Smallest String With A Given Numeric Value - Video Solutions

Problem Overview: You need to construct the lexicographically smallest string of length n such that the total numeric value of its characters equals k. Each character contributes a value where 'a' = 1, 'b' = 2, ..., 'z' = 26. The challenge is distributing this total value across n characters while keeping the string lexicographically smallest.

Approach 1: Greedy Backwards Approach (O(n) time, O(n) space)

This method builds the string from right to left. Start by assuming every position contains 'a', which contributes 1 each, giving a base value of n. The remaining value k - n must be distributed across characters, but to keep the string lexicographically smallest, you add extra value starting from the end of the string. For each position, increase the character by at most 25 (turning 'a' into 'z') and subtract the used value from the remainder. Iterating backward ensures larger letters appear later, preserving the smallest possible lexicographic order. This greedy distribution works because increasing characters later in the string has the least impact on lexicographic ordering. The approach relies on simple iteration and arithmetic, making it ideal for problems involving greedy strategies and string construction.

Approach 2: Incremental Forward Approach (O(n) time, O(n) space)

This approach constructs the result from left to right while ensuring enough value remains to fill the remaining positions. At index i, you decide the smallest possible character that still allows the remaining positions to reach the total k. For the current position, iterate possible character values and check whether the remaining k can still be achieved given the bounds (remaining_positions * 1) and (remaining_positions * 26). Once a valid character is found, append it and update the remaining sum. This strategy still uses greedy reasoning but enforces feasibility constraints at every step. It is slightly more reasoning-heavy than the backward method but useful when practicing constraint-based greedy construction often seen in greedy and string problems.

Recommended for interviews: The Greedy Backwards Approach is what most interviewers expect. It reaches the optimal O(n) time with very simple logic: fill the string with 'a', then distribute the remaining value from the end. Explaining the lexicographic reasoning clearly demonstrates strong greedy intuition. Mentioning the forward feasibility approach shows deeper understanding, but the backward greedy implementation is typically preferred for clarity and speed.