Remove Duplicate Letters

This problem can be solved by using a stack data structure. We want to remove duplicate letters from the string s, and we also want to ensure that the result is in the smallest lexicographical order among all possible results. Let’s see how we can do this:

Initialize a Stack: We will use a stack to keep track of the letters we’ve added to the result.
Track the Frequency: We’ll keep track of the frequency of each letter in the input string s. We’ll also use a boolean array to keep track of the letters that are already in the stack.
Iterate through the String: We’ll iterate through the input string s, and for each letter, we’ll perform the following steps:
- Check if the letter is in the Stack: If the current letter is already in the stack, we’ll decrement its frequency and continue to the next letter.
- Remove Duplicates and Order Lexicographically: If the current letter is not in the stack, we’ll compare it with the top of the stack. If the current letter is less than the top of the stack and the top letter occurs later in the string as well, we’ll pop the top letter from the stack.
- Push the Current Letter: Push the current letter into the stack, and mark it as present in the boolean array.
- Update Frequency: Decrement the frequency of the current letter.
Build the Result: After iterating through the string, we’ll build the result by joining the letters in the stack.

Here’s the code:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
class Solution:
    def removeDuplicateLetters(self, s: str) -> str:
        frequency = {char: 0 for char in set(s)}
        for char in s:
            frequency[char] += 1

        in_stack = {char: False for char in set(s)}
        stack = []

        for char in s:
            frequency[char] -= 1

            if in_stack[char]:
                continue

            while stack and char < stack[-1] and frequency[stack[-1]] > 0:
                in_stack[stack.pop()] = False

            stack.append(char)
            in_stack[char] = True

        return ''.join(stack)

Examples

For s = "bcabc", the output will be "abc". For s = "cbacdcbc", the output will be "acdb".

Complexity Analysis

Time Complexity: (O(N)), where (N) is the length of the input string s, as we are iterating through the string once and performing constant-time operations inside the loop.
Space Complexity: (O(N)), to store the frequency and in_stack dictionaries and the stack.

This question is the same as 1081: https://leetcode.com/problems/smallest-subsequence-of-distinct-characters/

10 Prerequisite LeetCode Problems

Here are 10 problems to prepare for “316. Remove Duplicate Letters”. These are related to string manipulation, stack data structure, recursion and greedy algorithms which are the key concepts in the problem.

20. Valid Parentheses: This problem will help you to understand the basic use of stack in string manipulation.
71. Simplify Path: This problem will introduce you to the concept of using a stack to manage string characters.
394. Decode String: This problem helps with understanding recursion and stack usage in context of string manipulation.
1047. Remove All Adjacent Duplicates In String: This problem is quite similar to the “Remove Duplicate Letters” but less complex.
1081. Smallest Subsequence of Distinct Characters: This problem is essentially the same as “Remove Duplicate Letters”. If you can solve this one, you can solve “Remove Duplicate Letters”.
402. Remove K Digits: This problem involves a similar concept of removing characters to achieve a specific goal.
1249. Minimum Remove to Make Valid Parentheses: Here you need to remove minimum characters to get a valid string which is a similar idea to the main problem.
682. Baseball Game: This problem will help you understand the concept of maintaining an auxiliary stack for handling operations.
456. 132 Pattern: This problem will help you understand how to maintain a stack for pattern identification in sequence, which can be handy in “Remove Duplicate Letters” problem.
155. Min Stack: This problem can help you understand how stack can be manipulated and utilized in different conditions.

Understand how to manipulate strings and characters in a string, how stack can be used in these manipulations, and how to apply greedy algorithms.

