Speaker 1: Have you ever found yourself wondering how computers actually manage
Speaker 1: these really complex challenges like optimizing delivery routes, or you know,
Speaker 1: recognizing faces in.
Speaker 2: Photos, or even just storing huge amounts of data efficiently.
Speaker 1: Exactly what if there was sort of a shortcut to
Speaker 1: understanding the basic logic behind so much of our modern tech.
Speaker 2: Well, in this deep dive, that's what we're doing. We're
Speaker 2: pulling back the curtain on classic computer science problems. And
Speaker 2: these aren't just you know, dusty academic exercise.
Speaker 1: Well is, They're not just for university courses, not at all.
Speaker 2: They're the foundational programming challenges that actually solve real world problems.
Speaker 1: And we've dug into a really comprehensive book covering these problems.
Speaker 1: Our mission today it's basically to pull out the most
Speaker 1: important bits of knowledge, the key insights for you.
Speaker 2: We'll unpack the core ideas, maybe reveal some surprising facts
Speaker 2: along the way, and.
Speaker 1: Show you how these these foundational concepts are like woven
Speaker 1: right into the fabric of our digital Worldfully, you'll have
Speaker 1: a few aha moments. Okay, So to kick things off,
Speaker 1: let's look at something that seems pretty simple on the surface.
Speaker 1: The Fibonacci sequence. You know, one, one, two, three, five, right,
Speaker 1: But I've heard this sequence can actually teach us some
Speaker 1: really profound lessons about computational efficiency. What's the story there,
Speaker 1: what's the hidden lesson?
Speaker 2: Yeah, it's fascinating. It really highlights the stark difference between
Speaker 2: just jumping in with a straightforward, what we might call
Speaker 2: a naive recursive solution, and more optimized ways of thinking.
Speaker 1: Okay, so what happens with that naive way?
Speaker 2: Well, get this Calculating just the twentieth Fibonacci number using
Speaker 2: that simple recursive function, it ends up making twenty ninety one.
Speaker 1: Separate function calls twenty one thousand for the twentieth number.
Speaker 1: That seems excessive.
Speaker 2: It's incredibly inefficient, yeah, because it just keeps recalculating the
Speaker 2: same values over and over and over.
Speaker 1: Again, right, recalculating things that already figured out. But there
Speaker 1: are better ways. You mentioned optimization.
Speaker 2: Absolutely, there's a technique called memoization. It was actually coined
Speaker 2: by computer scientist Donald Mitchee.
Speaker 1: Memoization like writing a memo to.
Speaker 2: Yourself kind of yeah, think it like a human memorization machine.
Speaker 2: The function, remember, the results had already calculated, so with memoization,
Speaker 2: that same twentieth number, it only takes thirty nine calls.
Speaker 1: Thirty nine down from almost twenty two thousand. That's huge.
Speaker 2: It's massive. And with this method you can actually calculate say,
Speaker 2: FIB fifty without the whole thing grinding to a halt.
Speaker 2: The naive version just wouldn't cope.
Speaker 1: Okay, So memorization is a big step up that the
Speaker 1: best we can do.
Speaker 2: Well. There's also what you might call an old fashioned
Speaker 2: iterative approach, just using a loop. Yeah, that approach runs
Speaker 2: its main loop at most and one times, So for
Speaker 2: the twentieth number, that's like nineteen loops, even fewer operations.
Speaker 1: Wow, okay, and this really matters.
Speaker 2: You know, this kind of difference can have a serious
Speaker 2: difference in a real world application. It's not just theory.
Speaker 2: It's about thinking efficiently before.
Speaker 1: You code, right, It's the difference between something working instantly
Speaker 1: and something maybe never finishing this sie So okay that speed.
Speaker 1: But efficiency isn't just about speed? Is it saving space?
Speaker 1: Virtual storage memory? That's also huge. How did these fundamental
Speaker 1: ideas help with that?
Speaker 2: Oh? Definitely? Yeah, Saving space often directly translates to saving money, right,
Speaker 2: virtual or real makes sense. So think about DNA the
Speaker 2: nucleotides ACG or T. That's it, just four possibilities. If
Speaker 2: you store a DNA sequence as a normal tech string,
Speaker 2: each letter, each character usually takes up eight bits.
Speaker 1: Okay, standard tech storage.
Speaker 2: But wait, since there are only four possible values, you
Speaker 2: don't actually need eight bits. You only need two bits
Speaker 2: per nuclear tie. You could say, you know A is zero, zero,
Speaker 2: C is zero, one, G is ten, T is eleven.
