Minimum Number of Pushes to Type Word I — Algorithm Visualization & Coding Challenge

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Understanding Minimum Number of Pushes to Type Word I

Detailed explanation and reference materials

Problem Overview

3014. Minimum Number of Pushes to Type Word I

Problem Overview

You are given a string word containing distinct lowercase English letters.

A telephone keypad contains 8 usable keys (2 to 9). Each key can be assigned any collection of lowercase English letters, but:

Every letter must be assigned to exactly one key.
A key may contain any number of letters.
The order of letters on a key determines the number of key presses:
- 1st letter → 1 push
- 2nd letter → 2 pushes
- 3rd letter → 3 pushes
- and so on.

Your task is to remap the keypad so that typing the given word requires the minimum total number of key presses.

Return the minimum number of pushes needed to type the entire word.

Key Insight

Since there are 8 available keys, the first 8 letters can each occupy the first position of a key, costing 1 push each.

After all first positions are filled:

The next 8 letters occupy the second position → 2 pushes each.
The next 8 letters occupy the third position → 3 pushes each.
Any remaining letters occupy the fourth position → 4 pushes each.

Because every character appears exactly once and all letters are distinct, the optimal strategy is simply to assign letters to the cheapest available positions.

Example 1

Input

word = "abcde"

Output

Explanation

There are only 5 letters, so each can be placed as the first letter on a different key.

Letter	Pushes
a	1
b	1
c	1
d	1
e	1

Total pushes:

1 + 1 + 1 + 1 + 1 = 5

Example 2

Input

word = "xycdefghij"

Output

Explanation

There are 10 distinct letters.

The first 8 letters occupy first positions on different keys.

The remaining 2 letters must be placed in second positions.

One optimal assignment is:

Letter	Pushes
x	1
c	1
e	1
f	1
g	1
h	1
i	1
j	1
y	2
d	2

Total pushes:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 = 12

Constraints

1 <= word.length <= 26
word contains only lowercase English letters.
Every character in word is distinct.

SEO Keywords

Minimum Number of Pushes to Type Word I
LeetCode 3014
Telephone Keypad Optimization
Greedy Algorithm
Keypad Remapping Problem
Minimum Key Presses
Distinct Characters
LeetCode Easy Greedy
DSA Greedy Problems
Algorithm Visualization

Why This Problem Matters

This problem demonstrates an important greedy optimization strategy.

Instead of trying every possible keypad mapping, we realize that only the push cost of each position matters. By always assigning letters to the cheapest available positions first, we achieve the minimum total cost.

This idea appears frequently in interview problems involving:

Greedy algorithms
Resource allocation
Cost minimization
Optimal assignment
Scheduling and placement

Instruction-by-Instruction Breakdown :

Main Function:

Enter Sample Input Here ---> Input Sentence

Enter Sample Output Here ---> Output Sentence

public static void main(String[] args) { ---> Simple Statement

String word1 = "abcde"; ---> Variable Value Assigned

System.out.println(minimumPushes(word1)); ---> Other Function Call

String word2 = "xycdefghij"; ---> Variable Value Assigned

System.out.println(minimumPushes(word2)); ---> Other Function Call

}//function end ---> Return Statement

Static Helper Function:

public static int minimumPushes(String word) { ---> Simple Statement

int n = word.length(); ---> Variable Value Assigned

int pushes = 0; ---> Variable Value Assigned

for (int i = 0; i < n; i++) { ---> For loop

pushes += (i / 8) + 1; ---> Variable Value Assigned

}//Loop End ---> Loop End

return pushes; ---> Return Statement

}//function end ---> Return Statement

Static Utility Functions , Classes and Global variables:

Utility Function is not required.

— Written by Saurabh Patil • B.Tech CSE • Software Developer

Reference Link

https://leetcode.com/problems/minimum-number-of-pushes-to-type-word-i/

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Minimum Number of Pushes to Type Word I — Algorithm Visualization & Coding Challenge

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🧠 Active Learning

📖 Passive Learning

🎯 Challenge Mode

Watch algorithms run step by step.

Understanding Minimum Number of Pushes to Type Word I

Problem Overview

3014. Minimum Number of Pushes to Type Word I

Problem Overview

Key Insight

Example 1

Explanation

Example 2

Explanation

Constraints

SEO Keywords

Why This Problem Matters

Instruction-by-Instruction Breakdown :

Main Function:

Static Helper Function:

Static Utility Functions , Classes and Global variables:

Categories

Reference Link

Starter Code

Think & Arrange, Don't Just Copy-Paste