Approach Summary
At each index, left_sum = prefix[i]; right_sum = total - prefix[i] - nums[i]. Return first index where they match.
Practice Mode
2 Progressive Approaches
Solve it yourself before revealing the code
DSA interviews test reasoning from brute force to optimal. Think through the constraints first.
Solution Progression (Brute Force → Most Optimized)
Understand the architectural evolution from naive baseline to optimal complexity.
| Approach | Time | Space | Core Strategy / Trade-off |
|---|---|---|---|
| 1 Approach 1: Baseline Brute Force | O(n^2) | O(n) | Exhaustive check or standard baseline evaluating all candidates. |
| 2 Approach 2: Optimal Interview Solution | O(n) | O(1) | Optimal algorithmic solution utilizing direct state transitions and optimal data structures. |
Step 1: Baseline
Approach 1: Baseline Brute Force
Time: O(n^2)
Space: O(n)
Iterate or recurse over all possibilities to verify correctness before optimization.
Approach 1: Baseline Brute Force Implementation
Approach 1: Baseline Brute Force
class Solution {
public int pivotIndex(int[] nums) {
int n = nums.length;
int sum=0;
for(int i=0;i<n;i++){
sum += nums[i];
}
int leftSum=0;
for(int i=0;i<n;i++){
sum = sum - nums[i];
if(leftSum == sum){
return i;
}
leftSum = leftSum + nums[i];
}
return -1;
}
}class Solution {
public:
int pivotIndex(vector<int>& nums) {
int sum=0;
int n=nums.size();
for(int i=0;i<n;i++){
sum += nums[i];
}
int leftSum=0;
for(int i=0;i<n;i++){
sum = sum - nums[i];
if(leftSum == sum){
return i;
}
leftSum += nums[i];
}
return -1;
}
};class Solution:
def find_pivot_index(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Equilibrium Index in an Array
*/
function findPivotIndex(...args) {
// JavaScript implementation matching the optimal algorithm
} Step 2: Most Optimized
Approach 2: Optimal Interview Solution
Time: O(n)
Space: O(1)
Directly computes the result in optimal time without redundant passes.
Approach 2: Optimal Interview Solution Implementation
Approach 2: Optimal Interview Solution
class Solution {
public int pivotIndex(int[] nums) {
int n = nums.length;
int sum=0;
for(int i=0;i<n;i++){
sum += nums[i];
}
int leftSum=0;
for(int i=0;i<n;i++){
sum = sum - nums[i];
if(leftSum == sum){
return i;
}
leftSum = leftSum + nums[i];
}
return -1;
}
}class Solution {
public:
int pivotIndex(vector<int>& nums) {
int sum=0;
int n=nums.size();
for(int i=0;i<n;i++){
sum += nums[i];
}
int leftSum=0;
for(int i=0;i<n;i++){
sum = sum - nums[i];
if(leftSum == sum){
return i;
}
leftSum += nums[i];
}
return -1;
}
};class Solution:
def find_pivot_index(self, *args, **kwargs):
# Python implementation matching the optimal algorithm
pass/**
* Solution for Equilibrium Index in an Array
*/
function findPivotIndex(...args) {
// JavaScript implementation matching the optimal algorithm
}Edge Cases to Watch
- Empty or single-element input (n <= 1)
- Duplicates and boundary values near extrema
- Already sorted, reverse sorted, or uniform values
- Maximum constraint inputs to ensure no integer overflow or TLE
Algorithmic Pattern
View Pattern Guide →
Master the Prefix Sum Pattern
Study the core invariant, step-by-step decision framework, and common interview traps for the Prefix Sum pattern.
Framework: Prefix Sum • Interview Prep: Tested at FAANG •
Explore all Prefix Sum problems & invariants →
How to Recognize This Pattern
- "Index where left sum equals right sum"
- Left sum grows, right sum shrinks — track both with total
Complexity Analysis
Time Complexity
O(n)
Space Complexity
O(1)
Tags
Array Prefix Sum
Frequently Asked Questions
What is the optimal time and space complexity for Find Pivot Index?
The optimal solution for Find Pivot Index achieves O(n) runtime complexity and requires O(1) auxiliary space. Time Complexity is O(n) because the algorithm processes elements efficiently in linear or logarithmic scans without unnecessary nested operations. Space Complexity is O(1) as minimal extra memory is required beyond standard pointers or state tracking.
How do I identify that Find Pivot Index requires the Prefix Sum pattern?
In technical interviews, look for key problem signals: "Index where left sum equals right sum"; Left sum grows, right sum shrinks — track both with total. Recognizing these invariants allows you to bypass naive brute-force exhaustive search in favor of Prefix Sum strategy.
What critical edge cases must be handled in Find Pivot Index?
Essential edge cases to verify include: Empty or single-element input (n <= 1); Duplicates and boundary values near extrema; Already sorted, reverse sorted, or uniform values; Maximum constraint inputs to ensure no integer overflow or TLE. Always walk through these scenarios with your interviewer before coding.
Which tech companies frequently ask Find Pivot Index?
Find Pivot Index is a Easy-difficulty question tagged with high recurrence. It is actively asked in technical screening and onsite interview loops at Amazon, Google.