From cc06dbe9196a5af3bbf63f0f4f893ac0592f4aff Mon Sep 17 00:00:00 2001 From: bovem Date: Wed, 25 Oct 2023 12:37:37 +0530 Subject: [PATCH] Added article on top k frequent elements --- README.md | 1 + content/contents.md | 2 +- .../index.md | 283 ++++++++++++++++++ .../top-k-frequent-brute-force.png | Bin 0 -> 95954 bytes .../top-k-frequent-cover.png | Bin 0 -> 214404 bytes .../top-k-frequent-problem-2.png | Bin 0 -> 64056 bytes .../top-k-frequent-problem.png | Bin 0 -> 48471 bytes 7 files changed, 285 insertions(+), 1 deletion(-) create mode 100644 content/posts/dsa/finding-most-frequent-elements-in-an-array/index.md create mode 100644 content/posts/dsa/finding-most-frequent-elements-in-an-array/top-k-frequent-brute-force.png create mode 100644 content/posts/dsa/finding-most-frequent-elements-in-an-array/top-k-frequent-cover.png create mode 100644 content/posts/dsa/finding-most-frequent-elements-in-an-array/top-k-frequent-problem-2.png create mode 100644 content/posts/dsa/finding-most-frequent-elements-in-an-array/top-k-frequent-problem.png diff --git a/README.md b/README.md index c9bb8cf..e38f5a8 100644 --- a/README.md +++ b/README.md @@ -31,6 +31,7 @@ Blogs on Self-Hosting, Homelab and DevOps Technologies. - Identifying Anagrams - Finding Elements in an Array that Sum Up to a Target Value - Group Anagrams in an Array + - Finding Most Frequent Elements in an Array ## Technologies Used - [Hugo Static Site Generator](https://gohugo.io/) diff --git a/content/contents.md b/content/contents.md index 0c13808..488a837 100644 --- a/content/contents.md +++ b/content/contents.md @@ -33,4 +33,4 @@ summary: "Index of all content" - Identifying Anagrams - Finding Elements in an Array that Sum Up to a Target Value - Group Anagrams in an Array - + - Finding Most Frequent Elements in an Array diff --git a/content/posts/dsa/finding-most-frequent-elements-in-an-array/index.md b/content/posts/dsa/finding-most-frequent-elements-in-an-array/index.md new file mode 100644 index 0000000..e8b6504 --- /dev/null +++ b/content/posts/dsa/finding-most-frequent-elements-in-an-array/index.md @@ -0,0 +1,283 @@ +--- +author: "Avnish" +title: "Finding Most Frequent Elements in an Array" +date: "2023-10-26" +description: "Implementing a topKFrequent(inputArray, k) function that takes an array of integers and a value k as inputs and returns top k most frequent elements." +tags: + [ + "data-structures", + "arrays", + "hashmaps", + "go", + "neetcode-150", + "leetcode-medium", + ] +categories: ["Data Structures"] +series: ["Data Structures and Algorithms"] +aliases: ["finding-most-frequent-elements-in-an-array", "top-k-frequent"] +ShowToc: true +TocOpen: false +comments: false +cover: + image: "top-k-frequent-cover.png" + linkFullImages: true + alt: "The topkFrequent function will return the top k most frequent elements in an array" + caption: "" + relative: false + responsiveImages: false +math: true +--- + +# Problem Statement + +We have to implement a `topKFrequent` function that takes an integer array and a value `k` as input and returns the `k` most frequent elements in the input array. For example, `topKFrequent({1, 1, 2, 2, 3, 5, 2}, 2)` will return the top `2` most frequent elements in the array i.e. `{2, 1}`. + +

Problem Statement for topKFrequent

+ +If multiple elements have the same frequency, then any of them could be returned in the solution as long as its length is `k`. + +

Problem Statement for topKFrequent

+ +# Brute Force Solution + +First, we have to gather the data for the frequency of array elements inside a hashmap. We have to group elements with the same frequency, so we'll invert the key and values in the hashmap from `element -> count` to `count -> [elements]`. + +

Brute Force solution to topKFrequent

+ +We can also extract a list of frequencies from this hashmap which will be sorted in descending order to extract the top `k` elements. + +## Psuedo-code for the Brute Force Solution + +```text +counter = HashMap() +loop index on array + if counter[array[index]] + counter[array[index]]+=1 + else + counter[array[index]]=1 + +reverseCounter = HashMap() +freq = [] +loop key, value in counter + if reverseCounter[value] + reverseCounter[value].append(key) + else + reverseCounter[value] = [key] + freq.append(value) + +sort(freq, descending=True) + +topKElements = [] +loop index on freq + value = reverseCounter[freq[index]] + for fq in value + topKElements.append(fq) + + if len(topKElements)==k + return topKElements +``` + +## Best Case Scenario + +The first loop over the array has $O(n)$ time complexity, where $n$ is the size of the input array. + +Let's assume that the second loop also has $O(n)$ time complexity (`length(counter) == length(reverseCounter)`). In the best-case scenario, there will be only one key in `reverseCounter` i.e. all elements have the same frequency, which decreases the time complexity of this loop to $O(1)$. + +The fastest sorting algorithm will sort the `freq` array in $O(n \log(n))$ time. + +The final loop (over `freq`) will execute `k` times. On each iteration, it will also loop over the list stored in `reverseCounter[freq[index]]`. Since the loop will exit as soon as the length of the result array reaches `k` its time complexity could be generalized to $O(k)$. + +Thus, the total time complexity of the best-case scenario for brute force solution will be $O(n) + O(1) + O(n \log(n)) + O(k)$, which could be generalized to $O(n \log n)$. + +## Worst Case Scenario + +In the worst-case scenario, all the elements in the input array will have distinct frequencies. Thus, the length of `counter` and `reverseCounter` will be the same resulting in total time complexity $O(n) + O(n) + O(n \log(n)) + O(k)$, which could also be generalized to $O(n \log n)$. + +## Code for Brute Force Solution + +```Go +package main + +import ( + "fmt" + "sort" +) + +func topKElements(inputArray []int, k int)([]int){ + + // counter hashmap for storing frequency data + // of elements in inputArray + // Time Complexity: O(n) + counter := make(map[int]int) + for index:=0;index0;freq--{ + value, key_exists := reverseCounter[freq] + if key_exists{ + for _, val := range value{ + topKElements = append(topKElements, val) + if len(topKElements) == k{ + return topKElements + } + } + } + + } + + return topKElements +} + +func main(){ + inputArray := []int{1, 1, 1, 2, 2, 3, 3, 4} + k := 3 + fmt.Println("Top", k, "elements in inputArray:", topKElements(inputArray, k)) + + inputArray = []int{1, 2} + k = 2 + fmt.Println("Top", k, "elements in inputArray:", topKElements(inputArray, k)) +} +``` + +
+ +Thank you for taking the time to read this blog post! If you found this content valuable and would like to stay updated with my latest posts consider subscribing to my RSS Feed. + +# Resources + +347. 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