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Guess the Number5:56 with Pasan Premaratne
In this video we're going to do something unusual - we're going to play a game where two of my friends try to guess a number. It's relevant, I promise!
Hey again. 0:00 In this video we're going to do something unusual. 0:01 We're going to play a game, and by we, I mean me and my two friends here, 0:03 Brittany and John. 0:07 This game is really simple, and you may have played it before. 0:08 It goes something like this, I am going to think of a number between 1 and 10, and 0:11 they have to guess what the number is. 0:15 Easy, right? 0:17 When they guess a number, I'll tell them if their guess is too high or too low. 0:19 The winner is the one with the fewest tries. 0:23 All right, John, let's start with you. 0:25 I'm thinking of a number between 1 and 10, what is it? 0:27 Between you and me, the answer is three. 0:30 JOHN: Quick question, does the range include one and ten? 0:33 PASAN: That is a really good question, and so 0:36 what John did right there was to establish the bounds of our problem. 0:38 No solution works on every problem, and an important part of algorithmic thinking is 0:42 to clearly define what the problem set is and clarify what values count as inputs. 0:46 Yeah, one and ten are both included. 0:51 JOHN: Is it one? 0:54 PASAN: Too low. JOHN: Is it two? 0:55 PASAN: Too low. 0:56 JOHN: Is it three? 0:56 PASAN: Correct. 0:57 Okay, so that was an easy one. 0:58 It took John three tries to get the answer. 1:00 Let's switch it over to Brittany and 1:03 play another round using the same number as the answer. 1:04 Okay Brittany, I'm thinking of a number between one and ten inclusive, so 1:07 both one and ten are in the range. 1:10 What number am I thinking of? 1:12 BRITTANY: Is it five? 1:13 PASAN: Too high. 1:14 BRITTANY: Two? 1:15 PASAN: Too low. 1:16 BRITTANY: Is it three? 1:16 PASAN: Correct. 1:17 All right, so 1:18 what we had there was two very different ways of playing the same game. 1:19 Somehow, with even such a simple game, 1:24 we saw different approaches to figuring out a solution. 1:26 To go back to algorithmic thinking for 1:29 a second, this means that with any given problem, there's no one best solution. 1:31 Instead what we should try and figure out is what solution works better for 1:36 the current problem. 1:40 In this first pass at the game they both took the same amount of turns 1:42 to find the answer. 1:46 So it's not obvious who has the better approach, 1:47 and that's mostly because the game was easy. 1:49 Let's try this one more time, now this time the answer is ten. 1:52 All right, John, you first. 1:56 JOHN: Is it one? 1:57 PASAN: Too low. 1:57 JOHN: Is it two? 1:58 PASAN: Still too low. 1:59 JOHN: Is it three? 2:00 PASAN: Too low. 2:00 JOHN: Is it four? 2:01 PASAN: Too low. 2:02 JOHN: Is it five? 2:02 PASAN: Still too low. 2:03 JOHN: Is it six? 2:04 PASAN: Too low. 2:04 JOHN: Is it seven? 2:05 PASAN: [LAUGH] Too low. 2:06 JOHN: Is it eight? 2:07 PASAN: [LAUGH] Too low. 2:07 JOHN: Is it nine? 2:08 PASAN: Too low. 2:09 JOHN: Is it ten? 2:10 PASAN: Correct, you got it. 2:10 Okay, so now same thing, but with Brittany this time. 2:12 BRITTANY: Is it five? 2:15 PASAN: Too low. 2:17 BRITTANY: Eight? PASAN: Too low. 2:18 BRITTANY: Is it nine? 2:19 PASAN: Still too low. 2:20 BRITTANY: It's ten. 2:21 PASAN: All right, so here we start to see a difference between their strategies. 2:21 When the answer was three they both took the same number of turns. 2:26 This is important. 2:29 When the number was larger, but not that much larger, ten in this case, 2:31 we start to see that Brittany's strategy did better. 2:35 She took four tries while John took 10. 2:38 We've played two rounds so far and 2:40 we've seen a different set of results based on the number they were looking for. 2:42 If you look at John's way of doing things, then the answer being ten, 2:46 the round we just played, is his worst case scenario. 