What is the time complexity of Substring XOR Queries?

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

What data structures are used to solve Substring XOR Queries?

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

What are the key insights for solving Substring XOR Queries?

Insight 1: The target decimal value of the substring is `first ^ second`. Compute this XOR value for each query to find the desired substring value. Insight 2: Since the maximum value for `first` and `second` is 10^9, the maximum decimal value of a substring can also be 10^9, which means the substring's length is at most 31 (since 2^30 < 10^9 < 2^31). This limits the search space for each start index in the string `s`.

Which companies ask LeetCode 2564. Substring XOR Queries in interviews?

This problem is frequently asked at Trilogy.

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Substring XOR Queries - LeetCode 2564 Solution

Q: How to solve Substring XOR Queries?

The solution uses a hash table (memo) to store the decimal values of all possible substrings of `s` up to a maximum length of 32, along with their starting and ending indices. The solution iterates through the string `s`, and for each starting position, it computes the decimal values of substrings up to length 32. These decimal values and their corresponding indices are stored in the `memo`. When processing the queries, it calculates the target decimal value using `first ^ second` and checks if this value exists in the `memo`. If it does, it appends the corresponding indices to the answer array; otherwise, it appends `[-1, -1]`.

Q: Which companies ask LeetCode 2564. Substring XOR Queries in interviews?

This problem is frequently asked at Trilogy.

Substring XOR Queries - Complete Solution Guide

Substring XOR Queries is LeetCode problem 2564, 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 binary string s , and a 2D integer array queries where queries[i] = [first i , second i ] . For the i th query, find the shortest substring of s whose decimal value , val , yields second i when bitwise XORed with first i . In other words, val ^ first i == second i . The answer to the i th query is the endpoints ( 0-indexed ) of the substring [left i , right i ] or [-1, -1] if no such substring exists. If there are multiple answers, choose the one with the minimum left i . Return

Detailed Explanation

The problem asks us to find, for each query, the shortest substring within a given binary string `s` such that the XOR of its decimal value with the first element of the query equals the second element of the query. The output should be an array of pairs, where each pair represents the start and end indices of the substring, or `[-1, -1]` if no such substring exists. If multiple substrings satisfy the condition, the one with the smallest starting index should be returned. The input consists of a binary string `s` and a 2D array `queries`. The constraints include the length of `s` being up to 10^4, the number of queries being up to 10^5, and the values within the queries being up to 10^9.

Solution Approach

The solution uses a hash table (memo) to store the decimal values of all possible substrings of `s` up to a maximum length of 32, along with their starting and ending indices. The solution iterates through the string `s`, and for each starting position, it computes the decimal values of substrings up to length 32. These decimal values and their corresponding indices are stored in the `memo`. When processing the queries, it calculates the target decimal value using `first ^ second` and checks if this value exists in the `memo`. If it does, it appends the corresponding indices to the answer array; otherwise, it appends `[-1, -1]`.

Step-by-Step Algorithm

Step 1: Initialize a hash table (memo) to store substring decimal values and their start/end indices.
Step 2: Iterate through the binary string `s` from left to right.
Step 3: If the current character is '0', check if the value '0' exists in the memo. If not, store the start and end index of '0'. Then, continue to the next character
Step 4: If the current character is '1', start building substrings from this index. For each substring up to length 32:
Step 5: Calculate the decimal value of the current substring.
Step 6: If the decimal value is not in the memo, store the start and end indices of the substring in the memo.
Step 7: After processing all substrings, iterate through the queries.
Step 8: For each query, calculate the target decimal value by XORing `first` and `second`.
Step 9: Check if the target value exists in the memo. If yes, append the corresponding indices from the memo to the result array. If not, append `[-1, -1]` to the result array.
Step 10: Return the result array.

Key Insights

Insight 1: The target decimal value of the substring is `first ^ second`. Compute this XOR value for each query to find the desired substring value.
Insight 2: Since the maximum value for `first` and `second` is 10^9, the maximum decimal value of a substring can also be 10^9, which means the substring's length is at most 31 (since 2^30 < 10^9 < 2^31). This limits the search space for each start index in the string `s`.
Insight 3: Using a hash table (or dictionary) to store precomputed substrings and their indices allows for efficient lookup when processing the queries. This avoids repeated calculations for the same substring values.
Insight 4: Leading zeros do not contribute to the decimal value, so '0' should be handled separately or skipped to optimize substring length if necessary.

Complexity Analysis

Time Complexity: O(n + q)

Space Complexity: O(n)

Topics

This problem involves: Array, Hash Table, String, Bit Manipulation.

Companies

Asked at: Trilogy.

