diff --git a/.DS_Store b/.DS_Store deleted file mode 100644 index e4db449..0000000 Binary files a/.DS_Store and /dev/null differ diff --git a/I2A_Algorithm_Analysis/Lecture-1.ipynb b/I2A_Algorithm_Analysis/Lecture-1.ipynb new file mode 100644 index 0000000..920b38c --- /dev/null +++ b/I2A_Algorithm_Analysis/Lecture-1.ipynb @@ -0,0 +1,673 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Algorithm Analysis and Complexity" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "#### **Algorithm**\n", + "

An algorithm is a way to tell a computer or a person what to do in a clear and organized way, like a recipe for making sandwich! . It is a series of steps required to get a paticular result .

\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### **Complexity**\n", + "

When we talk about the complexity of an algorithm, we're trying to figure out how long it might take to complete a task using that algorithm and how much computer memory it might need . We use this to compare different algorithms and choose the one that's most efficient for a particular task. So, complexity helps us understand how \"hard\" or \"easy\" it is for a computer to do a task using a specific set of instructions.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Asymtomatic Notation \n", + "\n", + "

Asymptotic notation is a way to describe the running time or space complexity of an algorithm based on the input size. In complexity analysis, we often use different ways to explain how an algorithm works as we give it larger and larger amounts of data to process. The three most commonly used ways to do this are known as Big O, Omega, and Theta notations.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Big O notation (O)**: \n", + "

This notation tells us the maximum amount of time or space an algorithm might use as the input size grows. It's like saying, \"In the worst case, the algorithm will take this much time or space.\" For instance, if an algorithm's running time is O(n), it means the time it takes will increase linearly or less with the input size n.

\n", + "\n", + "**Omega notation (Ω)**:

This notation gives us the minimum amount of time or space an algorithm might use as the input size grows. It's like saying, \"In the best case, the algorithm will take at least this much time or space.\" For example, if an algorithm's running time is Ω(n), it means the time it takes will increase linearly or more with the input size n.

\n", + "\n", + "**Theta notation (Θ)**: This notation provides a range, telling us both the upper and lower bounds on an algorithm's time or space use. It represents the typical or average scenario. If an algorithm's running time is Θ(n), it means the time it takes increases linearly with the input size n, and that's usually how it behaves on average." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Elaborating on Aysmptotic Notation " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Big O notation (O)** :

An upper bound on the performance of an algorithm refers to the maximum amount of time it can take, representing the worst-case scenario. This concept is expressed using Big O notation, which describes the asymptotic upper bound.\n", + "\n", + "In mathematical terms, if we denote the running time of an algorithm as f(n), we say that f(n) is O(g(n)) if there are positive constants C and n0 such that:\n", + "\n", + "

f(n) ≤ C * g(n) for all n ≥ n0.

\n", + "\n", + "This notation helps us characterize how the algorithm's performance scales concerning its input size, providing an upper limit on its time complexity.

