#Bellman Ford Algo

[b4b31]

All 25 algorithms: HOW TO NAVIGATE

SEARCHING:

Linear Search: Imagine you have a bunch of love letters, and you want to find a specific letter from someone special. You start by looking at the first letter and check if it's the one you're looking for. If it's not, you move on to the next letter and keep going until you find it or reach the end of the letters.

Binary Search: Your collection of love letters are arranged in alphabetical order. Binary search is like playing a guessing game where you try to find a secret love letter. You start by guessing the letter in the middle. If your guess is too late in the alphabet, you know the secret letter must be in the earlier part of the collection. If your guess is too early, you know the secret letter must be in the later part. You keep dividing the collection in half and guessing until you find the secret love letter.

Depth First Search: In your stack of love letters from different people you are going through each letter and exploring deeply before moving on to the next letter. If you find a reply or another love letter within a letter, you read and explore that before continuing with the rest of the stack.

Breadth First Search: In a box full of love letters from different people you are going through all the letters from the same sender before moving on to letters from other senders. You explore all the letters from one person, then move to the next person and explore their letters, and so on.

SORTING:

Insertion Sort: You want to arrange a messy pile of love letters in order of the senders name. With insertion sort, you start with an empty hand and pick one letter at a time from the messy pile. Each time you pick a letter, you put it in the correct position in your hand among the letters you've already sorted.

Heap Sort: You want to sort a big pile of love letters, based on the date they were written. Heap sort is like organizing the letters by putting the most recent one at the top. You keep picking the most recent letter and putting it in a separate pile until all the letters are sorted.

Selection Sort: You want to arrange a stack of love letters from different people in order of the length of the letter. With selection sort, you start by finding the shortest letter and put it aside. Then, you find the next shortest letter and put it next to the first one. You keep doing this until all the letters are arranged by length.

Merge Sort: You want to sort a big collection of love letters from different people, based on the emotions expressed. With merge sort, you divide the collection into smaller groups, sort each group individually based on emotions, and then merge them back together in the correct order. You keep dividing, sorting, and merging until all the letters are sorted.

Quick Sort: You want to sort love letters, based on the intensity of love expressed. With quick sort, you pick one letter as a "special letter" called the base. Then, you divide the line into two groups: letters with less intense expressions of love and letters with more intense expressions. You repeat this process for each group until all the letters are sorted.

Counting Sort: You want to sort a collection of love letters from different people, based on the number of words. Counting sort is like counting how many letters have a specific number of words and then putting them in order.

GRAPHS:

Kruskal’s Algorithm: Imagine you have a map with different locations connected by lines, and you want to build the shortest possible network of lines between all the locations. This algorithm helps you select and connect the lines in a way that forms the minimum spanning tree, which means the total length of the lines is minimized.

Dijkstra’s Algorithm: Think of a map with different locations and lines connecting them, and you want to find the shortest path from one location to another. This helps you find the path with the minimum total distance. You start at one location and keep moving to neighboring locations, always choosing the path with the shortest distance until you reach the destination.

Bellman-Ford Algorithm: Imagine a treasure map with different paths and each path having a certain cost. This algorithm helps you find the shortest path to the treasure by considering the costs of the paths. You keep comparing and updating the total cost of reaching each location until you find the shortest path.

Floyd-Warshall Algorithm: Picture a map with different routes connecting the locations, and you want to find the shortest path between all pairs of locations. This algorithm helps you calculate the shortest path between any two locations in the most efficient way. It considers all possible paths and updates the distances until it finds the shortest paths between all pairs of locations.

Topological Sort Algorithm: Imagine you have a list of tasks, and some tasks depend on others. This sort helps you order the tasks in such a way that no task depends on another task that comes later in the order. It ensures a proper sequence for completing the tasks without any dependency issues.

