![]() Strassen’s algorithm multiplies two matrices in O(n².8974) time.Ħ - Cooley–Tukey Fast Fourier Transform (FFT) algorithm is the most common algorithm for FFT. A simple method to multiply two matrices need 3 nested loops and is O(n³). The Divide and Conquer algorithm solves the problem in O(nLogn) time.ĥ - Strassen’s Algorithm is an efficient algorithm to multiply two matrices. The problem can be solved in O(n²) time by calculating distances of every pair of points and comparing the distances to find the minimum. ![]() ![]() The algorithm divides the array in two halves, recursively sorts them and finally merges the two sorted halves.Ĥ - Closest Pair of Points: The problem is to find the closest pair of points in a set of points in x-y plane. Finally, the algorithm recursively sorts the subarrays on left and right of pivot element.ģ - Merge Sort is also a sorting algorithm. The algorithm picks a pivot element, rearranges the array elements in such a way that all elements smaller than the picked pivot element move to left side of pivot, and all greater elements move to right side. Otherwise, if x is less than the middle element, then the algorithm recurs for left side of middle element, else recurs for right side of middle element.Ģ - Quicksort is a sorting algorithm. If the values match, return the index of middle. In each step, the algorithm compares the input element x with the value of the middle element in array. Combine: Appropriately combine the answersįollowing are some standard algorithms that are Divide and Conquer algorithms:ġ - Binary Search is a searching algorithm.Conquer: Recursively solve these subproblems.Divide: Break the given problem into subproblems of same type.Private static double MIN_VAL = Double.A very popular algorithmic paradigm, a typical Divide and Conquer algorithm solves a problem using following three steps: Output : Pair of points which are closer in the plane Example Dry Run Step 5: Finally the minimum is minimum of leftMin, rightMin and minFromStrip Step 4: Create a strip of coordinates from py array whose distance is less than min, and compute minValue from strip of coordinates which is calles minFromStrip Step 3: Recursively compute smallest distance from both left and right sub arrays leftMin and rightMin and then compute minimum of LeftMin and right which is called min. Step 2: Divide px array into two halves, The first subarray containts from px to px and second array contains from px to p Step 1: Find middle point of the px using (low+high)/2 Initialize low to 0 and high to n-1 (where n is length of the array) Step 0: Create an sorted array px which is sorted array of original array by x coordinate.Ĭreate a sorted array py which is sorted array of original array by y coordinate. So shortest distance is 1.4142135623730951Īlgorithm Input : Array of points represented using x and y coordinates Problem Statement Problem Description : Given n points in the plane, find smallest euclidean distance between them.ġ) Points are given by their x and y coordinates.Ģ) Euclidean distance between two points p1 = (x1, y1) and p2 = (x2, y2) is expressed as d(A, B) = √( (x1-x2) 2 + (y1-y2) 2 ) Constraints:ĭistance between (2, 3) and (5, 1) is 3.605551275463989ĭistance between (2, 3) and (12, 30) is 28.792360097775937ĭistance between (5, 1) and (12, 30) is 29.832867780352597
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