From the following list, extract a collection of numbers whose sum is 3165 . How efficient is yo

step 1 Hello, welcome to this lesson. In this lesson, we've been given a list that is from 1 to that ha

From the following list, extract a collection of numbers...

Key Concepts

Subset Sum Problem

This problem involves finding a subset of numbers from a given set that adds up to a specific target sum. It is a classic decision problem in computer science and forms the basis of many studies in combinatorial optimization and algorithm design.

NP-Completeness

The subset sum problem is an NP-complete problem, meaning that there is no known algorithm that can solve all instances of the problem efficiently (in polynomial time). This concept highlights the problem's computational difficulty and challenges in designing exact algorithms.

Brute-Force Approach

A brute-force solution to the subset sum problem examines all possible subsets of the given numbers, which leads to an exponential time complexity (O(2^n)). This method, while simple, becomes impractical for larger sets due to rapid growth in the number of potential subsets.

Dynamic Programming

Dynamic programming offers an alternative approach to solving the subset sum problem with pseudo-polynomial time complexity. This method uses a table to store intermediate results, allowing for a more efficient solution for problems where the target sum or the numbers in the set are not exceedingly large.

Computational Complexity

Assessing the efficiency of an approach to the subset sum problem involves an understanding of computational complexity, particularly time and space requirements. This concept is central to evaluating how algorithm performance scales with input size and helps in comparing different algorithmic strategies.

Transcript

00:01 Hello, welcome to this lesson.

00:02 In this lesson, we've been given a list that is from 1 to that has integers from 1 to 1000 and you're expecting the pair.

00:12 So the pair would be a, b, a times b would be close to 2, 4, 2, 4.

00:28 Okay, but here a and b would have to be in the range 1 to 1000.

00:40 Okay, so both a and b should be in a list.

00:44 Alright, so let's go on.

00:46 The first thing that we'll do is that let's have the list.

00:52 Okay, this list will contain values from 1 to 1000.

00:59 So i'll do x for x in range and i'll provide the range from 1 to 1001 because this one inclusive.

01:12 The one is inclusive.

01:16 The 100, 1001 is not inclusive.

01:21 Okay, so it'll go all the way to 1001 minus 1.

01:26 And now let me have a dictionary that will store key value pairs.

01:33 So the key would be, so for example, the key would be a and the value would be b.

01:40 So each time i'm actually doing, i'm inserting the key value, i'm going to check whether i already have that in there.

01:51 Okay, so that i don't insert ones that are already in because we are looking at pairs that are unique.

01:59 Okay, so let me create this dictionary.

02:03 So you're using python for this, but it's dictionary in python.

02:10 I'm going to say for i in the list that we have, i'm going to check if so that i goes from 1 to 1000.

02:24 So at each one, i'm going to divide the i by the 2, 4, 2, 4.

02:31 And if i divide in there's no remainder, then i'm going to say it is one of the factors and i'm going to the answer that it gives actually gives the, so if i divide a by 2, 4, 2, 4, and a is a factor, it will surely give an answer on your study to b.

02:54 But you're going to use mode.

02:56 Then if i see it has no remainder, that is apart from zero, i would actually do an integer division to get the one.

03:08 Let's go say if 2, 0, 2, 4, 2, 4, mode i is equals to zero.

03:26 It's equals to zero means that i can actually divide 2, 4, 2, 4 without remainder.

03:35 So i'm going to say key is equals to, i will now divide 2, 4, 2, 4 by i.

03:49 Okay.

03:50 Then i'll put the results into the ls dict.

03:56 But before then, let me check if the results is not ready.

03:59 So i'm going to say if key, okay, not in ls dict, i'm going to say ls dict, but update.

04:19 Then i'll put in the key.

04:22 I'll put in the key together with its value.

04:28 Its value is the i.

04:29 Because both the key and the i gives, if you multiply the i by the key, it gives the, so they are both factors...

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