Speaker 1: I see, so you're mapping the four options onto just
Speaker 1: two bits. That's clever.
Speaker 2: It's simple but effective. That bit string representation. That can
Speaker 2: slash the storage needed for DNA data by seventy five percent,
Speaker 2: from eight bits down to just two it's per.
Speaker 1: Nucleodide seventy five percent. That's enormous when you think about
Speaker 1: the scale of genomic data exactly.
Speaker 2: We saw an example I think where an original string
Speaker 2: was maybe eighty six hundred and forty nine bytes. Compressed
Speaker 2: this way, it dropped to just twenty three hundred and
Speaker 2: twenty bytes.
Speaker 1: That's a massive saving. Now, this brings up something interesting
Speaker 1: about choosing how to implement things in code, doesn't it.
Speaker 2: It does. Sometimes using a dictionary or a hash map
Speaker 2: for lookups, which theoretically should be super fast like one
Speaker 2: or constant time.
Speaker 1: Right, it's supposed to be instant regardless of size.
Speaker 2: Yeah, but in practice it can sometimes be less performant
Speaker 2: than a series of ifs. Really, why is that because
Speaker 2: of the hidden cost of running the hash function itself.
Speaker 2: The calculation to figure out where to look in the
Speaker 2: dictionary takes a little bit of time. So in really
Speaker 2: performance critical code you might actually need to run performance
Speaker 2: tests to see what's really faster in your specific case.
Speaker 2: Theory doesn't always win.
Speaker 1: That's a great point. Real world testing matters, and just quickly.
Speaker 1: Another example of level stuff is the xor operation right,
Speaker 1: used in.
Speaker 2: Absolutely xor is fundamental for certain types of unbreakable encryption.
Speaker 2: Another example of low level bit manipulation having powerful applications.
Speaker 1: Okay, so we've seen efficiency and speed efficiency in space
Speaker 1: down to the bits. What about problems that are more
Speaker 1: about logic rules constraints?
Speaker 2: Ah? Yeah, that brings us to a really elegant framework
Speaker 2: constraints satisfaction problems or CSPs.
Speaker 1: CSPs? What are they?
Speaker 2: Basically, there are a way to solve problems you can
Speaker 2: define abstractly by variables of limited domains that have constraints
Speaker 2: between them.
Speaker 1: Okay, break that down. Variables domains constraints.
Speaker 2: So variables are the things you need to decide on.
Speaker 2: Domains are the possible choices or values for each variable,
Speaker 2: and constraints are the rules that say which combinations of
Speaker 2: values are allowed.
Speaker 1: Gotcha, can you give an example?
Speaker 2: Sure? Think about the classic Australian map coloring problem. The
Speaker 2: regions or states are the variables. The possible colors are
Speaker 2: the domain, say red, green, blue, and the constraint the
Speaker 2: extrain is simple, no two neighboring regions can have the
Speaker 2: same color or Another famous one is the eight queens problem,
Speaker 2: placing eight chess queens on a board so none can
Speaker 2: attack each other.
Speaker 1: Ah okay, So the queens are variables, their positions are domains.
Speaker 2: Exactly, and the constraint is the no attacking rule. The
Speaker 2: core of solving these often involves a function, maybe called consistent,
Speaker 2: that just checks does putting this value here violate any rules?
Speaker 1: Okay, cool puzzles, But where do CSPs show up in
Speaker 1: the real world Outside of map coloring and chess.
Speaker 2: They're actually commonly used in scheduling. Think about scheduling staff
Speaker 2: in a hospital. People are variables. Timeslots are domains, and
Speaker 2: constraints are things like nurse A needs two days off
Speaker 2: or doctor B must be on call with surgency.
Speaker 1: Right, that makes sense complex scheduling anywhere else.
Speaker 2: Yeah. In motion planning for robotics, imagine guiding a robot
Speaker 2: arm to fit inside a narrow tube without hitting the sides.
Speaker 2: The tube walls are the constraints. The angles of the
Speaker 2: robot's joints are the variables, the possible movements of the domains.
Speaker 2: CSPs help figure out a valid sequence of moves.
Speaker 1: Fascinating. Okay, So from logic puzzles to navigating spaces finding
Speaker 1: a path from A to B. That's a massive area
Speaker 1: in computer science, right from simple lists to complex mazes.
Speaker 2: Oh huge. And we have different tools depending on the situation.
Speaker 2: For basic lists, if the data isn't sorted, you might
Speaker 2: just use a linear search look at everything one by one.
Speaker 1: Like scanning a whole bookshelf for one specific book exactly.
