What is the time complexity of Number of Ways to Select Buildings?

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

What data structures are used to solve Number of Ways to Select Buildings?

This problem uses String, Dynamic Programming, Prefix Sum. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Number of Ways to Select Buildings?

Insight 1: We need to find triplets of the form '010' or '101'. The solution focuses on iterating through the string and considering each character as the middle element of a potential triplet. Insight 2: Prefix sums (or counting occurrences so far) are crucial to efficiently determine the number of '0's and '1's to the left and right of each character.

Which companies ask LeetCode 2222. Number of Ways to Select Buildings in interviews?

This problem is frequently asked at Dream11.

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Number of Ways to Select Buildings - LeetCode 2222 Solution

Number of Ways to Select Buildings - Complete Solution Guide

Number of Ways to Select Buildings is LeetCode problem 2222, 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 0-indexed binary string s which represents the types of buildings along a street where: s[i] = '0' denotes that the i th building is an office and s[i] = '1' denotes that the i th building is a restaurant. As a city official, you would like to select 3 buildings for random inspection. However, to ensure variety, no two consecutive buildings out of the selected buildings can be of the same type. For example, given s = "0 0 1 1 0 1 " , we cannot select the 1 st , 3 rd , and 5 th bu

Detailed Explanation

The problem asks us to find the number of ways to select three buildings from a street such that no two consecutive selected buildings are of the same type. The street is represented by a binary string 's' where '0' represents an office and '1' represents a restaurant. We need to count the number of valid triplets of building indices that alternate between offices and restaurants (or vice-versa). For example, "010" and "101" are valid selections, but "001" or "110" are not.

Solution Approach

The provided solution iterates through the input string 's' once. For each character in 's', it considers that character as the middle element of a potential valid sequence ('010' or '101'). If the character is '0', it calculates the number of '1's to its left and the number of '1's to its right. The product of these two numbers represents the number of '101' sequences with that '0' as the middle element. Similarly, if the character is '1', it calculates the number of '0's to its left and the number of '0's to its right, and their product gives the number of '010' sequences with that '1' as the middle element. The sum of these products for all characters in 's' gives the total number of valid ways to select the buildings.

Step-by-Step Algorithm

Step 1: Calculate the total number of '0's and '1's in the input string 's'.
Step 2: Initialize variables to track the number of '0's and '1's encountered so far while iterating through the string.
Step 3: Iterate through the string 's'.
Step 4: In each iteration, check if the current character is '0' or '1'.
Step 5: If the character is '0', calculate the number of '1's to the left (ones_so_far) and to the right (total_ones - ones_so_far). Add their product to the answer.
Step 6: If the character is '1', calculate the number of '0's to the left (zeros_so_far) and to the right (total_zeros - zeros_so_far). Add their product to the answer.
Step 7: Update the count of '0's or '1's encountered so far, depending on the character.
Step 8: After iterating through the entire string, return the calculated answer.

Key Insights

Insight 1: We need to find triplets of the form '010' or '101'. The solution focuses on iterating through the string and considering each character as the middle element of a potential triplet.
Insight 2: Prefix sums (or counting occurrences so far) are crucial to efficiently determine the number of '0's and '1's to the left and right of each character.
Insight 3: Avoid nested loops. By pre-calculating the total number of zeros and ones and using prefix sums, the solution achieves linear time complexity.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: String, Dynamic Programming, Prefix Sum.

Companies

Asked at: Dream11.