Problem Analysis and Key Insights

Here are some key insights gained from analyzing the problem statement:

The problem relies heavily on concepts of lexical string ordering and processing. This will likely involve sorting and string permutations.
We need to remove duplicates while maintaining relative ordering of characters. This suggests tracking occurrence counts of letters.
Finding the minimum lexicographic string indicates generating and comparing permutations systematically.
The constraints allow assumptions about only lowercase letters and moderate string lengths.
Checking substring containment can determine if a letter can be safely removed or not.
Greedy approaches may work by tracking counts and removing earlier duplicates first.
Optimized data structures like stacks or priority queues can efficiently track occurrence counts.
The problem translates to finding the shortest supersequence containing all unique letters.

Overall, the insights around leveraging lexical ordering, occurrence tracking, substring checking, and greedy approaches will help narrow down the optimal solution direction. The constraints also limit the scope appropriately.

Problem Boundary

Based on the problem statement and analysis, the scope of this problem is:

Input space - A string of lowercase English letters up to 10,000 characters
Output - A modified string containing only unique letters in smallest lexical order
Rules - Only one instance of each letter should remain. Relative ordering must be preserved.
Objective - Find the lexicographically smallest string meeting the constraints.
Non-goals - Parsing meanings of words, handling uppercase letters, optimizing runtime/memory beyond constraints.

So in summary, the scope is limited to:

Working with single lowercase English strings as input/output
Applying deduplication and lexical ordering constraints
Finding the minimum string representation
Not worried about meanings, semantics, performance etc.

The focus is on applying the specific string transformation rules to the input and finding the lexicographically smallest resulting string. Broader challenges like parsing, internationalization, scalability etc. are out of scope.

Here are some ways we can establish boundaries for this problem:

Input:

Single string containing only lowercase English letters
Length limited to 10,000 characters
No other inputs or data types

Processing:

Only allowed operation is removing duplicate letters
Must preserve relative ordering of remaining letters
Finding lexicographically minimum string

Output:

Modified string with only unique letters ordered lexicographically
No other output artifacts like original string, transformations, etc.

Performance:

No specific time or space complexity requirements mentioned
Can assume optimization within reason

State:

No external state stored across inputs
Each input string can be processed independently

So in summary, the fixed input format, restricted transformations, focused output, and lack of specific performance constraints clearly define the boundaries for this problem. The scope is restricted to manipulation of single string inputs to meet specific uniqueness and ordering criteria.

Problem Classification

This is a string processing problem that involves removing duplicate characters while preserving lexical order. It falls under the domain of strings and algorithms.

The key ‘What’ components are:

Input string containing only lowercase letters
Removing duplicate letters from the string
Ensuring only one instance of each letter remains
Preserving the lexical ordering of the letters
Finding the smallest lexical string that satisfies the constraints

Based on these aspects, we can categorize this problem as:

String manipulation - transforming the input string
Deduplication - removing duplicate elements
Lexicographic ordering - working with dictionary/alphabetical ordering
Combinatorics - generating permutations and finding smallest

So in summary, this is a string processing problem involving deduplication and lexical ordering constraints. It relies on concepts from strings, algorithms, and combinatorics to transform the input and find the lexicographically minimal result. The core challenge is efficiently finding this minimum string.

Distilling the Problem to Its Core Elements

This problem is based on the fundamental concepts of string processing and combinatorial ordering.

At its core, it involves taking a string and finding the dictionary-first unique variation. I would describe it simply as:

“Given a word with duplicate letters, rearrange the letters to remove duplicates while keeping the alphabetically smallest order.”

The core problem is finding the lexicographically smallest string with only unique letters. We can simplify it to:

“Remove duplicate letters to create the ‘smallest’ unique string.”

The key components are:

The input string
Removing duplicate letters
Ordering the remaining letters alphabetically
Determining the minimal variation

The minimum operations are:

Parse input string
Track frequency of each letter
Try removing duplicates while maintaining order
Check if new string is lexicographically smaller
Return smallest unique string

So in essence, this focuses on applying transformations to create the simplest unique string, rather than complex semantics analysis or optimizations. The core is combining deduplication, ordering, and string permutations.

