What is the time complexity of Find Occurrences of an Element in an Array?

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

What data structures are used to solve Find Occurrences of an Element in an Array?

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

What are the key insights for solving Find Occurrences of an Element in an Array?

Insight 1: The core task is to efficiently locate the indices where the target integer `x` appears in the input array `nums`. Insight 2: Pre-computing and storing the indices of `x` allows for faster processing of multiple queries.

Which companies ask LeetCode 3159. Find Occurrences of an Element in an Array in interviews?

This problem is frequently asked at IBM, J.P. Morgan.

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Find Occurrences of an Element in an Array - LeetCode 3159 Solution

Find Occurrences of an Element in an Array - Complete Solution Guide

Find Occurrences of an Element in an Array is LeetCode problem 3159, 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 an integer array nums , an integer array queries , and an integer x . For each queries[i] , you need to find the index of the queries[i] th occurrence of x in the nums array. If there are fewer than queries[i] occurrences of x , the answer should be -1 for that query. Return an integer array answer containing the answers to all queries. Example 1: Input: nums = [1,3,1,7], queries = [1,3,2,4], x = 1 Output: [0,-1,2,-1] Explanation: For the 1 st query, the first occurrence of 1 is at

Detailed Explanation

The problem asks us to find the indices of specific occurrences of a given integer `x` within an integer array `nums`. For each query in the `queries` array, we need to determine the index of the `queries[i]`-th occurrence of `x` in `nums`. If `x` appears fewer than `queries[i]` times in `nums`, the result for that query should be -1. The output is an array containing the results for each query.

Solution Approach

The provided solution first identifies all indices in the `nums` array where the value `x` is present. These indices are stored in a separate list/array. Then, for each query in the `queries` array, it checks if the requested occurrence number is valid (i.e., not greater than the total number of occurrences of `x`). If the occurrence number is valid, the index corresponding to that occurrence is retrieved from the pre-computed list of indices. Otherwise, -1 is returned, indicating that the requested occurrence does not exist.

Step-by-Step Algorithm

Step 1: Iterate through the `nums` array.
Step 2: For each element in `nums`, check if it is equal to `x`.
Step 3: If an element is equal to `x`, store its index in a list or array (e.g., `x_indices`).
Step 4: After iterating through `nums`, determine the total number of occurrences of `x` (i.e., the size of the `x_indices` list).
Step 5: Iterate through the `queries` array.
Step 6: For each query value `q`, check if `q` is greater than the total number of occurrences of `x`.
Step 7: If `q` is greater than the number of occurrences, append -1 to the `answer` array.
Step 8: Otherwise (if `q` is valid), access the `(q - 1)`-th element in the `x_indices` array and append its value (which represents the index of the q-th occurrence of `x` in the original array) to the `answer` array.
Step 9: Return the `answer` array.

Key Insights

Insight 1: The core task is to efficiently locate the indices where the target integer `x` appears in the input array `nums`.
Insight 2: Pre-computing and storing the indices of `x` allows for faster processing of multiple queries.
Insight 3: Handling the edge case where the query number exceeds the total number of occurrences of `x` is crucial for correctness.

Complexity Analysis

Time Complexity: O(n + m)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table.

Companies

Asked at: IBM, J.P. Morgan.

Find Occurrences of an Element in an Array | LeetCode 3159

Medium

Array Hash Table

Time: O(n + m)Space: O(n)

Solution Code

Available in:

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

class Solution {
    public int[] occurrencesOfElement(int[] nums, int[] queries, int x) {
        List<Integer> x_indices = new ArrayList<>();
        for (int i = 0; i < nums.length; i++) {
            if (nums[i] == x) {
                x_indices.add(i);
            }
        }
        int num_occurrences = x_indices.size();
        
        int[] answer = new int[queries.length];
        for (int i = 0; i < queries.length; i++) {
            int q = queries[i];
            if (q > num_occurrences) {
                answer[i] = -1;
            } else {
                answer[i] = x_indices.get(q - 1);
            }
        }
        
        return answer;
    }
}

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Problem Info

Description

Problem 3159: Find Occurrences of an Element in an Array - Detailed explanation and solution approaches.

Topics

Array Hash Table

Companies

IBMJ.P. Morgan

Stats

Difficulty:Medium

Languages:4

Companies:2

Problem #:3159

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

9 steps

1
Step 1: Iterate through the `nums` array.
2
Step 2: For each element in `nums`, check if it is equal to `x`.
3
Step 3: If an element is equal to `x`, store its index in a list or array (e.g., `x_indices`).
4
Step 4: After iterating through `nums`, determine the total number of occurrences of `x` (i.e., the size of the `x_indices` list).
5
Step 5: Iterate through the `queries` array.
6
Step 6: For each query value `q`, check if `q` is greater than the total number of occurrences of `x`.
7
Step 7: If `q` is greater than the number of occurrences, append -1 to the `answer` array.
8
Step 8: Otherwise (if `q` is valid), access the `(q - 1)`-th element in the `x_indices` array and append its value (which represents the index of the q-th occurrence of `x` in the original array) to the `answer` array.
9
Step 9: Return the `answer` 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(n + m)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is determined by the two iterations: one through `nums` and one through `queries`. The space complexity depends on how many times `x` appears in `nums`. The maximum space required is when all elements in `nums` are equal to `x`, leading to O(n) space.

📖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

Without Precomputation

Instead of pre-computing and storing the indices of x, you could iterate through `nums` for each query and count occurrences until you reach the requested occurrence number. However, this approach is much less efficient.

Time: O(n*m) in the worst case, where n is the length of `nums` and m is the length of `queries`. For each query, you might need to iterate through the entire `nums` array.Space: O(1), excluding the output array.

Trade-offs: Use this approach if memory usage is extremely limited and you are sure that the sizes of `nums` and `queries` will always be very small, since it avoids the overhead of creating and storing x_indices. However, the O(n*m) time complexity makes it much slower than the precomputation method for larger inputs.

✨

Key Insights

1Insight 1: The core task is to efficiently locate the indices where the target integer `x` appears in the input array `nums`.
2Insight 2: Pre-computing and storing the indices of `x` allows for faster processing of multiple queries.
3Insight 3: Handling the edge case where the query number exceeds the total number of occurrences of `x` is crucial for correctness.

📚

Key Terms Explained

For Students

Array

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

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Edge Cases

Edge case 1: `x` does not appear in `nums`. In this case, the `x_indices` list will be empty, `num_occurrences` will be 0, and all queries will return -1, which is the correct behavior.
Edge case 2: `queries` is empty. In this case, the loop that processes queries will not execute, and an empty list/array will be returned, which is also the correct behavior.
Edge case 3: A query asks for an occurrence beyond the existing number of occurrences of x. The if condition `q > num_occurrences` handles this correctly, returning -1.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Off-by-one errors when accessing the `x_indices` list. Remember that list indices start at 0, so the `q`-th occurrence is located at index `q - 1`.

✗Common mistake 2: Not handling the case where the query number exceeds the number of occurrences of `x`. Forgetting to return -1 in such cases will lead to incorrect results and potential index out of bounds exceptions.

✗Common mistake 3: Not deallocating memory in C. Failing to `free(x_indices)` can lead to memory leaks.

✅

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 specific log entries. You might want to find the 5th occurrence of a particular error message in a log file.

🏦Real-world scenario 2: Finding the positions of a particular gene in a DNA sequence. You might want to know the location of the 3rd instance of a certain genetic marker.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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 8, 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 14

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

@DevExpert92Jul 7

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 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 do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

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 Occurrences of an Element in 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 hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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