Number of Ways to Select Buildings | LeetCode 2222

Medium

String Dynamic Programming Prefix Sum

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

Solution Code

Available in:

class Solution {
    public long numberOfWays(String s) {
        int total_zeros = 0;
        int total_ones = 0;
        
        for (int i = 0; i < s.length(); i++) {
            if (s.charAt(i) == '0') {
                total_zeros++;
            } else {
                total_ones++;
            }
        }
        
        long ans = 0;
        int zeros_so_far = 0;
        int ones_so_far = 0;
        
        for (int i = 0; i < s.length(); i++) {
            char charAtI = s.charAt(i);
            if (charAtI == '0') {
                // This '0' is the middle element for a "101" sequence.
                // Number of ways = (ones on the left) * (ones on the right)
                ans += (long) ones_so_far * (total_ones - ones_so_far);
                zeros_so_far++;
            } else { // char == '1'
                // This '1' is the middle element for a "010" sequence.
                // Number of ways = (zeros on the left) * (zeros on the right)
                ans += (long) zeros_so_far * (total_zeros - zeros_so_far);
                ones_so_far++;
            }
        }
        
        return ans;
    }
}

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Problem Info

Description

Problem 2222: Number of Ways to Select Buildings - Detailed explanation and solution approaches.

Topics

String Dynamic Programming Prefix Sum

Companies

Dream11

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2222

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

8 steps

1
Step 1: Calculate the total number of '0's and '1's in the input string 's'.
2
Step 2: Initialize variables to track the number of '0's and '1's encountered so far while iterating through the string.
3
Step 3: Iterate through the string 's'.
4
Step 4: In each iteration, check if the current character is '0' or '1'.
5
Step 5: If the character is '0', calculate the number of '1's to the left (ones_so_far) and to the right (total_ones - ones_so_far). Add their product to the answer.
6
Step 6: If the character is '1', calculate the number of '0's to the left (zeros_so_far) and to the right (total_zeros - zeros_so_far). Add their product to the answer.
7
Step 7: Update the count of '0's or '1's encountered so far, depending on the character.
8
Step 8: After iterating through the entire string, return the calculated answer.

💡

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 time complexity is linear because we iterate through the string a fixed number of times (twice). The space complexity is constant because we only use a few integer variables, regardless of the input size.

📖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 combinations of three buildings and check if they satisfy the condition. This would involve three nested loops.

Time: O(n^3), where n is the length of the input string.Space: O(1)

Trade-offs: The brute force approach is simple to understand but very inefficient for larger input strings. The main solution offers a much better time complexity.

✨

Key Insights

1Insight 1: We need to find triplets of the form '010' or '101'. The solution focuses on iterating through the string and considering each character as the middle element of a potential triplet.
2Insight 2: Prefix sums (or counting occurrences so far) are crucial to efficiently determine the number of '0's and '1's to the left and right of each character.
3Insight 3: Avoid nested loops. By pre-calculating the total number of zeros and ones and using prefix sums, the solution achieves linear time complexity.

📚

Key Terms Explained

For Students

Dynamic Programming

Breaking complex problems into smaller subproblems and storing results.

String

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

Edge Cases

Edge case 1: Input string contains only '0's or only '1's. The algorithm correctly returns 0 because there are no valid triplets in this case.
Edge case 2: Input string is very long. The algorithm handles this case efficiently because it has a linear time complexity.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Using nested loops to find the triplets, which results in a time complexity of O(n^3) and leads to Time Limit Exceeded (TLE) errors.

✗Common mistake 2: Not considering the case where the middle element is '0' and trying to find '010' sequences instead of '101', or vice-versa. The problem asks for *any* alternating sequence.

✅

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: Analyzing sequences of events to identify patterns. For example, analyzing a log file to find sequences of errors or successful operations.

🏦Real-world scenario 2: Signal processing, where alternating patterns in a signal can indicate specific events or conditions.

💡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

String problems often involve sliding windows or two pointers. Consider if the character set is limited (lowercase letters = only 26 possibilities).

🎯 Interview Tip

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

⚠️ Watch Out

Mutating strings directly in languages where strings are immutable. Use StringBuilder or arrays.

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: August 2, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 14

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 7

❓

Frequently Asked Questions

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) complexity.

How do I identify if a problem needs dynamic programming?

DP problems typically have: 1) Overlapping subproblems (same calculation repeated), 2) Optimal substructure (optimal solution uses optimal solutions to subproblems). Look for keywords like "minimum/maximum," "count ways," "is it possible," or "longest/shortest."

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 "Number of Ways to Select Buildings"?

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

🤖 Need help with this problem?