How do you solve Minimum Number of Pushes to Type Word II on LeetCode?

Minimum Number of Pushes to Type Word II (LeetCode #3016) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Distributing letters evenly across keys minimizes total pushes.

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

The optimal solution for Minimum Number of Pushes to Type Word II runs in O(n log n) time and uses O(n) space. This complexity arises from counting the frequencies (O(n)) and sorting them (O(n log n)). The space is used to store the frequency counts.

What is the brute force solution for Minimum Number of Pushes to Type Word II?

The brute force approach for Minimum Number of Pushes to Type Word II is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute-force approach, we try every possible mapping of letters to keys and calculate the total number of pushes required for each mapping. This method is straightforward but inefficient due to the exponential number of combinations. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Number of Pushes to Type Word II?

Minimum Number of Pushes to Type Word II uses the following concepts: Hash Table, String, Greedy, Sorting, Counting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Minimum Number of Pushes to Type Word II?

Always think about how to optimize your solution after the brute force. Explain your thought process clearly when discussing mappings. Practice calculating frequencies and distributions with small examples.

What are common mistakes when solving Minimum Number of Pushes to Type Word II?

Failing to count letter frequencies correctly. Not considering how to evenly distribute letters across keys.

#3016

Minimum Number of Pushes to Type Word II

Medium

Hash TableStringGreedySortingCountingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(n)

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Intuition

Time O(n log n)Space O(n)

The optimal approach involves counting the frequency of each letter and distributing them evenly across the available keys. This minimizes the total pushes required by ensuring that no key is overloaded with too many letters.

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Algorithm

4 steps

1Step 1: Count the frequency of each letter in the word.
2Step 2: Sort the frequencies in descending order.
3Step 3: Distribute the letters across the keys, ensuring that the most frequent letters get the least number of pushes.
4Step 4: Calculate the total pushes based on the distribution.

solution.py11 lines

1# Full working Python code
2from collections import Counter
3
4def min_pushes_optimal(word):
5    freq = Counter(word)
6    frequencies = sorted(freq.values(), reverse=True)
7    pushes = 0
8    for i, count in enumerate(frequencies):
9        pushes += (i // 8 + 1) * count
10    return pushes
11

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Complexity note: This complexity arises from counting the frequencies (O(n)) and sorting them (O(n log n)). The space is used to store the frequency counts.

1Distributing letters evenly across keys minimizes total pushes.
2The frequency of letters directly influences the optimal mapping.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.