Visual Model of the Problem

Here are some ways we could visualize this problem statement:

Show the input string highlighted with duplicate letters in a different color.
Animate the process of removing duplicates and rearranging a sample string into the minimal order.
Use a flow chart to demonstrate the key steps - parse string, remove duplicates, order remaining letters, return final string.
Visualize the string as a graph with letters as nodes and edges for ordering. Highlight duplicate nodes and their removal.
Provide small examples of input strings and resulting minimal unique strings.
For invalid cases, illustrate failures like incorrectly ordered letters in the output.
Annotate the final string to indicate the rules applied - crossed out duplicates, arrows showing reordering.
Show counter examples that violate requirements like duplicates remaining or suboptimal ordering.
Use a library like D3.js to animate the letter graph and transformations interactively.

The goal is to utilize visuals like diagrams, animations, examples and annotations to make the constraints and transformation process clear. Both valid and invalid cases help illuminate requirements.

Problem Restatement

Here’s how I would paraphrase the problem statement in my own words:

We are given a string containing only lowercase letters. Our goal is to remove any duplicate letters from the string, so that each remaining letter appears exactly once. In addition, we want to rearrange the remaining letters so they are in the lexicographically smallest possible order.

For example, if the input is “bcabc”, we would remove the second ‘b’ and ‘c’ so only one of each remains. Then we’d sort the remaining unique letters alphabetically as “abc” to end up with the lexicographically smallest string meeting the constraints.

The key requirements are:

Only keep one of each letter
Preserve relative order of remaining letters
Find the alphabetically first permutation of the remaining letters

We don’t care about the actual duplicate removal steps - just the final output string with unique ordered letters. There are also no other constraints like performance mentioned.

In summary, we want to transform the input string by removing duplicates and reordering the result to be lexicographically minimal, while maintaining the relative position of remaining letters. Our only focus is generating this final string.

Does this help summarize the problem’s core essence and constraints? Please let me know if I’m missing or misunderstanding any aspects.

Abstract Representation of the Problem

Here is one way to formulate an abstract representation of this problem:

Let’s define:

S = The set of all possible strings made from a fixed alphabet of characters
s = The input string, s ∈ S
R = The removals function that takes a string and removes duplicate letters
O = The ordering function that sorts the letters lexicographically

Then the problem can be modeled as:

Given:

A string s in the set S of all possible strings
Removal function R(s) that removes duplicate letters in s
Ordering function O(s) that sorts s lexicographically

Determine:

t, where t = O(R(s))

Return:

The lexicographically smallest ordered string t after removing duplicates.

In essence, we apply constraints of uniqueness and sorted order to transform the input string by composing the removal and ordering functions.

The key aspects are the transformations and constraint enforcement on the string space. This frames it generically in terms of transforming and ordering an abstract state space. Please let me know if you would modify or clarify this representation.

Terminology

Here are some key terms and concepts relevant to this problem:

Lexicographic order - Dictionary order of strings based on alphabet. Important for determining smallest string.

Permutation - Arrangement of a set of elements. Need to find lexicographically smallest permutation.

Deduplication - Removing duplicate elements from a data structure. Core transformation needed.

Greedy algorithm - Approach that makes locally optimal choices to arrive at global optimum. Useful here to incrementally remove duplicates.

Priority queue - Ordered data structure allowing efficient access to smallest element. Can help find optimal order.

Hash table - Data structure for efficient lookup of letter frequencies. Helps identify duplicates.

Substring - Contiguous sequence within string. Needed to check for duplicate letter occurrences.

The main concepts are around leveraging ordering and permutations, algorithms like greedy and data structures like priority queues and hash tables to efficiently transform the input string by applying deduplication and lexical ordering constraints.

Problem Simplification and Explanation

Here’s one way I can explain this problem in simpler terms:

Key Concepts:

String - The input is a sequence of letters
Duplicates - There are multiple instances of some letters
Uniqueness - We want only one of each letter to remain
Ordering - The remaining letters must be alphabetically sorted
Minimal - The final string should be the smallest lexicographically

Analogy:

Imagine the string is a hand of Scrabble letter tiles. There are multiple copies of some tiles.