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The typical step-by-step process for conducting Big-O runtime analysis can be outlined as follows:\n", + "\n", + "Identify the nature of the input and define the role of 'n' within it.\n", + "Describe the algorithm's maximum number of operations in relation to 'n.'\n", + "Discard all lower-order terms.\n", + "Omit any constant factors from the analysis." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Constant Multiplication: \n", + "If f(n) = c.g(n), then O(f(n)) = O(g(n)) ; where c is a nonzero constant.
\n", + "2. Polynomial Function: \n", + "If f(n) = a0 + a1.n + a2.n2 + —- + am.nm, then O(f(n)) = O(nm).
\n", + "3. Summation Function: \n", + "If f(n) = f1(n) + f2(n) + —- + fm(n) and fi(n)≤fi+1(n) ∀ i=1, 2, —-, m, <\n", + "then O(f(n)) = O(max(f1(n), f2(n), —-, fm(n))). br>\n", + "4. Logarithmic Function: \n", + "If f(n) = logan and g(n)=logbn, then O(f(n))=O(g(n)) br>\n", + "; all log functions grow in the same manner in terms of Big-O." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The algorithms can be classified as follows from the best-to-worst performance (Running Time Complexity): \n", + "\n", + "▪ A logarithmic algorithm – O(logn)
\n", + "    Runtime grows logarithmically in proportion to n.
\n", + "▪ A linear algorithm – O(n)
\n", + "  Runtime grows directly in proportion to n.
\n", + "▪ A superlinear algorithm – O(nlogn)
\n", + "    Runtime grows in proportion to n.
\n", + "▪ A polynomial algorithm – O(nc)
\n", + "    Runtime grows quicker than previous all based on n.
\n", + "▪ A exponential algorithm – O(cn)
\n", + "    Runtime grows even faster than polynomial algorithm based on n.
\n", + "▪ A factorial algorithm – O(n!)
\n", + "    Runtime grows the fastest and becomes quickly unusable for even \n", + " small values of n.
" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "▪ Logarithmic algorithm – O(logn) – Binary Search.
\n", + "▪ Linear algorithm – O(n) – Linear Search.
\n", + "▪ Superlinear algorithm – O(nlogn) – Heap Sort, Merge Sort.
\n", + "▪ Polynomial algorithm – O(n^c) – Strassen’s Matrix Multiplication, Bubble Sort, Selection Sort, Insertion Sort, Bucket Sort.
\n", + "▪ Exponential algorithm – O(c^n) – Tower of Hanoi.
\n", + "▪ Factorial algorithm – O(n!) – Determinant Expansion by Minors, Brute force Search algorithm for Traveling Salesman Problem.
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Big Omega" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Big – Omega (Ω) notation specifies the asymptotic (at the extreme) lower bound for a function f(n)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Steps to find Big Omega " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Break the program into smaller segments.\n", + "2. Find the number of operations performed for each segment(in terms of the input size) assuming the given input is such that the program takes the least amount of time.\n", + "3. Add up all the operations and simplify it, let’s say it is f(n).\n", + "4. Remove all the constants and choose the term having the least order or any other function which is always less than f(n) when n tends to infinity, let say it is g(n) then, Big – Omega (Ω) of f(n) is Ω(g(n))." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " Big – Ω notation is the least used notation for the analysis of algorithms because it can make a correct but imprecise statement over the performance of an algorithm. Suppose a person takes 100 minutes to complete a task, using Ω notation, it can be stated that the person takes more than 10 minutes to do the task, this statement is correct but not precise as it doesn’t mention the upper bound of the time taken. Similarly, using Ω notation we can say that the worst-case running time for the binary search is Ω(1), which is true because we know that binary search would at least take constant time to execute." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Big Theta**" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Big Theta specifies asymptotic bounds (both upper and lower) for a function f(n) and provides the average time complexity of an algorithm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Steps To find Big Theta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. Break the program into smaller segments.\n", + "2. Find all types and number of inputs and calculate the number of operations they take to be executed. Make sure that the input cases are equally distributed.\n", + "3. Find the sum of all the calculated values and divide the sum by the total number of inputs let say the function of n obtained is g(n) after removing all the constants, then in Θ notation its represented as Θ(g(n))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Stable Matching \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Imagine you have a group of boys and a group of girls, and they want to find their best match for a dance. But here's the catch: everyone has their own preferences. Boys have a list of girls they like from most to least, and girls have a list of boys they like from most to least.