2:49 He will take the maximum number of turns, ten, to guess it. 2:53 When we picked a random number like three, it was hard to differentiate which 2:56 strategy was better, because they both performed exactly the same, but 3:01 in John's worst case scenario a clear winner in terms of strategy emerges. 3:06 In terms of algorithmic thinking, we're starting to get a sense that the specific 3:10 value they're searching for may not matter as much as where that value 3:15 lies in the range that they have been given. 3:19 Identifying this helps us understand our problem better. 3:22 Let's do this again for a range of numbers from 1 to 100. 3:26 We'll start by picking five as an answer to trick them. 3:29 Okay, so this time we're going to run through the exercise again, but 3:32 this time from 1 to 100, and both 1 and 100 are included. 3:35 JOHN: Is it one? 3:39 PASAN: At this point without even having to run through it we can guess how many tries 3:40 John is going to take. 3:43 Since he starts at one and 3:44 keeps going he's going to take five tries as we're about to see. 3:45 JOHN: Is it five? 3:48 PASAN: Cool, correct. 3:49 Okay, now for Brittany's turn. 3:49 BRITTANY: Is it 50? 3:51 PASAN: Too high. 3:53 BRITTANY: Is it 25? 3:54 PASAN: Still too high. 3:55 BRITTANY: Is it 13? 3:56 PASAN: Too high. 3:57 BRITTANY: Is it seven? 3:58 PASAN: Too high. 3:59 BRITTANY: Is it four? 4:00 PASAN: Too low. 4:01 BRITTANY: Is it six? 4:02 PASAN: Too high. 4:03 BRITTANY: Is it five? 4:04 PASAN: Correct. 4:06 Let's evaluate. 4:07 John took five tries, Brittany, on the other hand, took seven tries. 4:08 So John wins this round, but again, 4:12 in determining whose strategy is preferred there is no clear winner right now. 4:14 What this tells us is that it's not particularly useful to look at 4:18 the easy answers where we arrive at the number fairly quickly because it's at 4:22 the start of the range. 4:26 Instead, let's try one where we know John is going to do poorly. 4:27 Let's look at his worse case scenario where the answer is 100 and 4:31 see how Brittany performs in such a scenario. 4:35 Okay, John, let's do this one more time, 1 through 100, again. 4:38 JOHN: Is it one? 4:41 PASAN: We can fast-forward this scene because, well, we know what happens. 4:42 John takes 100 tries. 4:45 All right, Brittany, you're up. 4:47 BRITTANY: Is it 50? 4:49 PASAN: Too low. 4:50 BRITTANY: Is it 75? 4:51 PASAN: Too low. 4:52 BRITTANY: 88? 4:53 PASAN: Too low. 4:53 BRITTANY: 94? 4:54 PASAN: Too low. 4:55 BRITTANY: Is it 97? 4:56 PASAN: Too low. 4:57 BRITTANY: 99? 4:58 PASAN: Too low. 4:59 BRITTANY: 100. 5:00 PASAN: Okay, so that took Brittany seven turns again, and 5:02 this time she is the clear winner. 5:05 If you compare their individual performances for the same number set, 5:07 you'll see that Brittany's approach leaves John's in the dust. 5:11 When the answer was five, so 5:14 right around the start of the range, John took five turns, but 5:16 when the answer was 100, right at the end of the range, he took 100 tries. 5:19 It took him 20 times the amount of tries to get that answer compared to Brittany. 5:23 On the other hand, if you compare Brittany's efforts, 5:28 when the number was five, she took seven tries, but 5:31 when the number was one hundred, she took the same amount of tries. 5:34 This is pretty impressive. 5:37 If we pretend that the number of tries is the number of seconds it takes Brittany 5:38 and John to run through their attempts, this is a good estimate for 5:43 how fast their solutions are. 5:46 Okay, we've done this a couple of times, and Brittany and John are getting tired. 5:49 Let's take a break. 5:52 In the next video we'll talk about the point of this exercise. 5:53
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