Speaker 2: But if the data is sorted, you can use the
Speaker 2: much faster binary search.
Speaker 1: That's like opening a phone book right to the middle
Speaker 1: than the middle of the remaining half right.
Speaker 2: Much quicker, precisely. But what about something more complex like
Speaker 2: a maze. How does a computer navigate that? What does
Speaker 2: this all mean for finding your way through complex spaces?
Speaker 1: Yeah? How does that work?
Speaker 2: Well? Two fundamental approaches are depth first search or DFS
Speaker 2: and Brett first search or BFS.
Speaker 1: DFS and BFS.
Speaker 2: Okay. DFS uses a data strictually call a stack. I
Speaker 2: think last and first out, like a stack of plates.
Speaker 1: Got it last, one on, first, one off right?
Speaker 2: So DFS goes deep down one path, explores as far
Speaker 2: as it can. If it hits a dead end, it
Speaker 2: backtracks and tries another.
Speaker 1: Branch, So it dives deep first.
Speaker 2: Yeah. The paths that finds can sometimes seem unnatural, though,
Speaker 2: and they're usually not the shortest paths.
Speaker 1: It just finds a path okay, so not necessarily the
Speaker 1: best path, just one that works. What about BFS.
Speaker 2: BFS uses a queue. Think first and first out like
Speaker 2: waiting in line.
Speaker 1: Okay, fifo.
Speaker 2: So DFS explores outwards from the start layer by layer.
Speaker 2: It checks all neighbors one step away, then all neighbors
Speaker 2: two steps away, and so on.
Speaker 1: Ah, spreading out evenly exactly.
Speaker 2: And because of that systematic exploration, BFS always finds the
Speaker 2: shortest path in terms of the number of steps or edges,
Speaker 2: assuming the cost of each step is the same.
Speaker 1: Okay, So BFS guarantees the shortest path. DFS might be
Speaker 1: faster to find any path, but not the shortest sounds
Speaker 1: like a trade off.
Speaker 2: It often is. Yeah, choosing between them is sometimes a
Speaker 2: trade off between the possibility of finding a solution quickly
Speaker 2: and the certainty of finding the shortest pass.
Speaker 1: Makes sense. Are there more advanced methods?
Speaker 2: Oh? Yes, then you get into things like a search
Speaker 2: A is more sophisticated. It uses a priority queue and
Speaker 2: something called a heuristic.
Speaker 1: Okay, priority queue and a heuristic. What does that mean?
Speaker 2: A priority Q is like a queue where items have
Speaker 2: different levels of importance, so the most promising options get
Speaker 2: looked at first, and a heuristic is basically an educated
Speaker 2: gas or a rule of thumb to estimate how close
Speaker 2: you are to the goal.
Speaker 1: An estimate. How does a use that?
Speaker 2: Oh, combines the actual cost to get to a certain point,
Speaker 2: we call it GN with the estimated cost from that
Speaker 2: point to the finish line. That's hn the heuristic. It
Speaker 2: prioritizes exploring paths that seem to have the lowest total cost,
Speaker 2: both actual and estimated, So.
Speaker 1: It's using an estimate to guide its search more intelligently exactly.
Speaker 2: For mazes, a common heuristic is the Manhattan distance, just
Speaker 2: the horizontal plus vertical distance to the goal, ignoring walls
Speaker 2: for the estimate like distance in city blocks. Okay, and
Speaker 2: using a good heuristic like that, A not only finds
Speaker 2: the optimal shortest path, but it far outperforms BFS because
Speaker 2: it explores way fewer dead ends. It's much more focused.
Speaker 1: That sounds really powerful. And the nice thing is if
Speaker 1: you write these search algorithms well generically.
Speaker 2: Right, they become incredibly versatile. These same search functions can
Speaker 2: be easily adapted for solving a diverse set of problems,
Speaker 2: like that old brain teaser the missionaries and Cannibal's problem
Speaker 2: is just another state space to search.
Speaker 1: Right, Okay, Moving beyond mazes and paths, let's talk about graphs.
Speaker 1: You mentioned graphs earlier with maps. They seem really fundamental.
Speaker 2: They are. The world of graph algorithms is surprisingly broad
Speaker 2: in their applicability, so much can be modeled as.
Speaker 1: A graph like the map. Example, cities are vertices, connections,
Speaker 1: or edges.
Speaker 2: Exactly, and graphs can be undirected like a two way
Speaker 2: road or direct like a one way street, and the
Speaker 2: edges can be unweighted just showing a connection exists, or
Speaker 2: weighted showing a cost like distance or travel time.
