What is the time complexity of Smallest String With A Given Numeric Value?

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

What data structures are used to solve Smallest String With A Given Numeric Value?

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

What are the key insights for solving Smallest String With A Given Numeric Value?

Insight 1: To obtain the lexicographically smallest string, we should prioritize using 'a's as much as possible from the beginning of the string. Insight 2: Placing larger characters ('z', 'y', etc.) towards the end of the string is crucial for achieving the smallest lexicographical order.

Which companies ask LeetCode 1663. Smallest String With A Given Numeric Value in interviews?

This problem is frequently asked at Lendingkart Technologies.

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Smallest String With A Given Numeric Value - LeetCode 1663 Solution

Smallest String With A Given Numeric Value - Complete Solution Guide

Smallest String With A Given Numeric Value is LeetCode problem 1663, 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

The numeric value of a lowercase character is defined as its position (1-indexed) in the alphabet, so the numeric value of a is 1 , the numeric value of b is 2 , the numeric value of c is 3 , and so on. The numeric value of a string consisting of lowercase characters is defined as the sum of its characters' numeric values. For example, the numeric value of the string "abe" is equal to 1 + 2 + 5 = 8 . You are given two integers n and k . Return the lexicographically smallest string with length eq

Detailed Explanation

The problem asks us to find the lexicographically smallest string of a given length `n` with a specific numeric value `k`. The numeric value of a string is the sum of the positions of its characters in the alphabet (a=1, b=2, ..., z=26). We are given `n` and `k` as input, and the output should be the string meeting these conditions.

Solution Approach

The solution uses a greedy approach to build the lexicographically smallest string. It initializes a string of length `n` with all 'a's. Then, it iterates from the end of the string towards the beginning. For each position, it adds the largest possible value to the character at that position (up to a maximum of 25 to convert 'a' to 'z') such that the total numeric value of the string remains equal to `k`. This process effectively distributes the remaining numeric value (`k - n`) from the end of the string to the beginning, ensuring the lexicographically smallest result.

Step-by-Step Algorithm

Step 1: Initialize a string (or character array) of length `n` with all 'a's. This creates a base string with a numeric value of `n`.
Step 2: Calculate the remaining numeric value that needs to be added: `k -= n`.
Step 3: Iterate through the string from right to left (from index `n-1` to 0).
Step 4: In each iteration, calculate the value to add to the current character: `add_val = min(k, 25)`. This ensures that we don't exceed the value needed (`k`) and that the character remains within the range 'a' to 'z'.
Step 5: Update the character at the current position: `res[i] = 'a' + add_val` (or equivalent character manipulation).
Step 6: Reduce the remaining value by the added value: `k -= add_val`.
Step 7: Continue iterating until we reach the beginning of the string or `k` becomes 0.
Step 8: Convert the character array/vector back to a string and return the result.

Key Insights

Insight 1: To obtain the lexicographically smallest string, we should prioritize using 'a's as much as possible from the beginning of the string.
Insight 2: Placing larger characters ('z', 'y', etc.) towards the end of the string is crucial for achieving the smallest lexicographical order.
Insight 3: A greedy approach works here because we can always fill the string from right to left with the largest possible character (up to 'z') that doesn't exceed the remaining required numeric value.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: String, Greedy.

Companies

Asked at: Lendingkart Technologies.