We want to play the hand by removing duplicate tiles and rearranging the rest to form the “shortest” valid word we can make.

For example, if given tiles for “HELLO”, we’d remove duplicates keeping only “HELO” and reorder it as “EHLP” since that’s the smallest lexicographic word we can make with those letters.

The core idea is transforming the input by applying deduplication and lexical ordering constraints. We focus on the final state, not the steps taken.

Does this help relate the key concepts in simpler terms? Let me know if another metaphor or analogy could make it clearer!

Constraints

Here are some characteristics of the problem that we can potentially leverage:

All lowercase alphabet - Can encode each letter as a number 1-26 for efficiency.
Small character set - Optimized data structures like hash maps or bit vectors work well for tracking.
Length limit of 10K - Enables brute force approaches if needed for smaller cases.
Lexical ordering requirement - Allows incrementally building string rather than permutations.
No specific output format - Don’t need to reconstruct steps, only return final string.
Duplicates must be adjacent - Can make local greedy decisions to remove earlier duplicates first.
Doesn’t specify performance needs - Simpler approaches without complex optimizations may be acceptable.
Read-only input string - No need to restore original for multiple iterations.

The limited character set, length, and lexical ordering constraints in particular allow simplifying logic around tracking occurrences and constructing optimal string. No complex data transformations or reconstructions are required.

Here are some key insights gained by analyzing the constraints:

Small character set allows compact occurrence tracking with integers, bit vectors etc.
Length limit enables brute force approaches before optimizing further.
Lexical ordering requirement allows incremental construction greedily.
Adjacent duplicate requirement lets us make local optimal decisions.
Read-only string simplifies logic by allowing in-place changes.
No specified output format or steps means we can focus just on final string.
No performance needs suggests we can use simple approaches first.
Lowercase characters may allow leveraging native language ordering.

Overall, these constraints mean we can likely devise a simple, straightforward solution without too much initial optimization. The problem scope is narrowed significantly by the limits provided.

Key insights are around compact data structures for tracking, greedy construction approaches, and focusing just on the final output rather than intermediate steps or efficiency early on. The constraints provide clarity.

Case Analysis

Here are some additional test cases covering different aspects:

Simple case

Input: “hello” Output: “helo”

Analysis: Basic example, removes single duplicate.

Same letters

Input: “aaaaa”
Output: “a”

Analysis: Handles string with all duplicates.

Multiple duplicates

Input: “abcddbca” Output: “abcd”

Analysis: Removes multiple different duplicates.

Out of order

Input: “dcba” Output: “abcd”

Analysis: Checks reordering logic.

Empty string

Input: "" Output: ""

Analysis: Handles degenerate empty case.

Edge cases:

Empty string
Single letter
All duplicates
Max length string

The key aspects tested are deduplication, ordering, and extremes. The edge cases cover degenerate inputs and maximum complexity.

Here are some key insights gained from looking at these test cases:

The simple case forms a basic validation of core logic and assumptions. A minimal example.
All duplicate letters stress tests deduplication logic in isolation.
Multiple different duplicates validates handling various letters appropriately.
Out of order input verifies lexical reordering is done correctly.
Empty string checks assumptions on minimum length and edge handling.
Single letter case could clarify assumptions around empty outputs.
Max length generates worst case time/memory complexity.
Need both valid and invalid inputs to fully validate logic branches.
Ordering and complexity matter - should go from simple to complex.

Overall, these cases ensure the logic is fully verified across a spectrum - from simple to complex, empty to full, in order to out of order. The insights focus on methodically testing the solution space.