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pseudo Code :" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``` python\n", + " function stable_matching(men, women):\n", + " Initialize all men and women as free\n", + " Initialize an empty dictionary to keep track of engagements\n", + "\n", + " while there is a man who is free and has not proposed to every woman:\n", + " select a free man 'm'\n", + " select the highest-ranked woman 'w' in 'm's preference list to whom 'm' has not yet proposed\n", + " if 'w' is free:\n", + " 'm' and 'w' become engaged\n", + " Add the engagement (m, w) to the engagements dictionary\n", + " else:\n", + " if 'w' prefers 'm' over her current fiance 'm2':\n", + " 'w' and 'm' become engaged, and 'm2' becomes free\n", + " Update the engagements dictionary to replace (m2, w) with (m, w)\n", + "\n", + " return the engagements dictionary\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Code For Stable Matching " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Men's Matches: [1, 2, 0]\n", + "Women's Matches: [2, 0, 1]\n" + ] + } + ], + "source": [ + "def stable_matching(men_preferences, women_preferences):\n", + " n = len(men_preferences) # Number of men/women\n", + "\n", + " # Initialize the match lists for men and women\n", + " men_matches = [-1] * n # Initially, no one is matched\n", + " women_matches = [-1] * n\n", + "\n", + " # Create a dictionary to store women's current proposals\n", + " women_current_proposals = {i: 0 for i in range(n)}\n", + "\n", + " # While there exist unmatched men\n", + " while men_matches.count(-1) > 0:\n", + " for man in range(n):\n", + " if men_matches[man] == -1:\n", + " woman = men_preferences[man][women_current_proposals[man]]\n", + "\n", + " # Check if the woman is currently unmatched\n", + " if women_matches[woman] == -1:\n", + " women_matches[woman] = man\n", + " men_matches[man] = woman\n", + " else:\n", + " # If the woman is currently matched, compare preferences\n", + " current_man = women_matches[woman]\n", + "\n", + " if women_preferences[woman].index(man) < women_preferences[woman].index(current_man):\n", + " men_matches[man] = woman\n", + " men_matches[current_man] = -1\n", + "\n", + " # Increment the proposal count for each man\n", + " for man in range(n):\n", + " women_current_proposals[man] += 1\n", + "\n", + " return men_matches, women_matches\n", + "\n", + "# Example preferences (0-indexed)\n", + "men_preferences = [\n", + " [1, 0, 2],\n", + " [2, 1, 0],\n", + " [0, 2, 1]\n", + "]\n", + "\n", + "women_preferences = [\n", + " [1, 0, 2],\n", + " [2, 1, 0],\n", + " [0, 2, 1]\n", + "]\n", + "\n", + "men_matches, women_matches = stable_matching(men_preferences, women_preferences)\n", + "print(\"Men's Matches:\", men_matches)\n", + "print(\"Women's Matches:\", women_matches)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Stable matching algorithms have several practical applications in the real world, where you need to pair or match individuals or entities based on their preferences. Here are some practical applications of stable matching:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "1. Medical Residency Matching: The National Resident Matching Program (NRMP) in the United States uses stable matching algorithms to match medical students with residency programs. Medical students rank their preferred programs, and programs rank their preferred students. The algorithm ensures that each student is matched with a program, and the resulting matches are stable, preventing students or programs from wanting to break their commitments.\n", + "\n", + "2. Job Matching: Job markets for new graduates or professionals often use stable matching algorithms. For example, doctors looking for hospital positions or teachers seeking teaching positions can rank their preferred locations or institutions. The matching process ensures that each candidate gets a job, and the job placements are stable.\n", + "\n", + "3. College Admissions: In some countries, college admissions are also managed using stable matching algorithms. Students rank their preferred colleges, and colleges rank their preferred students. This process helps ensure that students are assigned to colleges fairly, and it prevents issues where students might later wish to transfer to their preferred institutions.\n", + "\n", + "4. Dating and Online Matching: Online dating platforms often use algorithms inspired by stable matching to connect individuals based on their preferences and interests. The goal is to create matches where both parties are mutually interested and satisfied.\n", + "\n", + "5. School Choice: In school districts where parents can choose the school their child attends, stable matching algorithms are used to assign students to schools. Parents rank their preferred schools, and the algorithm ensures that each student is assigned to a school, taking into account school capacity and distance.\n", + "\n", + "6. Kidney Exchange Programs: In kidney exchange programs, patients in need of a kidney transplant may have willing donors, but they may not be compatible with their intended recipient. Stable matching algorithms are used to find cycles of donors and recipients, allowing multiple pairs to exchange kidneys in a way that maximizes successful transplants.\n", + "\n", + "7. Roommate Matching: College dormitories and shared housing arrangements often use stable matching algorithms to pair roommates. Students or tenants rank their preferences for roommates, and the algorithm tries to find compatible and stable roommate assignments.\n", + "\n", + "8. Scheduling and Shift Assignments: In industries such as healthcare and manufacturing, stable matching algorithms can be used to assign workers to shifts or schedules based on their preferences and qualifications. This helps in creating fair and stable work assignments.\n", + "\n", + "9. Resource Allocation: Stable matching algorithms are also used in resource allocation scenarios, such as allocating slots for advertising, scheduling appointments, or distributing resources among different entities.\n", + "\n", + "In all these applications, stable matching algorithms help ensure that the resulting matches are both efficient and stable, reducing the likelihood of dissatisfaction or disputes among the matched entities.\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##