Smallest String With A Given Numeric Value | LeetCode 1663

Medium

String Greedy

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

Solution Code

Available in:

class Solution {
    public String getSmallestString(int n, int k) {
        // Initialize the result as an array of 'a's, which is the lexicographically smallest base.
        // This has a numeric value of n.
        char[] res = new char[n];
        for (int i = 0; i < n; i++) {
            res[i] = 'a';
        }
        
        // We need to increase the sum by k - n.
        k -= n;
        
        // To keep the string lexicographically smallest, we should put larger characters
        // at the end. So, we iterate from right to left.
        for (int i = n - 1; i >= 0; i--) {
            // If no more value needs to be added, we can stop.
            if (k == 0) {
                break;
            }
            
            // The maximum value we can add to a character 'a' is 25 (to make it 'z').
            int add_val = Math.min(k, 25);
            
            // Update the character by adding the calculated value.
            res[i] = (char) ( 'a' + add_val);
            
            // Decrease the remaining value to be distributed.
            k -= add_val;
        }
        
        return new String(res);
    }
}

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Problem Info

Description

Problem 1663: Smallest String With A Given Numeric Value - Detailed explanation and solution approaches.

Topics

String Greedy

Companies

Lendingkart Technologies

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:1663

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: Initialize a string (or character array) of length `n` with all 'a's. This creates a base string with a numeric value of `n`.
2
Step 2: Calculate the remaining numeric value that needs to be added: `k -= n`.
3
Step 3: Iterate through the string from right to left (from index `n-1` to 0).
4
Step 4: In each iteration, calculate the value to add to the current character: `add_val = min(k, 25)`. This ensures that we don't exceed the value needed (`k`) and that the character remains within the range 'a' to 'z'.
5
Step 5: Update the character at the current position: `res[i] = 'a' + add_val` (or equivalent character manipulation).
6
Step 6: Reduce the remaining value by the added value: `k -= add_val`.
7
Step 7: Continue iterating until we reach the beginning of the string or `k` becomes 0.
8
Step 8: Convert the character array/vector back to a string and return the result.

💡

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(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is O(n) because we iterate through the string of length `n` once. The space complexity is O(n) because we store the resulting string of length `n`.

📖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

Instead of building the string character by character, we can calculate the number of 'z's and 'a's directly using integer division and modulo operations. This potentially avoids the explicit loop.

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

Trade-offs: This approach might be slightly faster in practice, but less intuitive to understand compared to the greedy approach, as it requires some math.

✨

Key Insights

1Insight 1: To obtain the lexicographically smallest string, we should prioritize using 'a's as much as possible from the beginning of the string.
2Insight 2: Placing larger characters ('z', 'y', etc.) towards the end of the string is crucial for achieving the smallest lexicographical order.
3Insight 3: A greedy approach works here because we can always fill the string from right to left with the largest possible character (up to 'z') that doesn't exceed the remaining required numeric value.

📚

Key Terms Explained

For Students

Greedy Algorithm

Making the best choice at each step without looking ahead.

String

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

Edge Cases

Edge case 1: `n = 1`, `k = 1`. The solution correctly returns "a".
Edge case 2: `n = 1`, `k = 26`. The solution correctly returns "z".
Edge case 3: `k = n`. The solution returns a string of all 'a's.
Edge case 4: `k = 26 * n`. The solution returns a string of all 'z's.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Iterating from left to right instead of right to left. This leads to a lexicographically larger string because the 'z's will be placed at the beginning.

✗Common mistake 2: Not handling the case where `k < n` properly or not initializing the string with 'a's. This can lead to incorrect results or errors.

✗Common mistake 3: Not considering the edge cases where `k` is close to `n` or `26*n`, potentially leading to incorrect character assignment.

✅

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: This algorithm can be applied in scenarios where you need to generate strings that adhere to certain constraints, such as password generation with specific complexity rules and lexicographical ordering.

🏦Real-world scenario 2: It can also be used in data compression techniques where assigning shorter strings to more frequent values results in better compression ratios. This problem uses a similar principle.

💡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

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

⚠️ 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: July 14, 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

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

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 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.

What are common greedy problem patterns?

Activity selection (sort by end time), interval scheduling (sort by start/end), Huffman coding (always combine smallest), fractional knapsack (sort by value/weight ratio), and minimum spanning tree. Look for problems where local decisions don't affect future options.

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 "Smallest String With A Given Numeric Value"?

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 greedy techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?