sum - left_sum - num`.
Step 5: Check if `left_sum` is equal to `right_sum`. If they are equal, return the current index `i`.
Step 6: If `left_sum` is not equal to `right_sum`, update `left_sum` by adding the current element `num` to it.
Step 7: After the loop finishes, if no pivot index is found, return -1.

Key Insights

Insight 1: The problem can be efficiently solved using the concept of prefix sum, by calculating the total sum of the array in advance.
Insight 2: Instead of calculating left and right sums repeatedly, we can maintain a running left sum and deduce the right sum by subtracting the left sum and the current element from the total sum.
Insight 3: Handle edge cases like an empty array or when the first element is the pivot by considering the sums to its left and right.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Prefix Sum.

Companies

Asked at: Agoda, Attentive, Citigroup, Coupang, Nvidia, PayPal, eBay.

Find Pivot Index | LeetCode 724

Easy

Array Prefix Sum

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

Solution Code

Available in:

class Solution {
    public int pivotIndex(int[] nums) {
        int totalSum = 0;
        for (int num : nums) {
            totalSum += num;
        }
        int leftSum = 0;
        for (int i = 0; i < nums.length; i++) {
            int rightSum = totalSum - leftSum - nums[i];
            if (leftSum == rightSum) {
                return i;
            }
            leftSum += nums[i];
        }
        return -1;
    }
}

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Problem Info

Description

Problem 724: Find Pivot Index - Detailed explanation and solution approaches.

Topics

Array Prefix Sum

Companies

AgodaAttentiveCitigroupCoupangNvidiaPayPaleBay

Stats

Difficulty:Easy

Languages:4

Companies:7

Problem #:724

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

7 steps

1
Step 1: Calculate the total sum of all elements in the input array `nums`.
2
Step 2: Initialize `left_sum` to 0.
3
Step 3: Iterate through the `nums` array using a loop with index `i` and element `num`.
4
Step 4: Inside the loop, calculate the `right_sum` as `total_sum - left_sum - num`.
5
Step 5: Check if `left_sum` is equal to `right_sum`. If they are equal, return the current index `i`.
6
Step 6: If `left_sum` is not equal to `right_sum`, update `left_sum` by adding the current element `num` to it.
7
Step 7: After the loop finishes, if no pivot index is found, return -1.

💡

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 determined by the number of iterations over the input array. The space complexity is determined by the amount of auxiliary memory used that scales with the input size. Since only a few constant-size variables are used, the space complexity is constant.

📖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

Prefix Sum Array

Create a prefix sum array where each element represents the sum of all elements up to that index in the original array. Then, iterate through the prefix sum array to find the pivot index. For each index i, the left sum is prefixSum[i-1] (or 0 if i=0), and the right sum is prefixSum[n-1] - prefixSum[i].

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

Trade-offs: This approach has the same time complexity as the current solution but uses O(n) extra space for the prefix sum array. This approach could be considered when you need to perform multiple queries related to subarray sums, making the initial cost of building prefix sum array amortized over multiple queries.

✨

Key Insights

1Insight 1: The problem can be efficiently solved using the concept of prefix sum, by calculating the total sum of the array in advance.
2Insight 2: Instead of calculating left and right sums repeatedly, we can maintain a running left sum and deduce the right sum by subtracting the left sum and the current element from the total sum.
3Insight 3: Handle edge cases like an empty array or when the first element is the pivot by considering the sums to its left and right.

📚

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: Empty array (nums.length == 0). The code handles this case correctly because the loops will not execute, and -1 will be returned.
Edge case 2: Pivot index at the beginning (index 0). The `left_sum` is initialized to 0, which correctly handles the case where the sum of the elements to the right of index 0 equals 0.
Edge case 3: No pivot index exists. The loop completes without finding a pivot, and the function returns -1.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not initializing `left_sum` to 0. If `left_sum` is not initialized to 0, the condition for the first element to be a pivot index will not be evaluated correctly.

✗Common mistake 2: Incorrectly calculating the `right_sum`. The correct formula for `right_sum` is `total_sum - left_sum - num`, where `num` is the value of the element at the current index. Failing to subtract the current element will lead to incorrect results.

✗Common mistake 3: Early return. Returning from inside the loop prematurely can cause the function to not correctly identify a possible pivot further down the array.

✅

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: Load balancing. Consider an array representing the load on different servers. Finding the pivot index can help determine a point where the load is balanced across the servers.

🏦Real-world scenario 2: Data analysis. In time series data, finding a pivot point can help identify significant changes or shifts in trends, where the sum of changes before the pivot equals the sum of changes after.

💡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

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ 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: June 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

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 13

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 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.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

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 "Find Pivot Index"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether prefix sum techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?