Guide to High School Computer Science
  • 💻Introduction
    • windows & Python Development
    • macOS & Python Development
    • Visual Studio Code Settings
    • Set up Github
    • Author Page
  • 🧠Prerequisite Skills
    • Keyboard Typing
    • Files & Directories
    • Use of Command Line
    • Git & GitHub
    • Markdown
    • Starting Your Python Project
  • 🐍Python Programming
    • 🍎Python Basics
      • What is Python?
      • Procedural Programming & Programming Paradigms
      • String Formatting
      • Data Types
      • Input & Output to Console
      • Working with Numbers
      • Useful Built-in Functions
      • Math & Random Module
      • Boolean Data Object
      • Comparison, Logical, and Membership Operators
      • If Statements
      • Binary Decisions
      • Multiple Decisions
      • Nested Conditions
      • [EXTRA] Bitwise Operators
      • [EXTRA] Python Style Guide
    • ⏮️Iterations
      • Introduction to While Loops
      • Infinite Loop
      • Controlling Your While Loops
      • Introduction to For Loops
      • For Loops w/ Numeric Sequences
      • For Loops w/ Strings & Lists
      • Iterable Functions w/ For Loops
    • 📦Collections
      • Strings
        • String Basics
        • String Indexing
        • String Slicing
        • String Operators & Functions
        • Basic String Methods
        • String Methods Extended
        • String Methods Document
      • Tuples & Lists
        • Tuples
        • List Basics
        • List are Mutable
        • Adding Items to a List
        • Removing Items from a List
        • Search & Reverse a List
        • List Comprehension
        • List Methods Document
      • Sets
      • Dictionary
      • How to Store Multiple Data Items
    • 💡Defining Functions
      • Functions
      • print() vs return
      • Pre-determined Arguments
      • Nested Functions
      • Map & Filter
      • [Extra] Dynamic Arguments
    • 💾File I/O
      • How to Save Text to an External File
      • Reading CSV in Python
      • Reading JSON in Python
    • 🔨Basic Python Projects
      • Basic Calculator
        • Improving the calculator
        • Exercise Set 1
        • Exercise Set 2
        • 💎Streamlit Application #1
      • Basic Password Generator
        • Exercise Set 3
        • Exercises Related to Math
        • 💎Streamlit Application #2
      • A To-Do Task List
    • ⏳Introduction to Algorithmic Thinking
      • Big-O Notation
      • Basic Algorithms
        • Linear Search
        • Binary Search
        • Basic Sorting Algorithms
      • Recursion
      • Brute Force Algorithms
      • Greedy Algorithm
        • Time on Task (CCC 2013 J4)
        • Dijkstra’s Algorithm
      • Divide and Conquer
        • Merge Sort
      • Dynamic Programming
    • 🤯Object Oriented Programming
      • Class & Objects (Definitions)
      • OOP in Python
      • Encapsulation
      • Polymorphism
      • Inheritance & Overriding
      • Override Magic Methods
      • Case Study: 2D Vectors
      • Case Study: Deck of Cards
      • Exercise
      • Abstract Data Types
      • Case Study: Static 1D Array From Java
    • Competitive Programming
      • Is This Sum Possible?
        • Is the dataset sorted?
        • Searching for a value
        • Determine if the difference between an integer from the array and the target value exists
        • Sorting Algorithms
        • Using Two Pointers
      • Two Sum - LeetCode
        • Generate all possible pairs of values
        • Subtract each value from the target, see if the difference exists in the list
      • Longest Common Prefix - LeetCode
        • Compare all possible prefixes
        • Create the longest common prefix with the direct neighbour
      • Length of Last Word - LeetCode
        • Compare all possible prefixes
      • Where can I go from one point to another?
      • Sample Outline
    • IB Recipe Book
  • 💾Python & Databases
    • Intro to Databases & Data Modeling
      • Common Data Types in SQL
      • Introduction to ERDs
      • Primary Keys and Foreign Keys
      • Database Normalization
    • What is SQL?
      • Getting Started
      • SELECT Queries
        • Selection with Conditions
        • Selection with Fuzziness
        • Selection and Sorting in Order
        • Selection without Duplicates
        • Selection with Limited Number of Outputs
      • AGGREGATE Queries
        • Counting Rows
        • Sum, Average, Min/Max Queries
        • Working with Aggregate Queries
        • Power of using Groups
        • Exercise
      • Interacting with Multiple Table
      • Inserting Data
      • External Resource
  • ☕Java Essentials
    • Basics
      • Starting Java
      • Data & Variables
      • Handling User Inputs & Type Conversion
      • Arithmetic
      • IPO Model
      • Basic Built-in Methods
      • Exercise Questions
    • Conditionals
      • Boolean Operators
      • Compare Strings
      • If Statements
      • If Else Statements
      • Making Multiple Decisions
      • Using Switch
      • Flowchart Symbols
      • Exercise Questions
    • Iterations
      • While Loops
      • For Loop
      • Exercises
    • Java Type Casting
    • Strings
      • Common String Practices
      • String Formatting
      • Java Special Characters
    • Collection
      • Arrays
      • For Each Loop
      • ArrayList
      • Exercise Questions
    • Static Methods
      • (Aside) Clearing your Console
    • Randomness in Java
    • Delayed Output in Java
    • Java Output Formatting
    • Java Style Guide
  • 🛠️JavaScript Programming
    • Our Programming Editor & Workflow
      • Hello, world!
      • Commenting & Variables
      • Data in JavaScript
      • Operators
      • String Formatting
      • Getting User Input
    • JavaScript Exercise Set 1
    • Making Decisions
      • Comparing Values
      • Combining Boolean Comparisons
      • Creating Branches
    • JavaScript Exercise Set 2
    • While Loops
      • Infinite While Loop
      • While Loops and Numbers
      • While Loops and Flags
      • While loops w/ Strings
    • JavaScript Exercise Set 3
    • Subprograms & Functions
      • Creating a Function in JavaScript
      • Function with Input and Assignable Output
    • JavaScript Exercise Set 4
  • 💾Topics in CS
    • Computer Environments & Systems
      • Computer Components
        • In-depth Explanations
      • File Maintenance
      • Computer & Safety
      • Software Development
      • Bits & Binary
    • Careers related to Computer Science
    • Postsecondary Opportunities
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On this page
  • Characteristics of Brute Force Algorithms:
  • Example Brute Force Algorithms:
  • Constructing a Brute Force Solution
  • Sample Problem: Finding Factors of a Single Positive Integer
  1. Python Programming
  2. Introduction to Algorithmic Thinking