Speaker 1: So if we want the shortest path in an unweighted graph,
Speaker 1: the path with the fewest edges, we can just use
Speaker 1: BFS again, right.
Speaker 2: Yeah, BFS works perfectly for that. Like, if you were
Speaker 2: planning a hypothetical hyperloop network, BFS could find the route
Speaker 2: from say Boston to Miami with the minimum number of stops.
Speaker 2: Maybe it's Boston, Detroit, Washington, Miami, just three segments, three edges.
Speaker 1: Okay, but what if the goal isn't just one path,
Speaker 1: but connecting everything efficiently, like connecting all the major US
Speaker 1: cities with the minimum amount of track.
Speaker 2: Now you're talking about a minimum spanning tree or MST problem.
Speaker 2: The goal is to minimize the cost of building the
Speaker 2: network while ensuring everything is connected.
Speaker 1: How do you solve that?
Speaker 2: A common way is Jarnick's algorithm, sometimes called Prim's algorithm.
Speaker 2: It basically starts somewhere and greedily adds the cheapest edge
Speaker 2: that connects a new city to the growing network without
Speaker 2: creating a cycle.
Speaker 1: So it builds a network piece by piece, always picking
Speaker 1: the cheapest next connection pretty much.
Speaker 2: We saw a calculation using this for the fifteen largest
Speaker 2: US metropolitan statistical areas msas the minimum length of track
Speaker 2: needed to connect all of them was found to be
Speaker 2: five three hundred and seventy two miles. Crucial for planning
Speaker 2: infrastructure like railways or pipelines.
Speaker 1: Wow, and what about finding shortest paths in weighted graphs
Speaker 1: where edges have different costs like actual road distances. BFS
Speaker 1: won't work then, right, right?
Speaker 2: BFS only cares about the number of edges. For weighted graphs,
Speaker 2: you need something like Dykstra's algorithm.
Speaker 1: Dikester has heard of that one.
Speaker 2: It's designed to find the lowest cost path from a
Speaker 2: starting point to all other points in a weighted graph.
Speaker 2: It keeps track of the cheapest known way to reach
Speaker 2: each city and systematically explores outwards, always updating paths if
Speaker 2: it finds a cheaper wrap. Very important for things like
Speaker 2: GPS navigation.
Speaker 1: Absolutely, it seems like graphs are everywhere once you start looking.
Speaker 2: They really are. A huge amount of our world can
Speaker 2: be represented using graphs, and these algorithms are essential for
Speaker 2: efficiency in the telecommunications, shipping, transportation, and utility industries.
Speaker 1: Can you do some big examples.
Speaker 2: Sure, think about Walmart building out an efficient distribution network,
Speaker 2: making warehouses and stores. That's a graph problem. Or Google
Speaker 2: indexing the web. The entire Internet is a gigantic graph
Speaker 2: of linked pages.
Speaker 1: Right links are edges.
Speaker 2: Exactly or FedEx finding the right set of hubs to
Speaker 2: minimize delivery times and costs. It's all graph algorithms working
Speaker 2: behind the scenes.
Speaker 1: Okay, let's shift gears a bit now away from these
Speaker 1: more deterministic algorithms towards things that feel more intelligent or adaptive,
Speaker 1: like genetic algorithms. You mention they're less predictable.
Speaker 2: Yeah, genetic algorithms are less deterministic than most traditional methods,
Speaker 2: but that unpredictability can be a strength. Sometimes they can
Speaker 2: solve problems that other approaches cannot solve in a reasonable
Speaker 2: amount of time, especially really complex optimization problems.
Speaker 1: How do they work? You mentioned they have a biological background.
Speaker 2: They do. They simulate natural selection like evolution. You start
Speaker 2: with a population of pencil solutions called chromosomes.
Speaker 1: Chromosomes okay, like individuals, right, and.
Speaker 2: Each chromosome has genes, which are like its specific traits
Speaker 2: or parts of the solution. These individuals then compete in
Speaker 2: a sense. To solve the problem. Their success is measured
Speaker 2: by a fitness function, how well they do.
Speaker 1: The job Survival of the fittest basically exactly.
Speaker 2: The process involves creating an initial population, often randomly. Then
Speaker 2: you measure everyone's fitness. Then you select individuals for reproduction.
Speaker 2: Fitter ones are more likely to be chosen. Common methods
Speaker 2: are rulette, rule selection or tournament selection.
Speaker 1: Okay, select the best.
