What is the time complexity of Minimum Number of Pushes to Type Word II?

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

What data structures are used to solve Minimum Number of Pushes to Type Word II?

This problem uses Hash Table, String, Greedy, Sorting, Counting. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Minimum Number of Pushes to Type Word II?

Insight 1: The optimal mapping strategy is to assign the most frequent characters to the keys with the fewest number of pushes (i.e., the first 8 characters get assigned a cost of 1, the next 8 a cost of 2, and so on). Insight 2: We need to count the frequency of each character in the input word.

Which companies ask LeetCode 3016. Minimum Number of Pushes to Type Word II in interviews?

This problem is frequently asked at DE Shaw.

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Minimum Number of Pushes to Type Word II - LeetCode 3016 Solution

Minimum Number of Pushes to Type Word II - Complete Solution Guide

Minimum Number of Pushes to Type Word II is LeetCode problem 3016, 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 string word containing lowercase English letters. Telephone keypads have keys mapped with distinct collections of lowercase English letters, which can be used to form words by pushing them. For example, the key 2 is mapped with ["a","b","c"] , we need to push the key one time to type "a" , two times to type "b" , and three times to type "c" . It is allowed to remap the keys numbered 2 to 9 to distinct collections of letters. The keys can be remapped to any amount of letters, but

Detailed Explanation

The problem asks us to find the minimum number of pushes required to type a given word on a telephone keypad, where we are allowed to remap the letters to the keys numbered 2 to 9. Each key can have multiple letters, but each letter must be mapped to exactly one key. The cost to type a letter is the number of times the key to which it's mapped needs to be pushed. For example, if 'a' is mapped to key '2', typing 'a' requires one push; if 'b' is mapped to key '2', typing 'b' requires two pushes; and so on.

Solution Approach

The solution uses a greedy approach. It first counts the frequency of each character in the word. Then, it sorts the frequencies in descending order. After that, it iterates through the sorted frequencies and calculates the total number of pushes. The first 8 most frequent characters will cost 1 push each, the next 8 will cost 2 pushes each, and so on. This assignment strategy guarantees the minimum total pushes because it prioritizes assigning the most frequent characters to keys with the least number of pushes.

Step-by-Step Algorithm

Step 1: Count the frequency of each character in the input string 'word'. Store these frequencies in a hash map (or similar data structure).
Step 2: Extract the frequencies from the hash map and store them in a list or array.
Step 3: Sort the list of frequencies in descending order.
Step 4: Initialize a variable 'total_pushes' to 0.
Step 5: Iterate through the sorted frequencies. For each frequency at index 'i', calculate the 'push_cost' as (i // 8) + 1. This represents how many times you need to press a button for the character at the ith most frequent position.
Step 6: Multiply the frequency by the 'push_cost' and add the result to 'total_pushes'.
Step 7: After iterating through all frequencies, return 'total_pushes'.

Key Insights

Insight 1: The optimal mapping strategy is to assign the most frequent characters to the keys with the fewest number of pushes (i.e., the first 8 characters get assigned a cost of 1, the next 8 a cost of 2, and so on).
Insight 2: We need to count the frequency of each character in the input word.
Insight 3: Sorting the frequencies in descending order allows us to greedily assign the most frequent characters to the lowest-cost pushes.

Complexity Analysis

Time Complexity: O(N)

Space Complexity: O(1)

Topics

This problem involves: Hash Table, String, Greedy, Sorting, Counting.

Companies

Asked at: DE Shaw.

Minimum Number of Pushes to Type Word II | LeetCode 3016

Medium

Hash Table String Greedy Sorting Counting

Time: O(N)Space: O(1)

Solution Code

Available in:

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

class Solution {
    public int minimumPushes(String word) {
        Map<Character, Integer> counts = new HashMap<>();
        for (char c : word.toCharArray()) {
            counts.put(c, counts.getOrDefault(c, 0) + 1);
        }

        List<Integer> freqs = new ArrayList<>(counts.values());
        Collections.sort(freqs, Collections.reverseOrder());

        int totalPushes = 0;
        for (int i = 0; i < freqs.size(); i++) {
            int freq = freqs.get(i);
            int pushCost = (i / 8) + 1;
            totalPushes += freq * pushCost;
        }

        return totalPushes;
    }
}

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Problem Info

Description

Problem 3016: Minimum Number of Pushes to Type Word II - Detailed explanation and solution approaches.

Topics

Hash Table String Greedy Sorting Counting

Companies

DE Shaw

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:3016

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

7 steps

1
Step 1: Count the frequency of each character in the input string 'word'. Store these frequencies in a hash map (or similar data structure).
2
Step 2: Extract the frequencies from the hash map and store them in a list or array.
3
Step 3: Sort the list of frequencies in descending order.
4
Step 4: Initialize a variable 'total_pushes' to 0.
5
Step 5: Iterate through the sorted frequencies. For each frequency at index 'i', calculate the 'push_cost' as (i // 8) + 1. This represents how many times you need to press a button for the character at the ith most frequent position.
6
Step 6: Multiply the frequency by the 'push_cost' and add the result to 'total_pushes'.
7
Step 7: After iterating through all frequencies, return 'total_pushes'.

💡

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)

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is dominated by the character counting and sorting of the frequencies. The space complexity is primarily due to the hash map or array used to store character frequencies.

📖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

Using a Priority Queue (Heap)

Instead of sorting the frequencies, we can use a min-heap (priority queue) to extract the frequencies in descending order. We can iterate and re-insert the frequencies appropriately into the heap as we calculate each push cost.

Time: O(N + KlogK), where N is the length of the input and K is number of distinct characters.Space: O(K)

Trade-offs: This approach has the same time and space complexity as the main solution. While it may be conceptually different, the constant factors involved might make it slightly slower due to the overhead of heap operations. The sorting method is often more efficient for smaller, fixed sized sets like in this problem.

✨

Key Insights

1Insight 1: The optimal mapping strategy is to assign the most frequent characters to the keys with the fewest number of pushes (i.e., the first 8 characters get assigned a cost of 1, the next 8 a cost of 2, and so on).
2Insight 2: We need to count the frequency of each character in the input word.
3Insight 3: Sorting the frequencies in descending order allows us to greedily assign the most frequent characters to the lowest-cost pushes.

📚

Key Terms Explained

For Students

Hash Table

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

Greedy Algorithm

Making the best choice at each step without looking ahead.

String

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

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty word. The code implicitly handles this case by returning 0, as the character counts will be empty, and no pushes will be calculated.
Edge case 2: Word with only one distinct character. The code will correctly assign a push cost of 1 to this character and calculate the total pushes as the length of the word.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not sorting the character frequencies. Without sorting, the greedy assignment of characters to keys will not be optimal, and the resulting number of pushes will not be minimized.

✗Common mistake 2: Incorrectly calculating the 'push_cost'. The push cost is determined by the index of the character's frequency in the sorted list, specifically `(i // 8) + 1`, NOT directly proportional to the frequency.

✅

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: Optimizing data compression algorithms where the most frequent characters are encoded with shorter codes, similar to Huffman coding.

🏦Real-world scenario 2: Designing efficient keyboard layouts or menu structures in software applications where the most frequently used functions or characters are easily accessible.

💡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

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate 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 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

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

@AlgoMasterJul 14

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

@InterviewProJul 7

❓

Frequently Asked Questions

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.

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.

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 "Minimum Number of Pushes to Type Word II"?

For this medium-level Hash Table 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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