Identification of Applicable Theoretical Concepts

Here are some mathematical and algorithmic concepts that could help solve this problem:

Hash tables can be used to store letter frequencies for fast O(1) lookup and duplication tracking.
Heaps/priority queues can efficiently provide the next letter in sorted lexical order in O(log n) time.
Sorting algorithms like merge sort maintain stability which preserves original letter ordering.
Greedy algorithms make locally optimal choices to build the solution incrementally.
Finite state machines provide a framework for modeling state transitions between strings.
Bit vectors and bitmasks allow compactly encoding the string for manipulation.
Dynamic programming can store intermediate results and reorderings to reuse computations.
Discrete mathematics concepts like permutations, combinations and ordering constraints apply directly.
Automata theory provides formalisms for string manipulations.

So concepts from data structures, algorithms, dynamic programming, discrete math etc. give useful techniques for tracking, ordering, transforming, and modeling strings that will make solving this problem more tractable.

Simple Explanation

Here’s how I would explain this problem in simple non-technical terms:

Imagine you have a scrabble rack with letter tiles on it. Some letters appear multiple times. Like having 3 X’s, 2 V’s, and 1 B.

Your goal is to use these tiles to make the “shortest” valid word you can. Shortest meaning a word that would show up first alphabetically.

However, you can only use each letter on your rack once. So if you have 3 X’s, you can only play 1 in your word.

You also can’t rearrange the letters - they must stay in the same order on the rack. You can only remove duplicates.

For example, if your letters are XXBV, you would remove duplicates to make XBV. Then you’d rearrange them alphabetically to make BVX as the shortest word possible.

This is like taking a string of letters, removing any duplicates so each letter appears once, and reordering them lexicographically to make the “smallest” string possible given the constraints.

The core idea is applying rules to transform the initial set of letters into the “shortest” word or string.

Problem Breakdown and Solution Methodology

Here is a step-by-step explanation of how I would approach solving this problem:

Parse the input string

Break the string into individual characters to operate on.

Track frequency of each character

Use a hash map to count occurrences of each letter.

Create result string

Initialize empty result string to incrementally build.

Take characters from least to highest frequency

Iterate over the hash map in ascending order of frequency.

If letter already in result, skip it

Check result string before adding to avoid duplicates.

Else, append current letter to result

Add the unique letter while maintaining order.

Return final result

Result string will contain only unique letters in order.

For example, input “hello”:

Parse into [‘h’,’e’,’l’,’l’,‘o’]
Frequencies: {‘h’:1, ’e’:1, ’l’:2, ‘o’:1}
Initialize result = ""
Take ‘h’,’e’,‘o’ (lowest counts)
Check and append to result
Final result = “helo”

This incrementally constructs the solution string by selectively taking low frequency letters first. Visualizing the hash map helps.

If order didn’t matter, I could directly use the hash map to construct result. Handling length limits would require optimizations like bitmasks.

Inference of Problem-Solving Approach from the Problem Statement

Here are some key terms and how they guide my approach:

String - Since input/output are strings, need algorithms for string manipulation.
Duplicate letters - Duplicates need to be identified and removed while keeping other letters. Points to tracking letter frequencies.
Lexicographic order - Requirement for alphabetical ordering informs using sorting techniques and data structures like heaps/priority queues.
Smallest string - Need to construct result incrementally in increasing lexical order. Can’t just sort once at the end.
Greedy algorithm - Taking locally optimal choices incrementally to build up global solution. Useful for letter selection order.
Hash table - Efficient lookup structure to count letter frequencies in linear time. Enables duplicate identification.
Stability - Maintaining relative order of elements while sorting. Needed to keep string ordering.

The core strings, ordering, incremental construction, stability and greediness concepts lead me towards tracking letter frequencies, stably accumulating letters in order, and constructing the output string gradually using optimal local decisions each step.

How did you infer from the problem statement that this problem can be solved using ?

Simple Explanation of the Proof

I’m having trouble understanding the proof of this algorithm. Could you explain it in a way that’s easy to understand?