Speaker 2: Then what then comes crossover? You take two parent solutions
Speaker 2: and combine parts of them to create one or two
Speaker 2: children's solutions, hoping to mix good traits, mixing gen right.
Speaker 2: And finally, there's mutation, making small random changes to some individuals.
Speaker 2: This helps maintain diversity of the population and prevents getting
Speaker 2: stuck too early on a sub optimal solution. You repeat
Speaker 2: this cycle fitness, selection, crossover, mutation over many generations.
Speaker 1: That's a really cool analogy. Can they solve actual problems?
Speaker 2: Oh? Yeah, they can tackle things like that. Send plus
Speaker 2: more money. Cryptoithmetic puzzle we mentioned earlier, which is also
Speaker 2: a CSP. You can represent the letters and digits and
Speaker 2: let the genetic algorithm evolve toward a valid assignment.
Speaker 1: Huh. Solving a logic puzzle through simulated evolution. What else?
Speaker 2: Something may be more surprising optimizing list compression. It turns
Speaker 2: out that for many compression algorithms, the order of the
Speaker 2: items will affect the compression ratio.
Speaker 1: The order matters really for some algorithms.
Speaker 2: Yes, So for a list of say twelve names, maybe
Speaker 2: standard compression gets it down to one hundred and sixty
Speaker 2: five bytes, a genetic algorithm could try rearranging the order
Speaker 2: of those names and found an order that compressed down
Speaker 2: to one hundred and fifty nine bytes.
Speaker 1: Okay, from one to sixty five seems like a small gain.
Speaker 2: It might seem small for twelve names, but imagine optimizing
Speaker 2: the order for millions of items. Now. Could you find
Speaker 2: the absolute best order for those twelve names by checking
Speaker 2: every possibility twelve names?
Speaker 1: That's twelve factorial permutations? Right, that's huge.
Speaker 2: It's four hundred and seventy nine thousand, one thousand, six
Speaker 2: hundred possible orders. Absolutely unfeasible to check them all. Brute
Speaker 2: force is impossible, right, No way, And that's where genetic
Speaker 2: algorithms shine. They don't guarantee the absolute, perfect optimal solution,
Speaker 2: but they're great at finding very good, near optimal solutions
Speaker 2: for problems where finding the true optimum is computationally impossible
Speaker 2: or would take like the age of the universe.
Speaker 1: So they're a practical way to tackle incredibly complex optimization.
Speaker 1: Are there downsides?
Speaker 2: Well, As we said, they're less deterministic. Run it twice
Speaker 2: you might get slightly different results. It could also be
Speaker 2: something of a black box. It's not always clear why
Speaker 2: the solution they found work so well, and we don't
Speaker 2: really know if we found the optimal order just a good.
Speaker 1: One, gotcha, but still useful any wild applications.
Speaker 2: People have used them for computer generated art, evolving images
Speaker 2: made of polygon to resemble photographs, and even genetic programming,
Speaker 2: where the things evolving aren't just data but actual pieces
Speaker 2: of computer code programs that write programs.
Speaker 1: WHOA, Okay, that's mind bending, all right. Another area dealing
Speaker 1: with complexity finding hidden structure in data. We have more
Speaker 1: data than ever, how do we make sense of it
Speaker 1: if we don't even know what we're looking for.
Speaker 2: That's where clustering comes in. It's a key technique when
Speaker 2: you want to learn about the structure of a data set,
Speaker 2: but you do not know ahead of time. It's constituent parts.
Speaker 1: Finding groups without knowing the groups beforehand exactly.
Speaker 2: K means clustering is a very common type. It's a
Speaker 2: form of unsupervised learning. You don't train it with labeled examples.
Speaker 2: It finds the inherent groupings in the data itself.
Speaker 1: Okay, K means How might that be used?
Speaker 2: Say?
Speaker 1: In business?
Speaker 2: Imagine you run a grocery store. You have tons of
Speaker 2: data about who buys what. When you can use K
Speaker 2: means to cluster customers based on demographics, purchase history, day
Speaker 2: of the week.
Speaker 1: They shop and what would that tell you?
Speaker 2: You might discover hidden patterns, like maybe there's a distinct
Speaker 2: cluster of younger shoppers prefer to shop on Tuesdays. You
Speaker 2: didn't know that group existed, but the algorithm found.
Speaker 1: It, and then you could use that insight.
Speaker 2: Right, you could run an ad specifically targeting them on
Speaker 2: Mondays or Tuesdays, making your marketing much more effective.
Speaker 1: Makes sense? How does the K means algorithm actually work?
Speaker 1: Is it complex?