Flood Fill Algorithm: Picture a coloring book with different shapes. This algorithm helps you fill a shape with a specific color. You start by selecting a shape and filling it with the desired color. Then, you move to neighboring shapes and fill them if they are the same color as the starting shape. You continue this process until you’ve filled all the connected shapes with the chosen color.

Lee Algorithm: Imagine you have a maze, and you want to find the shortest path from the starting point to the end point. This algorithm helps you explore the maze step by step to find the shortest path. You start at the beginning and keep moving to neighboring cells, marking them with the number of steps taken until you reach the destination.

ARRAYS:

Kadane’s Algorithm: Imagine you have an array representing the number of posts baked each day. This algorithm helps you find the longest consecutive period of baking the most posts. You start with the first day and keep adding the posts counts, but if the sum becomes negative, you start over with the next day, searching for the longest streak of baking the most posts.

Floyd’s Cycle Detection Algorithm: Picture an array of post reviews, where each element represents a unique review. This algorithm helps you find if there is a repeating pattern of reviews in the array. You have two pointers—one moving slowly and another moving faster. If the pointers meet, it means there is a repeating pattern of reviews in the array.

Knuth-Morris-Pratt Algorithm: Imagine you have an array representing a series of post ingredients, and you want to find occurrences of a specific ingredient pattern within the array. This algorithm helps you efficiently find instances of the ingredient pattern within the array. It uses a smart way of skipping unnecessary ingredient comparisons based on previously matched patterns, helping you identify the relevant occurrences efficiently.

Quick Select Algorithm: Picture an array of posts sizes, and you want to find the post size that ranks at a specific position when the array is sorted. Quick select algorithm helps you find the post size at the desired position efficiently by partitioning the array based on pivot elements (post sizes), narrowing down the search space iteratively until the desired position is found.

Boyer-Moore Majority Vote Algorithm: Imagine you have an array of post flavors, where each element represents a flavor preference. This algorithm helps you find the most popular post flavor within the array—the flavor that appears more frequently than any other. It iterates through the array, canceling out pairs of different flavors, and the majority flavor eventually remains as the most popular one.

BASICS:

Huffman Coding Compression Algorithm: Imagine you have a collection of love letters, and you want to send them to your sweetheart with reduced file size to save storage or transmission space. This algorithm helps you compress the letters by assigning shorter codes to the most frequently used letters or words, and longer codes to the less frequent ones. This way, you can represent the love letters using fewer bits, making them more efficient to store or send.

Euclid's Algorithm: Picture a scenario where you have a huge archive of posts that you want to distribute equally among your blogs. This algorithm helps you find the largest possible number of posts you can distribute, ensuring each blog gets an equal number without any posts left over. You keep dividing the posts into smaller groups until you can no longer divide them evenly, ensuring a fair distribution.

[algowalker]

Understanding Dijkstra's Algorithm: A Pathfinding Breakthrough

In the realm of computer science and graph theory, Dijkstra's algorithm stands as a fundamental tool for finding the shortest path between nodes in a weighted graph. Named after its Dutch inventor Edsger W. Dijkstra, this ingenious algorithm has had a profound impact on various fields, including transportation, networking, and robotics. By effectively navigating through intricate networks, Dijkstra's algorithm has become an indispensable component in numerous applications that require optimized routes and efficient resource allocation.

What is Dijkstra's Algorithm?

Dijkstra's algorithm is a versatile and elegant solution to the single-source shortest path problem in a graph. The problem involves finding the shortest path from a specific starting node to all other nodes in the graph. The algorithm operates on graphs with non-negative weights, meaning the path's weight must be greater than or equal to zero. Although primarily designed for finding the shortest path, it can also be used to find the minimum cost or time to traverse from one node to another, making it invaluable in real-world scenarios.

How Does Dijkstra's Algorithm Work?

The algorithm's functionality revolves around iteratively exploring nodes in the graph while updating the shortest distance to each node from the starting point. Initially, all nodes are assigned a distance value of infinity, except the source node, which is set to zero. The algorithm then prioritizes exploring nodes with the smallest distance, expanding its reach as it progresses.