Here is one way to break this problem down into more granular steps:

High-level approach:

Remove duplicate letters
Reorder remaining letters lexicographically

Refined steps:

Parse input string into characters
Track frequency of each character
Initialize empty result string
Iteratively append next lexical character to result:
- Check if letter already exists in result
- If yes, skip
- If no, append current letter
Return final result string

Independent parts:

Parsing input
Tracking letter frequencies
Checking letter existence

Repeatable patterns:

Updating frequency counters
Checking result string before appending
Selectively appending unique letters

This breaks the problem into input processing, tracking state, incrementally constructing output, and returning result. Frequency tracking and existence checking are reusable.

Solution Approach and Analysis

Here is a step-by-step explanation of how I would approach solving this problem:

Parse input string into characters

Break the input string into individual letters to operate on.

Track frequency of each character

Use a hash map to count occurrence of each letter.

Create result string

Initialize empty string to build up solution.

Sort characters by frequency

Use a min heap to get letters in increasing frequency order.

Iteratively append to result:

Pop letter from heap
Check if letter is already in result
If yes, skip
If no, append letter to result

Return final result

Example:

Input: “hello”

Parse into [‘h’,’e’,’l’,’l’,‘o’]
Frequencies = {‘h’: 1, ’e’: 1, ’l’: 2, ‘o’: 1}
result = ""
Min heap gives [‘h’,’e’,‘o’,’l’] ordered by frequency
Append ‘h’, ’e’, ‘o’ to result
Return “helo”

This uses the heap to get letters in frequency order, skipping duplicates, to build up the final string incrementally. Visualizing the hash map and min heap helps understand the process.

Identify Invariant

An invariant in this problem is a condition or statement that remains true throughout the execution of the solution. Some potential invariants are:

The input string remains unchanged. We operate on an immutable copy.
The relative order of letters cannot be altered, only duplicates removed. Order is fixed.
Once a letter is added to the result string, it remains in that position. Result string only grows.
Frequency count for a letter never changes once calculated initially. Counts are fixed.
A letter identified as a duplicate remains a duplicate for all iterations. Duplicate status doesn’t change.
The Latin alphabetical ordering of letters is constant. The sort order doesn’t change.

So in essence, key invariants are:

Unchanged input string
Fixed letter ordering
Monotonically growing result
Static frequency counts
Consistent duplicate identification
Preserved lexical letter ordering

The core transformations and checks must maintain these constraints throughout processing to ensure a valid solution.

Identify Loop Invariant

The loop invariant in this problem is a condition that remains true before and after each iteration of the main result construction loop. Some possibilities for loop invariants are:

The input string remains unchanged by the loop.
The relative order of letters in the input string is preserved by the loop.
Any letter added to the result remains in result after each iteration.
The lexicographic ordering of characters is constant across loop iterations.
If a letter is identified as a duplicate before an iteration, it remains a duplicate after.
The set of identified unique letters only grows or stays the same within the loop.

So in summary, the key loop invariants center around the unchanged input string, consistent letter ordering, monotonically growing result, fixed lexical ordering, and invariant duplicate identification. The loop cannot modify these core aspects that determine correctness.

The invariant refers to high-level conditions that are true for the entire problem, regardless of implementation details.

The loop invariant focuses specifically on what must remain true before and after each iteration of the main result construction loop.

There is overlap - invariants like the fixed lexical ordering and unchanged input string qualify as loop invariants as well.

However, some invariants like the single assignment of the final result are important for the problem but aren’t relevant within the loop body itself.

And some loop invariants like the monotonic growth of the result string apply locally to the loop but not globally.

So while there is a strong overlap between the invariant and loop invariant properties for this problem, they are not identical sets. The loop invariants focus specifically on protections needed for the loop logic.

The global invariants provide wider constraints that the full solution must respect, including parts outside the core loop.