Speaker 2: The algorithm itself is surprisingly simple conceptually. First, you decide
Speaker 2: how many clusters you want to find, that's the K.
Speaker 2: Then you initialize K centroids, which are just the starting
Speaker 2: center points for each cluster, often placed randomly.
Speaker 1: Okay, pick k random starting points.
Speaker 2: Then you repeat two steps. Step one, assign clusters. You
Speaker 2: go through every single data point and assign it to
Speaker 2: the cluster whose centroid is closest.
Speaker 1: Assign each point to its nearest center.
Speaker 2: Step two, generate centroids. For each cluster. You calculate the
Speaker 2: mean the average position of all the points currently assigned
Speaker 2: to it. That mean becomes the new centroid for that cluster.
Speaker 1: Okay, move the center to the average location of its points.
Speaker 2: Exactly, and you just keep repeating those two steps. Assigned points,
Speaker 2: update centroids until the centroids stop moving much or converge.
Speaker 2: The points naturally group around these centers.
Speaker 1: Huh, elegant. Where else does k meines use besides customer segmentation?
Speaker 2: Oh, lots of places. It helps with pattern recognition in biology,
Speaker 2: maybe identifying groups of incongruous cells that might signal a
Speaker 2: problem finding anomalies. Yeah. In image recognition, pixels themselves can
Speaker 2: be data lights. You could cluster pixels by color to
Speaker 2: segment an image into regions.
Speaker 1: Okay.
Speaker 2: Even in political science, it's used to group voters based
Speaker 2: on survey responses or demographics to find voters to target
Speaker 2: and understand their underlying concerns without predefining the groups.
Speaker 1: Powerful stuff for finding structure in the unknown. Now, let's
Speaker 1: talk about the elephant in the AI room, neural networks.
Speaker 1: When we hear about deep learning, it's usually neural nets.
Speaker 2: Right, almost always, yes, especially the really impressive advances in
Speaker 2: AI lately, they often concern neural networks, particularly deep ones
Speaker 2: with many layers.
Speaker 1: So what are they? Fundamentally, they're inspired by the brain.
Speaker 2: That's the core idea they mimic in a very simplified way,
Speaker 2: the structure of biological neurons. A basic unit, a neuron
Speaker 2: takes several inputs. Each input has a weight associated with it,
Speaker 2: representing its importance.
Speaker 1: Inputs have weights.
Speaker 2: The neurons sums up these weighted inputs and then applies
Speaker 2: an activation function to the total. This function determines the
Speaker 2: neuron's output, whether it fires and how strongly.
Speaker 1: Okay weighted Some than an activation and these neurons are connected.
Speaker 2: Yes, they're organized into layers. You have an input layer
Speaker 2: that receives the raw data, one or more hidden layers
Speaker 2: where the computation happens, and an output layer that gives
Speaker 2: a final result. The outputs from neurons in one layer
Speaker 2: become the inputs for neurons in the next layer.
Speaker 1: A network of connected layers. But how do they learn?
Speaker 1: How does it go from random connections to say, recognizing
Speaker 1: a case through training.
Speaker 2: It's a process of showing the network vast amounts of
Speaker 2: labeled data, like millions of images, each tagged as cat
Speaker 2: or not cat.
Speaker 1: Learning by example, exactly.
Speaker 2: When the network makes a prediction, say it calls a
Speaker 2: cat picture a dog, you calculate the error, the difference
Speaker 2: between its output and the correct answer. This air signal
Speaker 2: is then propagated backward through the network using a process
Speaker 2: called back propagation.
Speaker 1: Backpropagation calculates the error.
Speaker 2: Then what backpropagation helps figure out how much each connection's
Speaker 2: weight contributed to the error. Then an optimization algorithm, usually
Speaker 2: gradient descent, is used to slightly adjust those weights. It
Speaker 2: nudges them in a direction that should reduce the error.
Speaker 1: Next time adjusting the weights to get closer to the
Speaker 1: right answer precisely.
Speaker 2: And there's a learning rate parameter that controls how big
Speaker 2: those adjustments are. Too big and you might overshoot too small,
Speaker 2: and learning takes forever. You repeat this process forward pass
Speaker 2: calculate air backpropagate adjust weights millions of times.
Speaker 1: It sounds computationally intensive.
Speaker 2: Training can be yes, But what's fascinating is that the
Speaker 2: network figures out the important features on its own. It
Speaker 2: does not care what the various attributes represent in human terms.
Speaker 1: It just finds patterns.