Start by marking the distance of the source node as zero and all other nodes as infinity.

Select the unvisited node with the smallest distance and mark it as the current node.

Explore all the neighbors of the current node and calculate their tentative distances from the source node. Update their distance if the newly calculated value is smaller.

Mark the current node as visited to avoid redundant calculations.

Repeat steps 2 to 4 until all nodes have been visited.

The Greedy Nature of Dijkstra's Algorithm:

One of the key aspects of Dijkstra's algorithm is its greedy nature. At each step, the algorithm selects the node with the smallest distance and explores its neighbors. This greedy approach ensures that once a node is visited, its distance from the source node is guaranteed to be the shortest. However, this also means that if the graph contains negative weights, Dijkstra's algorithm may not yield correct results. For graphs with negative weights, another algorithm, like the Bellman-Ford algorithm, should be used.

Applications of Dijkstra's Algorithm:

Transportation Networks: Dijkstra's algorithm is widely employed in GPS systems and navigation applications to find the shortest route between two locations. It enables users to avoid traffic congestion and efficiently reach their destinations.

Computer Networks: In computer networking, Dijkstra's algorithm is essential for routing data packets across the internet. It helps data find the most efficient path from the source to the destination, ensuring minimal delays and congestion.

Robotics and AI: Dijkstra's algorithm plays a crucial role in robotics, allowing autonomous robots to plan their movements efficiently, avoiding obstacles and reaching their targets with minimum energy consumption.

Resource Management: The algorithm's ability to find the shortest path with minimal cost has made it invaluable in managing resources, such as scheduling tasks in project management or optimizing supply chain logistics.

FOR MORE INFO :-

What is Dijkstra Algo

What is Bellman-ford

[noella-oop]

Week of March 20 - March 26

Hey there! Here’s my weekly blog post. Hope you enjoy!

What did you do this past week?

This past week, I finished the allocator project. I thought I was nearly done with it over break, but there was a bug with the HackerRank so I had to fix my solution. It was an easy fix (I wasn’t reading and allocating the blocks the right way in my ReadAllocator.c++). A quick sort method fixed the issue in 2 seconds. 

Other than that, we learned about C++ arrays and classes. We also tried implementing the vector class code from scratch (a little more difficult than I thought it would be). 

Outside of this class, I worked on and completed my Compilers project which is due tomorrow. I also have my second Algorithms exam tomorrow, so most of my time this weekend has been spent studying for that. 

What's in your way?

I have to get started on the next project as soon as it comes out. These next few weeks are going to get busy due to midterms and projects, so I hope to organize my time as well as possible.

What will you do next week?

Hope get started on the new project. I also need to complete the final portion of my Compilers project (I’m almost done with the parser)! I also need to survive my next few midterms, so it’s going to be a crazy week.

What's my experience of the class?

I’m still enjoying the class. It’s super interesting and engaging, and I feel like I can truly use what I’m learning in my future CS career. Professor Downing has roll call attendance in class, and I don’t really know what he uses it for (since attendance isn’t a part of our grade). I missed class for the first time on Wednesday because I had an awful migraine. Because of my bad luck, that was obviously the day I got called on to answer a question in class. My attendance grade dropped to a 75% and initially I was panicking. However, I got called again on friday, and since I was there and able to answer, my attendance grade went back up to 100%. Like I said, I don’t really know what Professor Downing uses roll call attendance for, but I’m grateful my attendance was able to get back to 100%! :)

What's my pick-of-the-week or tip-of-the-week?