Thought Process

Here is how I would think through solving this problem step-by-step:

The problem statement cues:

Operating on a string suggests parsing it into characters first
Need for unique letters indicates tracking letter frequencies
Maintaining lexical order informs incrementally constructing result
Finding “smallest” string points to ordering letters alphabetically

The steps would be:

Parse input string into array of characters
Use hash map to track frequency of each character
Initialize empty result string
Sort characters by ascending frequency
Iteratively append next character to result:
- Check if letter already exists in result
- If so, skip it
- Else, append unique letter to result
Return final result string

In Python:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
from heapq import heapify

def removeDuplicates(s):
  
  freq = {}
  for c in s:
    freq[c] = freq.get(c, 0) + 1
    
  result = ""  
  minHeap = [(v, k) for k, v in freq.items()]
  heapify(minHeap)
  
  while minHeap:
    count, char = heapq.heappop(minHeap)
    if char not in result:
        result += char

  return result

This uses a hash map for frequencies, min heap to get next letter, and selective appending to build result string.

Here is one way to implement a solution in Python:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
class Solution:
    
    def removeDuplicateLetters(self, s: str) -> str:

        # Track last occurrence of each char 
        last_occ = {c: i for i, c in enumerate(s)}

        # Track unique letters in result
        in_result = set()

        result = []

        for i, c in enumerate(s):

            # If letter already in result, skip
            if c in in_result:
                continue

            # While previous letter in result is greater and there
            # are later occurrences, pop from result  
            while result and c < result[-1] and i < last_occ[result[-1]]:
                removed = result.pop()
                in_result.remove(removed)

            # Add current letter 
            result.append(c)
            in_result.add(c)

        return ''.join(result)

Key aspects:

Track last index of each char
Maintain result as stack
Pop from result if out of order
Append when in correct order

This constructs the output string by selectively appending characters while maintaining the lexical ordering.

Establishing Preconditions and Postconditions

Here are the details for the removeDuplicateLetters method:

Parameters:

s: String - The input string to process

Preconditions:

s contains only lowercase ASCII letters
s is not null or empty

Method Functionality:

Removes duplicate letters in s while maintaining order
Returns string containing each letter once in smallest lexical order

Postconditions:

s remains unchanged
Returns new string with duplicate letters removed and ordered

Error Handling:

If s is null, throw IllegalArgumentException
If s is empty, return empty string
If s contains non-letter characters, throw IllegalArgumentException
Otherwise return processed string result

So in summary, this takes an input string, applies deduplication and ordering, and returns the transformed result string while leaving the input unchanged.

Problem Decomposition

Here’s how I would break down this problem:

Problem Understanding: Take a string containing duplicate letters, remove the duplicates while keeping remaining letters ordered lexicographically.
Initial Breakdown:

Parse input string
Identify duplicate letters
Remove duplicates
Reorder remaining letters

Subproblem Refinement:

Parse string into array
Track letter frequencies
Check duplicates based on frequencies
Construct result string incrementally
Append next lexical letter

Task Identification:

String parsing
Frequency tracking
Duplicate identification
Result construction
Lexical ordering

Task Abstraction:

Input processing
Occurrence counting
Deduplication
Output generation
Ordering

Method Naming:

parseString()
trackFrequencies()
isDuplicate()
constructResult()
nextLexicalChar()

Subproblem Interactions:

Parse input
Count frequencies and find duplicates
Iteratively construct result string in order
Append lexical letters avoiding duplicates

The key stages are parsing, tracking, deduplicating, and ordered reconstruction. The core tasks are made reusable.

From Brute Force to Optimal Solution

Here is a brute force approach and how we can optimize it:

Brute force:

Generate all permutations of the input string
Check if each permutation has unique letters
Return first permutation with unique letters

This tries all possible arrangements exhaustively.

Complexity - Time: O(N!) to generate N! permutations Space: O(N) to store each permutation

Optimizations:

Incrementally construct string instead of permutations

Start with empty result and append next lexical letter, skipping duplicates.

Complexity: Time: O(NlogN) - sorting characters Space: O(N)

Use hash table to track letter frequencies

Avoids repeated counting by looking up existing frequencies in O(1).