Speaker 2: Yeah, we saw examples classifying iris flowers based on four measurements,
Speaker 2: or different wine cultivars based on thirteen chemical properties. The
Speaker 2: network just learns the underlying patterns linking inputs to outputs
Speaker 2: without needing explicit rules.
Speaker 1: So what does this all mean? They're incredibly powerful, clearly,
Speaker 1: but are there drawbacks? You mentioned black box before.
Speaker 2: That's a big one. They're often something of a black box.
Speaker 2: I can give you the right answer, but it's very
Speaker 2: difficult to understand why they gave that answer, what features
Speaker 2: they relied on. This lack of interpretability could be a
Speaker 2: major issue in sensitive areas like medical diagnosis or loan applications.
Speaker 1: Right, you need to be able to explain the decision
Speaker 1: any other downsides.
Speaker 2: They also often require very large data sets for training.
Speaker 2: We're talking potentially millions of training images for a good
Speaker 2: image classifier. Gathering and labeling that much data can be
Speaker 2: a huge undertaking millions.
Speaker 1: Okay, so expensive to train, potentially hard to interpret. But
Speaker 1: once trained, that's the good news.
Speaker 2: While training is computationally expensive, using a pre trained network
Speaker 2: is actually very fast and efficient.
Speaker 1: Ah, so the heavy lifting is done beforehand exactly.
Speaker 2: That's why you see things like Apple's core mL framework.
Speaker 2: It lets developers easily incorporate powerful, pre trained neural network
Speaker 2: models directly into their apps. The training was done on
Speaker 2: big servers, but the app on your phone can use
Speaker 2: the result instantly.
Speaker 1: And that enables all sorts of cool stuff we use
Speaker 1: every day.
Speaker 2: Totally. It's enabling things like practical voice recognition Siri, Alexa,
Speaker 2: Google Assistant, and image recognition like Facebook automatically suggesting tags
Speaker 2: for faces in your photos.
Speaker 1: Or even handwriting recognition. I know my phone can search
Speaker 1: my handwritten notes.
Speaker 2: Now yep, that's often neural networks too. They're really changing
Speaker 2: what's possible in user phasing applications.
Speaker 1: Okay, fantastic overview. Now for a quick bonus round a
Speaker 1: few more classic problems. First up, the knapsack problem sounds
Speaker 1: like a story.
Speaker 2: It is often told that way. A thief with a
Speaker 2: knapsack of limited capacity trying to steal the most valuable items.
Speaker 2: But it represents a really common computational need finding the
Speaker 2: best use of limited resources given a finite set of usage.
Speaker 1: Options, maximizing value within a budget or capacity exactly.
Speaker 2: We're usually talking about the one variant, meaning for each item,
Speaker 2: you either take the whole thing or you leave it.
Speaker 2: You can't take.
Speaker 1: Half, Okay, take it or leave it. How hard is
Speaker 1: that to solve?
Speaker 2: Well, if you try brute force checking every possible combination
Speaker 2: of items, you're looking at two end different possible subsets.
Speaker 2: Where n is the number of items.
Speaker 1: Exponential growth gets big.
Speaker 2: Fast, very fast. For just eleven items, that's two thousan
Speaker 2: forty eight combinations. Manageable maybe, but scale that up it
Speaker 2: quickly becomes untenable for a large number.
Speaker 1: Yeah, so brute forces out for anything non trivial. Is
Speaker 1: there a smarter way?
Speaker 2: Yes? This is where dynamic programming are often comes in.
Speaker 2: We mentioned it briefly before.
Speaker 1: Right breaking the problem down.
Speaker 2: Instead of solving the big problem directly, dynamic programming solves
Speaker 2: smaller sub problems first and uses those solutions to build
Speaker 2: up to the final answer, storing intermediate results to avoid recomputation.
Speaker 2: How much better is it for that example? With eleven
Speaker 2: items and a knapsack capacity of seventy five, dynamic programming
Speaker 2: only needs to do about eight hundred and twenty five
Speaker 2: calculations roughly end time, ce the capacity down from twenty
Speaker 2: forty eight. That's a significant improvement.
Speaker 1: Definitely much more scalable. Where else does this idea apply?
Speaker 2: The technique is widely applicable. Think about a university deciding
Speaker 2: how to allocate its athletic budget. They have a limited budget,
Speaker 2: the knapsack various sports programs items, each with a cost
Speaker 2: and an expected return, maybe in alumni donations or prestige.
Speaker 2: They want to pick the set of programs that gives
Speaker 2: the best return within budget. That's a knapsack problem.
Speaker 1: Huh, never thought of it that way, Okay, next bonus.
