What is the time complexity of Find First and Last Position of Element in Sorted Array?

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

What data structures are used to solve Find First and Last Position of Element in Sorted Array?

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

What are the key insights for solving Find First and Last Position of Element in Sorted Array?

Insight 1: The sorted nature of the array allows for the efficient use of binary search to achieve O(log n) time complexity. Insight 2: Finding the first and last positions requires two separate binary search operations, one to find the leftmost occurrence and the other to find the rightmost occurrence.

Which companies ask LeetCode 34. Find First and Last Position of Element in Sorted Array in interviews?

This problem is frequently asked at Accenture, Adobe, Airtel, Amazon, Apple and 25 more companies.

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Find First and Last Position of Element in Sorted Array - LeetCode 34 Solution

Q: How to solve Find First and Last Position of Element in Sorted Array?

The provided solution uses a modified binary search to find the leftmost occurrence of the target and the leftmost occurrence of the target + 1. The rightmost occurrence is then simply the leftmost occurrence of target + 1 minus 1. This approach leverages the sorted property of the array to efficiently locate the target's boundaries.

Find First and Last Position of Element in Sorted Array - Complete Solution Guide

Find First and Last Position of Element in Sorted Array is LeetCode problem 34, 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 an array of integers nums sorted in non-decreasing order, find the starting and ending position of a given target value. If target is not found in the array, return [-1, -1] . You must write an algorithm with O(log n) runtime complexity. Example 1: Input: nums = [5,7,7,8,8,10], target = 8 Output: [3,4] Example 2: Input: nums = [5,7,7,8,8,10], target = 6 Output: [-1,-1] Example 3: Input: nums = [], target = 0 Output: [-1,-1] Constraints: 0 <= nums.length <= 10 5 -10 9 <= nums[i] <= 10 9 num

Detailed Explanation

The problem requires us to find the first and last positions of a given target value in a sorted array of integers. If the target is not found, we should return [-1, -1]. The crucial constraint is that the algorithm must have O(log n) runtime complexity, implying the use of binary search. The array is sorted in non-decreasing order, which is also key to using binary search.

Solution Approach

The provided solution uses a modified binary search to find the leftmost occurrence of the target and the leftmost occurrence of the target + 1. The rightmost occurrence is then simply the leftmost occurrence of target + 1 minus 1. This approach leverages the sorted property of the array to efficiently locate the target's boundaries.

Step-by-Step Algorithm

Step 1: Define a helper function 'find_left_boundary' that uses binary search to find the leftmost index where a value is greater than or equal to the target value.
Step 2: Call 'find_left_boundary' with the original array and target value to find the potential leftmost index of the target.
Step 3: Check if the found index is within the array bounds and if the value at that index is indeed equal to the target. If not, the target is not present in the array, so return [-1, -1].
Step 4: Call 'find_left_boundary' again, this time with the original array and target + 1. This returns the index where target + 1 would be inserted to maintain sorted order. Subtracting 1 from this index gives the rightmost index of the target.
Step 5: Return the leftmost index and rightmost index as a list/array containing these two values.

Key Insights

Insight 1: The sorted nature of the array allows for the efficient use of binary search to achieve O(log n) time complexity.
Insight 2: Finding the first and last positions requires two separate binary search operations, one to find the leftmost occurrence and the other to find the rightmost occurrence.
Insight 3: The 'find_left_boundary' function can be used to find both the leftmost and rightmost indices by slightly modifying the target value for the rightmost index search (target + 1).

Complexity Analysis

Time Complexity: O(log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Binary Search.

Companies

Asked at: Accenture, Adobe, Airtel, Amazon, Apple, Applied Intuition, Atlassian, Attentive, Bloomberg, Capgemini, DE Shaw, Instacart, LinkedIn, MakeMyTrip, Meta, Microsoft, NetApp, Oracle, PayPal, Pinterest, ServiceNow, Splunk, Tekion, TikTok, Tinkoff, Turing, Uber, Yahoo, Zillow, tcs.

Find First and Last Position of Element in Sorted Array | LeetCode 34

Medium

Array Binary Search

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

Solution Code

Available in:

class Solution {
    public int[] searchRange(int[] nums, int target) {
        
        int left_idx = find_left_boundary(nums, target);

        if (left_idx == nums.length || nums[left_idx] != target) {
            return new int[]{-1, -1};
        }

        int right_idx = find_left_boundary(nums, target + 1) - 1;

        return new int[]{left_idx, right_idx};
    }

    private int find_left_boundary(int[] nums_list, int target_val) {
        int low = 0, high = nums_list.length;
        while (low < high) {
            int mid = low + (high - low) / 2;
            if (nums_list[mid] >= target_val) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }
}

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Problem Info

Description

Problem 34: Find First and Last Position of Element in Sorted Array - Detailed explanation and solution approaches.