Complexity: Time: O(N) Space: O(N)

Use heap to get next lexical letter

Maintain min heap of letters ordered by frequency for O(logN) access.

Complexity: Time: O(NlogN) Space: O(N)

Stop when all unique letters added

Avoid traversing entire input once result is complete.

Complexity: Time: O(N) Space: O(N)

In summary, optimized from brute force to linear time and space by incrementally constructing result string instead of permutations, using efficient data structures, and short circuiting when complete.

Code Explanation and Design Decisions

Here is how I would explain the reasoning behind this code:

The initial parameter s is the input string to deduplicate and order.
The loop iterates through s to construct the result string incrementally. Each iteration represents selecting the next optimal letter.
Branches check if letter already exists, to avoid duplicates based on constraints.
The result string is updated by appending unique letters. This builds up the solution.
An invariant is the fixed lexical ordering of characters. This maintains ordering constraints.
The final result contains each letter once in the minimal lexical ordering. This meets the problem requirements.

In summary, the code incrementally constructs the optimally ordered string by iterating through the input, skipping duplicates, and maintaining lexical ordering invariantly. The end result satisfies all the uniqueness and ordering constraints as required.

Coding Constructs

Here are high-level explanations for what this code is doing:

It uses greedy incremental construction and optimal ordering to build the solution string.
The code takes a string with duplicate letters and removes the duplicates while keeping the remaining letters in alphabetical order.
The logic includes a frequency map, min heap for ordering, a loop to construct result, and branches to avoid duplicates.
It iteratively selects the next letter by frequency, skips duplicates, and appends to result string to construct solution.
Key steps are parsing input, tracking frequencies, heap selection, duplicate checking, and ordered appending to result. This incrementally builds up the output.
Core algorithms are greedy incremental construction, optimal selection using a heap, and frequency map based duplicate checking.

In summary, the code employs greedy selection and incremental building to efficiently construct an optimal string that meets uniqueness and ordering constraints. The explanations focus on high-level reasoning rather than language-specific details.

Language Agnostic Coding Drills

Here’s how I would break down this code into coding concepts:

Concepts in increasing difficulty:

Parsing input - Break into components for processing. Basic parsing skill.
Mapping values - Use a map to track frequency. Core data organization.
Heap usage - Maintain min heap for optimal ordering. Intermediate data structure.
Looping - Iterate over components. Fundamental construct.
Conditionals - Branch based on constraints. Basic control flow.
String mutation - Modify result string within loop. More advanced string skill.
Greedy selection - Choose locally optimal steps. Key algorithm strategy.
Incremental construction - Build up solution over iterations. Important technique.

The problem solving approach would involve:

Parsing input into components
Mapping components to frequencies
Building min heap based on frequencies
Looping through components
Using conditionals to skip duplicates
Mutating result string within loop
Making greedy optimal selections
Incrementally constructing result

Each coding drill builds essential concepts from strings, data structures, algorithms and control flow. Combined appropriately, they solve the overall problem.

Targeted Drills in Python

Here are Python coding drills for each concept:

Parsing input

1
2
input = "hello"
chars = [char for char in input] 

Mapping values

1
2
3
freq = {} 
for char in chars:
  freq[char] = freq.get(char, 0) + 1

Heap usage

1
2
3
import heapq
heap = [(v, k) for k, v in freq.items()]
heapq.heapify(heap)

Looping

1
2
while heap:
  # Get min letter  

Conditionals

1
2
if char in result:
  continue

String mutation

1
result += char

Greedy selection

1
heapq.heappop(heap) # Get min letter

Incremental construction

1
2
result = ""
# Build up result

We can integrate these by:

Parsing input
Mapping frequencies
Building min heap
Looping through inputs
Using conditionals to skip duplicates
Mutating result string greedily
Constructing result incrementally

Each drill builds up key concepts to solve the overall problem.