https://rkilingar.me/categories/algo/ds/ Recent content in Algo/DS on RaviKiran Kilingar https://rkilingar.me/%3Clink%20or%20path%20of%20image%20for%20opengraph,%20twitter-cards%3E https://rkilingar.me/%3Clink%20or%20path%20of%20image%20for%20opengraph,%20twitter-cards%3E Hugo -- gohugo.io https://rkilingar.me/posts/taxicab-geometry/ Sat, 29 Jan 2022 10:07:30 +0530 https://rkilingar.me/posts/taxicab-geometry/ Problem Given two points $P_1$ & $P_2$ in a grid, and you need to reach from one of the cells to the other, Allowed moves will be up, down, left and right. What is the minimum steps required to reach the destination? TaxiCab Geometry and Manhattan Distance Going by euclidean geometry in a 2D surface, distance between any given two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $d = \sqrt{(y_2^{2}-y_1^{2})-(x_2^2-x_1^2)}$ This is the straight line distance drawn as a diagonal between the two points.