Skip to content

Latest commit

 

History

History
84 lines (65 loc) · 6.57 KB

problem-solving-techniques-guide.md

File metadata and controls

84 lines (65 loc) · 6.57 KB
Raw

Comprehensive Guide to Problem-Solving Techniques and Concepts

Techniques and Validity Considerations

  1. Two Pointer Technique

    • When to use: Problems involving searching, comparing elements, or processing arrays/strings.
    • Validity check: Valid when the problem involves linear data structures and can benefit from processing elements from both ends or maintaining a window.
    • Reasoning: Reduces time complexity by avoiding nested loops.
    • Deduction: If the problem mentions pairs, subarrays, or requires comparing elements, consider this technique.

  2. Sliding Window

    • When to use: Finding subarrays or substrings that satisfy certain conditions.
    • Validity check: Applicable when dealing with contiguous sequences and when the problem can be solved by expanding or contracting a window.
    • Reasoning: Efficiently processes subarrays by reusing computation from previous steps.
    • Deduction: If the problem involves finding a contiguous subset with certain properties, this technique may apply.

  3. Dynamic Programming (DP)

    • When to use: Problems exhibiting optimal substructure and overlapping subproblems.
    • Validity check: Valid when the problem can be broken down into simpler subproblems and their solutions can be combined to solve the original problem.
    • Reasoning: Avoids redundant calculations by storing solutions to subproblems.
    • Deduction: If you find yourself solving the same subproblems repeatedly in a recursive approach, DP might be applicable.

  4. Greedy Algorithms

    • When to use: Problems where making locally optimal choices leads to a global optimum.
    • Validity check: Ensure that the local optimal choice doesn't prevent finding the global optimum.
    • Reasoning: Simplifies decision-making by focusing on the best immediate choice.
    • Deduction: If the problem allows for step-by-step decision making without the need for looking ahead, consider a greedy approach.

  5. Divide and Conquer

    • When to use: Problems that can be broken down into smaller, similar subproblems.
    • Validity check: Ensure that the problem can be divided into independent subproblems and their solutions can be combined.
    • Reasoning: Simplifies complex problems by solving smaller instances and combining results.
    • Deduction: If the problem involves recursively breaking down a larger problem into smaller ones, this approach may be suitable.

  6. Binary Search

    • When to use: Searching in sorted arrays or when the search space can be systematically reduced.
    • Validity check: Applicable when the search space is sorted or can be represented as a range that can be halved in each step.
    • Reasoning: Efficiently reduces the search space by half in each iteration.
    • Deduction: If the problem involves finding a specific value or a condition in a sorted or monotonic sequence, consider binary search.

  7. Depth-First Search (DFS)

    • When to use: Exploring paths in graphs or trees, backtracking problems.
    • Validity check: Valid for problems involving graph traversal, path finding, or exhaustive search with backtracking.
    • Reasoning: Explores as far as possible along each branch before backtracking.
    • Deduction: If the problem involves exploring all possible paths or configurations, DFS might be appropriate.

  8. Breadth-First Search (BFS)

    • When to use: Finding shortest paths in unweighted graphs, level-order traversals.
    • Validity check: Applicable when you need to explore nodes in order of their distance from a starting point.
    • Reasoning: Guarantees finding the shortest path in unweighted graphs.
    • Deduction: If the problem involves finding the shortest path or processing nodes level by level, consider BFS.

Key Concepts

  1. Window's Start and End

    • Concept: In sliding window problems, maintain two pointers that define the current window being considered.
    • How to solve: Increment the end pointer to expand the window, and increment the start pointer to contract it. Update the solution based on the current window's properties.

  2. Optimal Substructure

    • Concept: A problem has optimal substructure if an optimal solution can be constructed from optimal solutions of its subproblems.
    • How to solve: Break the problem into smaller subproblems, solve them optimally, and combine these solutions to solve the original problem. Often used in dynamic programming.

  3. Backtracking

    • Concept: A general algorithm for finding all (or some) solutions to problems that incrementally builds candidates to the solution and abandons a candidate as soon as it determines the candidate cannot lead to a valid solution.
    • How to solve: Implement a recursive function that explores all possible choices. When a choice leads to an invalid path, backtrack by undoing the choice and exploring other options.

  4. Local Optimal Choice

    • Concept: In greedy algorithms, making the best possible decision at each step without regard for future consequences.
    • How to solve: At each step, choose the option that seems best at the moment. Ensure that this strategy leads to the global optimum for the problem at hand.

  5. Memoization

    • Concept: An optimization technique used primarily in dynamic programming to store the results of expensive function calls and return the cached result when the same inputs occur again.
    • How to solve: Use a data structure (often a hash table) to store results of subproblems. Before computing a subproblem, check if its result is already cached.

  6. State Machine

    • Concept: Represent the problem as a set of states and transitions between these states based on certain conditions or inputs.
    • How to solve: Define the possible states and the rules for transitioning between them. Implement the logic to move between states based on the input or conditions of the problem.

  7. Monotonic Stack/Queue

    • Concept: A stack or queue that maintains elements in a strictly increasing or decreasing order.
    • How to solve: When adding an element, remove elements that violate the monotonic property. This structure can efficiently solve problems involving finding the next greater/smaller element or maintaining a window of elements with certain properties.

Remember, the key to effective problem-solving is recognizing patterns and applying the appropriate technique. Practice analyzing problems to identify which of these concepts and techniques are applicable, and build experience in implementing them efficiently.