Brute Force Algorithms

PreviousRecursionNextGreedy Algorithm

Last updated 8 months ago

Brute force algorithms are straightforward methods for solving problems by trying all possible solutions until the correct one is found.

They don’t use any shortcuts or optimizations, which often makes them simple to implement but inefficient for large datasets.

Characteristics of Brute Force Algorithms:

  • Exhaustive Search: They explore all possible solutions.

  • Simplicity: Easy to understand and implement.

  • Inefficiency: Can be slow and resource-intensive, especially for large inputs.

  • Guaranteed Solution: They will always find a solution if one exists, given enough time.

Example Brute Force Algorithms:

  • Checking each element in a list sequentially.

  • Repeatedly swapping adjacent elements if they are in the wrong order.

  • Password Cracking: Trying all possible combinations until the correct one is found.

Constructing a Brute Force Solution

Sample Problem: Finding Factors of a Single Positive Integer

def factors1(num : int) -> list:
    result = []
    for divider in range(1, num+1):
        if num % divider == 0:
            result.append(divider)
    return result
  • The following program above is able to perfectly generate all the factors of a given positive integer.

  • This algorithm is a brute force solution as it compares all numbers from 1 to the given number.

  • If the given number was extremely large, the program would check all the numbers from 1 to the large number

  • Therefore: the performance of this algorithm is directly proportional to the value of the input

Factoring Optimization

def factors2(num: int) -> list:
    result = []
    end_point = int(num ** 0.5) + 1 # square root of our num
    
    for divider in range(1, end_point):
        quotient = num // divider
        remainder = num % divider
        if remainder == 0:
            result.append(divider)
            if quotient != divider:
                result.append(quotient)
    return result
  • This function is an optimized version of our previous code where our algorithm stops at the square root of the number rather than the integer argument.

  • The non-optimized factoring function is good because it is guaranteed to find an answer, but it will require more computation than necessary

factors1(99980001)
factors2(99980001)

This function call will do 99,980,001 comparison operations

This function call will do square root of 99980001 comparison operations which is 9,999 comparisons.

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