Substring XOR Queries | LeetCode 2564

Medium

Array Hash Table String Bit Manipulation

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

Solution Code

Available in:

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

class Solution {
    public int[][] substringXorQueries(String s, int[][] queries) {
        int n = s.length();
        Map<Integer, int[]> memo = new HashMap<>();

        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == '0') {
                if (!memo.containsKey(0)) {
                    memo.put(0, new int[]{i, i});
                }
                continue;
            }

            int currentVal = 0;
            for (int j = i; j < Math.min(n, i + 32); j++) {
                currentVal = (currentVal << 1) | (s.charAt(j) - '0');

                if (!memo.containsKey(currentVal)) {
                    memo.put(currentVal, new int[]{i, j});
                }
            }
        }

        int[][] ans = new int[queries.length][];
        for (int i = 0; i < queries.length; i++) {
            int first = queries[i][0];
            int second = queries[i][1];
            int target = first ^ second;
            ans[i] = memo.containsKey(target) ? memo.get(target) : new int[]{-1, -1};
        }

        return ans;
    }
}

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Problem Info

Description

Problem 2564: Substring XOR Queries - Detailed explanation and solution approaches.

Topics

Array Hash Table String Bit Manipulation

Companies

Trilogy

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2564

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

10 steps

1
Step 1: Initialize a hash table (memo) to store substring decimal values and their start/end indices.
2
Step 2: Iterate through the binary string `s` from left to right.
3
Step 3: If the current character is '0', check if the value '0' exists in the memo. If not, store the start and end index of '0'. Then, continue to the next character
4
Step 4: If the current character is '1', start building substrings from this index. For each substring up to length 32:
5
Step 5: Calculate the decimal value of the current substring.
6
Step 6: If the decimal value is not in the memo, store the start and end indices of the substring in the memo.
7
Step 7: After processing all substrings, iterate through the queries.
8
Step 8: For each query, calculate the target decimal value by XORing `first` and `second`.
9
Step 9: Check if the target value exists in the memo. If yes, append the corresponding indices from the memo to the result array. If not, append `[-1, -1]` to the result array.
10
Step 10: Return the result 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 + q)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is dominated by the initial scan of the string `s` and the processing of each query. The space complexity is dictated by the size of the hash table, which can grow up to O(n) in the worst-case scenario (e.g., a string with many distinct substring values).

📖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

Brute-Force

Iterate through all possible substrings for each query and check if the XOR condition is satisfied. This approach avoids using a hash table.

Time: O(n^3 * q), where n is the length of s and q is the number of queries.Space: O(1)

Trade-offs: This approach is much slower than the hash table approach, especially for large inputs. It's simpler to implement but not efficient. Useful when n is very small.

✨

Key Insights

1Insight 1: The target decimal value of the substring is `first ^ second`. Compute this XOR value for each query to find the desired substring value.
2Insight 2: Since the maximum value for `first` and `second` is 10^9, the maximum decimal value of a substring can also be 10^9, which means the substring's length is at most 31 (since 2^30 < 10^9 < 2^31). This limits the search space for each start index in the string `s`.
3Insight 3: Using a hash table (or dictionary) to store precomputed substrings and their indices allows for efficient lookup when processing the queries. This avoids repeated calculations for the same substring values.
4Insight 4: Leading zeros do not contribute to the decimal value, so '0' should be handled separately or skipped to optimize substring length if necessary.

📚

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!

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: The substring '0'. The code explicitly handles the case where the substring is '0'.
Edge case 2: No matching substring found. The code defaults to returning [-1, -1] if no substring matches the target value.
Edge case 3: A very long string `s` with many queries. The complexity analysis shows the solution handles this efficiently.
Edge case 4: The result of the XOR operation might be 0, requiring special handling to check for the substring '0'.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling the edge case where no substring satisfies the condition, resulting in incorrect output.

✗Common mistake 2: Incorrectly calculating the decimal value of the substrings, leading to incorrect XOR results.

✗Common mistake 3: Failing to consider the constraint on substring length and searching beyond the necessary range, impacting efficiency.

✗Common mistake 4: Not handling the edge case of the character '0' correctly, especially when it appears at the beginning of the string.

✅

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: Network packet analysis. This algorithm can be used to search for specific bit patterns (substrings) within network packets to identify potential security threats or analyze network traffic.

🏦Real-world scenario 2: Data compression. Finding repeating patterns within data can be used for data compression. This substring searching approach can be adapted to identify such patterns.

🎮Real-world scenario 3: DNA sequencing. Although simplified, the principle of searching for specific sequences within a string can be applied to analyzing DNA sequences.

💡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

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ 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 15, 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

❓

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.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

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 "Substring XOR Queries"?

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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