What is the time complexity of Count Number of Homogenous Substrings?

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

What data structures are used to solve Count Number of Homogenous Substrings?

This problem uses Math, String. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Count Number of Homogenous Substrings?

Insight 1: The problem can be solved efficiently by iterating through the string and keeping track of the current 'streak' of consecutive identical characters. Insight 2: The number of homogenous substrings ending at a particular index is equal to the length of the current streak. We can incrementally add the streak length to the total count.

Which companies ask LeetCode 1759. Count Number of Homogenous Substrings in interviews?

This problem is frequently asked at Virtu Financial.

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Count Number of Homogenous Substrings - LeetCode 1759 Solution

Count Number of Homogenous Substrings - Complete Solution Guide

Count Number of Homogenous Substrings is LeetCode problem 1759, 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 a string s , return the number of homogenous substrings of s . Since the answer may be too large, return it modulo 10 9 + 7 . A string is homogenous if all the characters of the string are the same. A substring is a contiguous sequence of characters within a string. Example 1: Input: s = "abbcccaa" Output: 13 Explanation: The homogenous substrings are listed as below: "a" appears 3 times. "aa" appears 1 time. "b" appears 2 times. "bb" appears 1 time. "c" appears 3 times. "cc" appears 2 tim

Detailed Explanation

The problem requires us to count the number of homogenous substrings within a given string 's'. A homogenous substring is defined as a contiguous sequence of characters where all characters are identical. The final result should be returned modulo 10^9 + 7 to prevent integer overflow, as the number of substrings can be quite large. The input is a string 's' consisting of lowercase letters, and the output is the count of homogenous substrings.

Solution Approach

The provided solution uses an iterative approach to traverse the string 's'. It maintains a 'streak' counter to track the length of the current homogenous substring. For each character, it checks if it's the same as the previous one. If it is, the streak is incremented. Otherwise, the streak is reset to 1. The current streak length is added to the total count of homogenous substrings, and the result is taken modulo 10^9 + 7 in each iteration.

Step-by-Step Algorithm

Step 1: Initialize 'ans' (the total count of homogenous substrings) to 0 and 'streak' (the length of the current homogenous substring) to 0.
Step 2: Iterate through the string 's' from left to right.
Step 3: For each character at index 'i', check if it's the same as the previous character (at index i-1).
Step 4: If the current character is the same as the previous one, increment the 'streak'. Otherwise, reset the 'streak' to 1.
Step 5: Add the current 'streak' to 'ans' and take the modulo 10^9 + 7 to prevent overflow.
Step 6: After iterating through the entire string, return 'ans'.

Key Insights

Insight 1: The problem can be solved efficiently by iterating through the string and keeping track of the current 'streak' of consecutive identical characters.
Insight 2: The number of homogenous substrings ending at a particular index is equal to the length of the current streak. We can incrementally add the streak length to the total count.
Insight 3: The modulo operation is crucial to prevent integer overflow, especially for large input strings.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Math, String.

Companies

Asked at: Virtu Financial.

Count Number of Homogenous Substrings | LeetCode 1759

Medium

Math String

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

Solution Code

Available in:

class Solution {
    public int countHomogenous(String s) {
        int MOD = (int)1e9 + 7;
        int ans = 0;
        int streak = 0;
        
        for (int i = 0; i < s.length(); i++) {
            if (i > 0 && s.charAt(i) == s.charAt(i-1)) {
                streak++;
            } else {
                streak = 1;
            }
            
            ans = (ans + streak) % MOD;
        }
        
        return ans;
    }
}

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Problem Info

Description

Problem 1759: Count Number of Homogenous Substrings - Detailed explanation and solution approaches.

Topics

Math String

Companies

Virtu Financial

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1759

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

6 steps

1
Step 1: Initialize 'ans' (the total count of homogenous substrings) to 0 and 'streak' (the length of the current homogenous substring) to 0.
2
Step 2: Iterate through the string 's' from left to right.
3
Step 3: For each character at index 'i', check if it's the same as the previous character (at index i-1).
4
Step 4: If the current character is the same as the previous one, increment the 'streak'. Otherwise, reset the 'streak' to 1.
5
Step 5: Add the current 'streak' to 'ans' and take the modulo 10^9 + 7 to prevent overflow.
6
Step 6: After iterating through the entire string, return 'ans'.

💡

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 algorithm processes each character in the input string once, performing a constant number of operations for each character. Therefore, the time complexity is directly proportional to the length of the string. The algorithm uses only a few integer variables, and their memory usage doesn't depend on the size of the input string, resulting in constant space complexity.

📖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

Mathematical Approach

Identify consecutive groups of the same character, calculate the number of homogenous substrings in each group using the formula n*(n+1)/2, where n is the length of the group, and then sum up the results, applying the modulo operation.

Time: O(n), where n is the length of the string 's'.Space: O(1)

Trade-offs: This approach is conceptually slightly different but achieves the same time and space complexity as the iterative approach. It might be more concise for some, but both are efficient.

✨

Key Insights

1Insight 1: The problem can be solved efficiently by iterating through the string and keeping track of the current 'streak' of consecutive identical characters.
2Insight 2: The number of homogenous substrings ending at a particular index is equal to the length of the current streak. We can incrementally add the streak length to the total count.
3Insight 3: The modulo operation is crucial to prevent integer overflow, especially for large input strings.

📚

Key Terms Explained

For Students

String

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

Edge Cases

Edge case 1: Empty string. The code implicitly handles this case because the loop won't execute, and the initial value of 'ans' (0) will be returned, which is correct.
Edge case 2: String with only one character. The code handles this correctly because 'streak' will be 1, and 'ans' will become 1.
Edge case 3: String with all the same characters (e.g., 'aaaaa'). The streak will continuously increase, and the sum of the streak values will represent the sum of integers from 1 to n, which is the correct number of homogenous substrings.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to apply the modulo operator at each step. This can lead to integer overflow and incorrect results, especially for long input strings.

✗Common mistake 2: Not handling the edge case of an empty or single-character string correctly. Although the presented solution implicitly handles these, it's important to consciously consider them during problem-solving.

✗Common mistake 3: Not correctly initializing the streak. The streak should start at 1 for the first character.

✅

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: Data compression. Identifying and counting homogenous sequences can be used in simple data compression algorithms.

🏦Real-world scenario 2: Bioinformatics. Analyzing DNA or protein sequences may involve identifying repeating patterns or homogenous segments, which this algorithm can help with.

💡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

Always test your solution with edge cases: empty input, single element, and boundary values.

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: October 18, 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

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

@AlgoMasterJun 29

❓

Frequently Asked Questions

What is the sliding window technique for string problems?

Sliding window maintains a "window" of characters with two pointers. Expand the right pointer to include characters, shrink from left when window violates constraints. Useful for substring problems, anagrams, and longest/shortest substring with properties.

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 "Count Number of Homogenous Substrings"?

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

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