Speaker 1: The traveling salesman problem TSP.
Speaker 2: Ah, the famous TSP. The goal sounds simple. You have
Speaker 2: a list of cities. You need to visit every single
Speaker 2: one exactly once and end up back where you started
Speaker 2: finding the absolute shortest possible route.
Speaker 1: Sounds like something every delivery company needs to solve daily.
Speaker 2: They do. But here's the catch. TSP is notoriously difficult.
Speaker 2: It's an NP hard problem. N P hard meaning meaning
Speaker 2: there's no known polynomial time algorithm they can guarantee finding
Speaker 2: the perfect shortest route quickly for any arbitrary number of cities.
Speaker 2: The complexity explodes. It becomes essentially impossible to solve the
Speaker 2: problem perfectly optimally for millions of cities in any reasonable timeframe.
Speaker 1: So companies like UPS or FedEx can't find the absolute,
Speaker 1: mathematically perfect route for all their trucks every day.
Speaker 2: Not perfectly. No, they use very sophisticated heuristics and approximation
Speaker 2: algorithms that find extremely good routes very close to optimal,
Speaker 2: but they likely aren't guaranteed to be the single shortest
Speaker 2: possible path out of the trillions and trillions of possibilities.
Speaker 1: For smaller instances like just a few cities.
Speaker 2: Oh yeah, for a small number, like visiting five cities
Speaker 2: in Vermont, brute force is feasible. You just generate all
Speaker 2: possible orderings permutations of the cities, calculate the total distance
Speaker 2: for each, and pick the shortest. We saw an example
Speaker 2: where the shortest path was three hundred and eighteen miles.
Speaker 1: Okay, so solvable for small N, but relies on approximations
Speaker 1: for large N. Got it last? One phone number mnemonics.
Speaker 2: Yeah, this is a fun one. Remember those old phone
Speaker 2: numbers that spelled out words like one eight hundred flowers?
Speaker 1: Sure, how do computers figure those out or help you
Speaker 1: find a new one, like maybe one ga zero sts
Speaker 1: for one, four, four, zero, seven eight seven.
Speaker 2: You can use algorithms that explore the combinations for each
Speaker 2: digit on the keypad to abc, three, def, et cetera.
Speaker 2: You have multiple letter options, you can use something like
Speaker 2: the Cartesian product mathematically or just nested loops in code
Speaker 2: to generate all possible letter combinations for the number sequence.
Speaker 1: And then you'd check that list against a dictionary to
Speaker 1: see if any parts spell actual words exactly.
Speaker 2: It's a systematic way to explore the possibilities and find
Speaker 2: those memorable combinations.
Speaker 1: Wow, Okay, what an incredible journey through these classic computer
Speaker 1: science problems. It's amazing how much ground we've covered, from
Speaker 1: the subtle efficiency games in fibonacci, right.
Speaker 2: Down to the bit level savings in compression, to.
Speaker 1: The strategic choices and the knapsack problem, navigating graphs with
Speaker 1: Diichstra or A, and then these adaptive methods like genetic
Speaker 1: algorithms and neural networks. It really shows how ingenious solutions
Speaker 1: can tackle seemingly impossible challenges.
Speaker 2: Absolutely, and I think the key takeaway is that knowledge
Speaker 2: is most valuable when you understand it and can apply
Speaker 2: it right. These aren't just abstract puzzles locked away in
Speaker 2: computer science to work.
Speaker 1: No, they're really fundamental.
Speaker 2: They're the building blocks that have shaped and continued to
Speaker 2: shape our technological world. They drive innovation in fields way
Speaker 2: beyond just programming. They offer these really powerful ways to
Speaker 2: analyze and approach problems in incredibly diverse areas.
Speaker 1: It's helping us that makes sense of complexity exactly. So
Speaker 1: here's a final thought for everyone listening. As you go
Speaker 1: about your day, think about a problem you encounter, maybe
Speaker 1: at work, maybe just in daily life. It could be simple,
Speaker 1: could be complex. How might you try to abstract it?
Speaker 1: Could you define it in terms of variables and constraints,
Speaker 1: or maybe nodes and edges in a graph. Could you
Speaker 1: even think of it as a population of competing solutions,
Speaker 1: like in a genetic algorithm.
Speaker 2: That's a great challenge applying these frameworks in unexpected places.
Speaker 1: Yeah, could one of these classic computer science approaches like
Speaker 1: the ones we've talked about today offer a surprising maybe
Speaker 1: even a powerful new way to understand or even solve
Speaker 1: that problem. Give it some thought,