#1663

Medium

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Smallest String With A Given Numeric Value

Find the lexicographically smallest string of length n with a given numeric value k using a greedy approach.

Problem Statement

You are given two integers n and k. Your task is to return the lexicographically smallest string of length n such that the sum of the character values is equal to k. Each character is a lowercase letter, and its numeric value is defined by its position in the alphabet, where 'a' = 1, 'b' = 2, ..., 'z' = 26.

The sum of the character values of the string must equal k, and you need to ensure that the string is lexicographically as small as possible. You should aim to minimize the character values from left to right while maintaining the required sum.

Examples

Example 1

Input: n = 3, k = 27

Output: "aay"

The numeric value of the string is 1 + 1 + 25 = 27, and it is the smallest string with such a value and length equal to 3.

Example 2

Input: n = 5, k = 73

Output: "aaszz"

Example details omitted.

Constraints

1 <= n <= 105
n <= k <= 26 * n

Solution Approach

Greedy Strategy

The solution can be approached greedily by iterating through the string from left to right. For each character, subtract the largest possible value from k (up to 26) while keeping the remaining string values valid. Start with 'a' and greedily adjust characters toward 'z' as needed.

Validation Invariant

At every step, ensure that the remaining characters can still sum to the required k. If the remaining characters can’t be adjusted appropriately, backtrack and try a smaller value for the current character.

Edge Case Handling

Ensure that the first character is adjusted such that there’s still enough sum remaining for the rest of the string. Edge cases include the smallest possible values for n and k, as well as very large strings with smaller values of k.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity is O(n), where n is the length of the string. This is because we process each character once, and at each step, we adjust the value of k based on a greedy choice. The space complexity is O(n), as we store the result string of length n.

What Interviewers Usually Probe

The candidate demonstrates an understanding of greedy algorithms.
The candidate can apply greedy choices within the constraints of the problem.
The candidate addresses edge cases and can explain the invariant validation process.

Common Pitfalls or Variants

Common pitfalls

Failing to account for the remaining sum after each greedy step.
Not considering the possibility of overshooting the required sum when selecting the largest valid character.
Misunderstanding the lexicographical order when adjusting the string’s characters.

Follow-up variants

Minimize the string length while still achieving a numeric sum equal to k.
Extend the problem to handle uppercase letters as well.
Solve the problem for multiple queries simultaneously, optimizing for performance.

FAQ

What is the pattern used in 'Smallest String With A Given Numeric Value'?

The pattern is greedy choice with invariant validation. You make greedy choices at each step while ensuring the remaining sum can still be achieved by future characters.

What happens if k is too large for the string length?

If k exceeds the possible maximum sum (26 * n), it's impossible to achieve the target sum, and the problem is unsolvable.

Can the string contain characters other than lowercase letters?

No, the string is restricted to lowercase alphabetic characters, where 'a' has a numeric value of 1 and 'z' has a numeric value of 26.

How can I optimize this solution for large inputs?

To optimize, iterate from left to right, adjusting characters greedily, and ensure you don't exceed the required sum. The time complexity is O(n), so it's already efficient.

What is the best strategy to handle edge cases in this problem?

Ensure that you check for both small and large values of n and k. Handle cases where k is very close to the maximum sum possible for the given string length.

terminal

Solution

Solution 1: Greedy

First, we initialize each character of the string to `'a'`, leaving a remaining value of $d=k-n$.

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class Solution:
    def getSmallestString(self, n: int, k: int) -> str:
        ans = ['a'] * n
        i, d = n - 1, k - n
        while d > 25:
            ans[i] = 'z'
            d -= 25
            i -= 1
        ans[i] = chr(ord(ans[i]) + d)
        return ''.join(ans)

Continue Practicing

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