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Problem Description: You are standing on a unique diamond-shaped platform composed of 5 tiles. These tiles are positioned at coordinates: (-1,0), (0,-1), (0,0), (0,1), and (1,0). From a starting position (xs,ys), you make random moves in one of four directions: left (decrease x by 1), right (increase x by 1), up (increase y by 1), or down (decrease y by 1). Each direction has the same probability and the direction of each move is entirely independent of previous moves. Determine the probability that you can reach a given destination (xe,ye) without stepping off the diamond platform. Constraints: (xs, ys) must be one of: (-1,0), (0,-1), (0,0), (0,1), (1,0) (xe, ye) must also be one of the above coordinates. Starting and ending coordinates are distinct: xs != xe or ys != ye Input: A single line containing four integers, denoting xs, ys, xe, ye respectively. Output: A single line showing the probability that you'll reach the destination before stepping off the platform. Sample input: -1 0 0 0 Sample Output: 0.25 Explanation: From the starting position, you have a 25% chance of moving right (and thus reaching the destination). Any other move would result in falling off the platform. [execution time limit] 4 seconds (py3) [memory limit] 1 GB [input] integer xs The x-coordinate of the starting position. [input] integer ys The y-coordinate of the starting position. [input] integer xe The x-coordinate of the end position. [input] integer ye The y-coordinate of the end position. [output] float Probability to reach end position before falling of platform.
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Senior Data Scientist

Interviewed at Agoda

3.9★
Oct 19, 2023

Problem Description: You are standing on a unique diamond-shaped platform composed of 5 tiles. These tiles are positioned at coordinates: (-1,0), (0,-1), (0,0), (0,1), and (1,0). From a starting position (xs,ys), you make random moves in one of four directions: left (decrease x by 1), right (increase x by 1), up (increase y by 1), or down (decrease y by 1). Each direction has the same probability and the direction of each move is entirely independent of previous moves. Determine the probability that you can reach a given destination (xe,ye) without stepping off the diamond platform. Constraints: (xs, ys) must be one of: (-1,0), (0,-1), (0,0), (0,1), (1,0) (xe, ye) must also be one of the above coordinates. Starting and ending coordinates are distinct: xs != xe or ys != ye Input: A single line containing four integers, denoting xs, ys, xe, ye respectively. Output: A single line showing the probability that you'll reach the destination before stepping off the platform. Sample input: -1 0 0 0 Sample Output: 0.25 Explanation: From the starting position, you have a 25% chance of moving right (and thus reaching the destination). Any other move would result in falling off the platform. [execution time limit] 4 seconds (py3) [memory limit] 1 GB [input] integer xs The x-coordinate of the starting position. [input] integer ys The y-coordinate of the starting position. [input] integer xe The x-coordinate of the end position. [input] integer ye The y-coordinate of the end position. [output] float Probability to reach end position before falling of platform.

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