Leetcode #411: Minimum Unique Word Abbreviation

In this guide, we solve Leetcode #411 Minimum Unique Word Abbreviation in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Problem Statement

A string can be abbreviated by replacing any number of non-adjacent substrings with their lengths. For example, a string such as "substitution" could be abbreviated as (but not limited to): "s10n" ("s ubstitutio n") "sub4u4" ("sub stit u tion") "12" ("substitution") "su3i1u2on" ("su bst i t u ti on") "substitution" (no substrings replaced) Note that "s55n" ("s ubsti tutio n") is not a valid abbreviation of "substitution" because the replaced substrings are adjacent.

Quick Facts

• Difficulty: Hard
• Premium: Yes
• Tags: Bit Manipulation, Array, String, Backtracking

Intuition

We must explore combinations of choices, but many branches can be pruned early.

Backtracking enumerates valid candidates while keeping the search space under control.

Approach

Use DFS to build candidates step by step, and backtrack when constraints are violated.

Pruning keeps the exploration practical for typical constraints.

Steps:

• Define the decision tree.
• DFS through choices and backtrack.
• Prune invalid paths early.

Example

Python Solution

Complexity

The time complexity is Exponential (worst case). The space complexity is O(depth).

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.