I’m currently taking my necessary Algorithms course to complete my degree in CS here. Although it’s a difficult class, and most students really don’t like it, I’m starting to really appreciate it. Granted, it isn’t easy to follow, but it super cool. Sorry if I sound super geeky here, but learning about some of the algorithms like Bellman-Ford, Ford-Fulkerson, and Dijkstra’s (who taught at UT) is super cool. We have our exam on dynamic programming and network flow tomorrow, and I spent most of this weekend studying for it. However, it wasn’t the worst thing ever. In fact, solving algorithm problems are just like cool puzzles where picking the right algorithm can help solve it. Anyways, my tip of the week is, if you haven’t taken algorithms, read a little bit about it before you take the class. However, if you have taken algorithms, keep on top of them. Algorithms are a vital part of programming interviews. Look back at interviews I bombed, the reason was because I didn’t learn algorithms yet, and the interviewer asked something about BFS, DFS, MST, etc. Next year is my last year at UT, but I know I’ll have to keep on top of my algo before I start looking for a full time job because that will be extremely important. So in short - really learn your algorithms: It will be worth it in the long run.

[algowalker]

Understanding Dijkstra's Algorithm: A Pathfinding Breakthrough

In the realm of computer science and graph theory, Dijkstra's algorithm stands as a fundamental tool for finding the shortest path between nodes in a weighted graph. Named after its Dutch inventor Edsger W. Dijkstra, this ingenious algorithm has had a profound impact on various fields, including transportation, networking, and robotics. By effectively navigating through intricate networks, Dijkstra's algorithm has become an indispensable component in numerous applications that require optimized routes and efficient resource allocation.

What is Dijkstra's Algorithm?

Dijkstra's algorithm is a versatile and elegant solution to the single-source shortest path problem in a graph. The problem involves finding the shortest path from a specific starting node to all other nodes in the graph. The algorithm operates on graphs with non-negative weights, meaning the path's weight must be greater than or equal to zero. Although primarily designed for finding the shortest path, it can also be used to find the minimum cost or time to traverse from one node to another, making it invaluable in real-world scenarios.

How Does Dijkstra's Algorithm Work?

The algorithm's functionality revolves around iteratively exploring nodes in the graph while updating the shortest distance to each node from the starting point. Initially, all nodes are assigned a distance value of infinity, except the source node, which is set to zero. The algorithm then prioritizes exploring nodes with the smallest distance, expanding its reach as it progresses.

Start by marking the distance of the source node as zero and all other nodes as infinity.

Select the unvisited node with the smallest distance and mark it as the current node.

Explore all the neighbors of the current node and calculate their tentative distances from the source node. Update their distance if the newly calculated value is smaller.

Mark the current node as visited to avoid redundant calculations.

Repeat steps 2 to 4 until all nodes have been visited.

The Greedy Nature of Dijkstra's Algorithm:

One of the key aspects of Dijkstra's algorithm is its greedy nature. At each step, the algorithm selects the node with the smallest distance and explores its neighbors. This greedy approach ensures that once a node is visited, its distance from the source node is guaranteed to be the shortest. However, this also means that if the graph contains negative weights, Dijkstra's algorithm may not yield correct results. For graphs with negative weights, another algorithm, like the Bellman-Ford algorithm, should be used.

Applications of Dijkstra's Algorithm:

Transportation Networks: Dijkstra's algorithm is widely employed in GPS systems and navigation applications to find the shortest route between two locations. It enables users to avoid traffic congestion and efficiently reach their destinations.

Computer Networks: In computer networking, Dijkstra's algorithm is essential for routing data packets across the internet. It helps data find the most efficient path from the source to the destination, ensuring minimal delays and congestion.

Robotics and AI: Dijkstra's algorithm plays a crucial role in robotics, allowing autonomous robots to plan their movements efficiently, avoiding obstacles and reaching their targets with minimum energy consumption.

Resource Management: The algorithm's ability to find the shortest path with minimal cost has made it invaluable in managing resources, such as scheduling tasks in project management or optimizing supply chain logistics.

FOR MORE INFO :-

What is Dijkstra Algo

What is Bellman-ford