Questions From the Following Lesson

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. For parameters a and b, both of which are ω(1), T(n) = T(n1/a) + 1, and T(b) = 1. Then T(n) is \n", + "\n", + " (A) θ(logalogbn)\n", + "\n", + " (B) θ(logabn)\n", + "\n", + " (C) θ(logblogan)\n", + "\n", + " (D) θ(log2log2n)\n", + "\n", + " Solution: Correct answer is (A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Explanation :
\n", + "→T(n) = T(n1/a)+1,
\n", + "→T(b) = 1
\n", + "→ n1/ak = b
\n", + "→ log(n1/ak) = log(b)
\n", + "→ ak = log(n) / log (b) = logb(n)
\n", + "→ k = logalogb(n)
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "= T(n1/ak) + k
\n", + "= T(b) + logalogb(n)
\n", + "= 1 + logalogb(n)
\n", + "= Θ(logalogb(n))
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2. Which one of the following is the recurrence equation for the worst-case time complexity of the Quicksort algorithm for sorting (n ≥ 2) numbers? In the recurrence equations given in the options below, c is a constant. \n", + "\n", + " (A) T(n) = 2T(n/2) + cn\n", + "\n", + " (B) T(n) = T(n-1) + T(0) + cn\n", + "\n", + " (C) T(n) = 2T(n-1) + cn\n", + "\n", + " (D) T(n) = T(n/2) + cn\n", + "\n", + " Solution: Correct answer is (B)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Explanation : In the worst case, the chosen pivot is always placed at a corner position and recursive call is made for the following:\n", + "\n", + "(a) For subarray on left of pivot which is of size n -1 in worst case.
\n", + "(b) For subarray on right of pivot which is of size 0 in worst case.
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3. An unordered list contains n distinct elements. The number of comparisons to find an element in this list that is neither maximum nor minimum is \n", + "\n", + " (A) θ(n log n)\n", + "\n", + " (B) θ(n)\n", + "\n", + " (C) θ(log n)\n", + "\n", + " (D) θ(1)\n", + "\n", + " Solution: Correct answer is (D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Explanation : Take first 3 elements. The middle of the 3 elements will be the element that is neither minimum nor maximum in the array. Hence O(1) time to compare 3 elements." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4. The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of \n", + "\n", + " (A) n\n", + "\n", + " (B) n2\n", + "\n", + " (C) n log n\n", + "\n", + " (D) n log2 n\n", + "\n", + " Solution: Correct answer is (C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Explanation: The number of comparisons that a comparison sort algorithm requires increases in proportion to Nlog(N), where N is the number of elements to sort. This bound is asymptotically tight:\n", + "\n", + "Given a list of distinct numbers (we can assume this because this is a worst-case analysis), there are N factorial permutations exactly one of which is the list in sorted order. The sort algorithm must gain enough information from the comparisons to identify the correct permutations. If the algorithm always completes after at most f(N) steps, it cannot distinguish more than 2^f(N) cases because the keys are distinct and each comparison has only two possible outcomes. Therefore,\n", + "\n", + "2^f(N) >= N! or equivalently f(N) >= log(N!).\n", + "Since log(N!) is Omega(NlogN), the answer is NlogN." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Arrange the following functions in increasing order of growth as n becomes large:\n", + "* 2^n
\n", + "* n^2
\n", + "* log(n)
\n", + "* n^0.5
\n", + "* 100n
\n", + "* 3^n
\n", + "* log(log(n))
\n", + "* n!
\n", + "* n * log(n)
\n", + "* n^3 * e^n
\n", + "\n", + "Explanation for the correct answer:\n", + "\n", + "* log(log(n)): This is a doubly logarithmic function, which grows slower than single logarithmic functions.\n", + "\n", + "* log(n): Logarithmic functions grow slower than polynomial or exponential functions.\n", + "\n", + "* n^0.5: Square root growth is slower than polynomial growth.\n", + "\n", + "* n * log(n): This is a function with a logarithmic factor and grows faster than logarithmic and square root functions but slower than polynomial or exponential functions.\n", + "\n", + "* 100n: This is a linear function and grows faster than the functions mentioned above.\n", + "\n", + "* n^2: This is a polynomial function and grows faster than all functions mentioned so far.\n", + "\n", + "* 2^n: Exponential growth dominates over polynomial, logarithmic, and linear functions.\n", + "\n", + "* 3^n: This is another exponential function that grows faster than all functions mentioned above.\n", + "\n", + "* n!: Factorial growth is much faster than any of the functions listed previously.\n", + "\n", + "* n^3 * e^n: This is an exponential growth function with a polynomial factor and grows faster than all other functions.\n", + "\n", + "So, the correct order from slowest growth to fastest growth is:\n", + "\n", + "log(log(n)) < log(n) < n^0.5 < n * log(n) < 100n < n^2 < 2^n < 3^n < n! < n^3 * e^n \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##

LeetCode 1583

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Problem Statement :