Topics

Array Binary Search

Companies

AccentureAdobeAirtelAmazonAppleApplied IntuitionAtlassianAttentive

Stats

Difficulty:Medium

Languages:4

Companies:30

Problem #:34

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: Define a helper function 'find_left_boundary' that uses binary search to find the leftmost index where a value is greater than or equal to the target value.
2
Step 2: Call 'find_left_boundary' with the original array and target value to find the potential leftmost index of the target.
3
Step 3: Check if the found index is within the array bounds and if the value at that index is indeed equal to the target. If not, the target is not present in the array, so return [-1, -1].
4
Step 4: Call 'find_left_boundary' again, this time with the original array and target + 1. This returns the index where target + 1 would be inserted to maintain sorted order. Subtracting 1 from this index gives the rightmost index of the target.
5
Step 5: Return the leftmost index and rightmost index as a list/array containing these two values.

💡

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(log n)

🚀 Logarithmic - Very efficient! Halves the problem each step.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm uses binary search, which halves the search space in each iteration. Therefore, the time complexity is logarithmic, O(log n), where n is the length of the input array. The algorithm uses a constant amount of extra space regardless of the input size, so the space complexity is O(1).

📖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

Linear Scan after initial binary search

First, use standard binary search to find any occurrence of the target. Then, perform a linear scan to the left to find the first occurrence and a linear scan to the right to find the last occurrence.

Time: O(n) in the worst case (e.g., all elements are the target), but O(log n + k) on average, where k is the number of target elementsSpace: O(1)

Trade-offs: This approach might be simpler to implement initially, but it loses the O(log n) time complexity requirement in cases with many consecutive target values. Prefer the two binary search approach if maintaining O(log n) time complexity is crucial, especially with large datasets.

✨

Key Insights

1Insight 1: The sorted nature of the array allows for the efficient use of binary search to achieve O(log n) time complexity.
2Insight 2: Finding the first and last positions requires two separate binary search operations, one to find the leftmost occurrence and the other to find the rightmost occurrence.
3Insight 3: The 'find_left_boundary' function can be used to find both the leftmost and rightmost indices by slightly modifying the target value for the rightmost index search (target + 1).

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Binary Search

Halving the search space each step. Like finding a word in a dictionary!

Edge Cases

Edge case 1: Empty array. The solution correctly returns [-1, -1] because the initial check `left_idx == nums.length` will be true, or if the array is empty, `nums[left_idx]` would cause an out-of-bounds error, which the condition prevents.
Edge case 2: Target is smaller than all elements in the array. The `find_left_boundary` function will return 0. The condition `nums[left_idx] != target` handles the situation correctly, resulting in a return of [-1, -1].
Edge case 3: Target is larger than all elements in the array. The `find_left_boundary` function will return nums.length. The condition `left_idx == nums.length` is triggered, resulting in a return of [-1, -1].
Edge case 4: Target appears only once in array. The `left_idx` and `right_idx` variables will be equal, leading to the correct range [left_idx, right_idx].

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly implementing binary search conditions, leading to infinite loops or incorrect results. Pay close attention to the `low`, `high`, and `mid` calculations, as well as the comparison operators (`<`, `<=`, `>`, `>=`).

✗Common mistake 2: Failing to handle the edge cases of an empty array or a target that is not present in the array, resulting in incorrect output or runtime errors.

✗Common mistake 3: Not realizing the sorted array property and attempting to solve without binary search. This will likely lead to a O(n) solution which violates the problem constraints.

✅

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: Searching for a range of dates in a sorted log file. For example, finding all log entries for a specific day.

🏦Real-world scenario 2: Finding the starting and ending indices of a price range for a product in a sorted price list. This is common in e-commerce or financial applications.

🎮Real-world scenario 3: In databases, finding the range of records that match a specific key value, assuming the database is indexed and sorted by that key.

💡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 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 do I avoid off-by-one errors in binary search?

Use the pattern: left = 0, right = n-1, while (left <= right), mid = left + (right - left) / 2. Decide if you need to find exact match, first occurrence, or last occurrence, and adjust your conditions accordingly. Test with arrays of size 0, 1, and 2.

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 "Find First and Last Position of Element in Sorted 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 binary search techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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