You are given a list of preferences for n friends, where n is always even.\n", + "\n", + "For each person i, preferences[i] contains a list of friends sorted in the order of preference. In other words, a friend earlier in the list is more preferred than a friend later in the list. Friends in each list are denoted by integers from 0 to n-1.\n", + "\n", + "All the friends are divided into pairs. The pairings are given in a list pairs, where pairs[i] = [xi, yi] denotes xi is paired with yi and yi is paired with xi.\n", + "\n", + "However, this pairing may cause some of the friends to be unhappy. A friend x is unhappy if x is paired with y and there exists a friend u who is paired with v but:\n", + "\n", + "x prefers u over y, and\n", + "u prefers x over v.\n", + "Return the number of unhappy friends.\n", + "

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Input:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "``\n", + "n = 4\n", + "preferences = [[1, 2, 3], [3, 2, 0], [3, 1, 0], [1, 2, 0]]\n", + "pairs = [[0, 1], [2, 3]]\n", + "``\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Explanation : \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Friend 0 and friend 1 are in a pair, but they are both unhappy because 0 prefers 1 over 2, and 1 prefers 0 over 3.\n", + "Friend 2 and friend 3 are in a pair, but they are both unhappy because 2 prefers 3 over 1, and 3 prefers 2 over 0." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def unhappyFriends(n, preferences, pairs):\n", + " # Create a dictionary to store preferences for each friend\n", + " prefs = {}\n", + " for i in range(n):\n", + " prefs[i] = preferences[i]\n", + " \n", + " # Create a dictionary to store partners for each friend\n", + " partners = {}\n", + " for x, y in pairs:\n", + " partners[x] = y\n", + " partners[y] = x\n", + " \n", + " unhappy_count = 0\n", + "\n", + " # Check happiness for each pair\n", + " for x in range(n):\n", + " y = partners[x]\n", + " x_prefs = prefs[x]\n", + " index_of_y = x_prefs.index(y) # Index of y in x's preferences\n", + " for i in range(index_of_y):\n", + " u = x_prefs[i] # Friend u who is preferred over y\n", + " v = partners[u] # Partner of u\n", + " if prefs[u].index(x) < prefs[u].index(v):\n", + " unhappy_count += 1\n", + " break\n", + " \n", + " return unhappy_count\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.0" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/I2A_Algorithm_Analysis/README.md b/I2A_Algorithm_Analysis/README.md index 765c5a3..7478163 100644 --- a/I2A_Algorithm_Analysis/README.md +++ b/I2A_Algorithm_Analysis/README.md @@ -1,4 +1,43 @@ -# Skunks Skool -Skunks Skool Tutorials +# Algorithm Analysis and Complexity +## Introduction +This repository is dedicated to the study and analysis of algorithms and their complexity. Understanding algorithmic design and analysis is essential for developing efficient and effective solutions to a wide range of computational problems. +## Table of Contents +1. [Algorithm Analysis](#algorithm-analysis) +2. [Complexity Analysis](#complexity-analysis) +3. [Stable Matching](#stable-matching) +4. [Contributing](#contributing) +5. [License](#license) + +## Algorithm Analysis +In this section of the repository, you will find materials and resources related to the analysis of algorithms. This includes: + +- **Big O Notation**: Explanation and examples of Big O notation, which is used to describe the upper bound on the time complexity of an algorithm. + +- **Time and Space Complexity**: Discussions on time complexity, space complexity, and their analysis. + +- **Asymptotic Analysis**: Exploring how algorithms behave as input size approaches infinity and how this analysis helps us compare and classify algorithms. + +## Complexity Analysis +This section focuses on the analysis of algorithmic complexity. It includes: + +- **Worst-case, Best-case, and Average-case Analysis**: Understanding the differences between these types of complexity analysis and when to use them. + + +- **Practical Examples**: Real-world examples of algorithm complexity analysis, helping you apply these concepts to actual problems. + +## Stable Matching +Stable matching is a specific problem in the domain of algorithmic problems. In this section, you will find information on: + +- **Stable Marriage Problem**: Explanation and implementation of the stable marriage problem, a classic problem in matching theory. + +- **Applications**: Discussing real-world applications of stable matching, such as in online dating algorithms and hospital-resident matching. + +## Contributing +We welcome contributions from the community to enrich the resources in this repository. If you have algorithm analysis techniques, complexity analysis examples, or additional content related to stable matching that you'd like to share, please feel free to create a pull request. Check out our [contributing guidelines](CONTRIBUTING.md) for more details. + +## License +This repository is open-source and available under the [MIT License](LICENSE). Please review the license file for more information about how you can use and distribute the contents of this repository. + +Thank you for being a part of our algorithm analysis and complexity community! We hope you find the resources here valuable in your journey to mastering algorithms and their analysis.