Mark loves to move fast. So he made a spaceship that works in 4-dimensional space. He wants to use the spaceship to complete missions as fast as possible. In each mission, the spaceship starts at (0, 0, 0, 0) and needs to end up at (a, b, c, d). To do this, he instructs the spaceship's computer to execute a series of moves, where each move is a unit step in one of the eight cardinal directions: (+1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1,0), (0, 0, 0, +1). Unfortunately, he also moved fast when building the spaceship, so there is a bug in the spaceship's code. The first move will be executed once, the second move will be executed twice, the third move will be executed thrice, and so on. In general, the i-th move will be executed ¿ times. For any four integers a, b, c, d, let f(a, b, c, d) be the minimum number of moves of a mission that ends up at (a, b, c, d). Compute the sum of f(a, b, c, d) over all points (with integer coordinates) such that -A < a < A-B < b

Mark loves to move fast. So he made a spaceship that works in 4-dimensional space. He wants to use the spaceship to complete missions as fast as possible. In each mission, the spaceship starts at (0, 0, 0, 0) and needs to end up at (a, b, c, d). To do this, he instructs the spaceship's computer to execute a series of moves, where each move is a unit step in one of the eight cardinal directions: (+1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1,0), (0, 0, 0, +1). Unfortunately, he also moved fast when building the spaceship, so there is a bug in the spaceship's code. The first move will be executed once, the second move will be executed twice, the third move will be executed thrice, and so on. In general, the i-th move will be executed ¿ times. For any four integers a, b, c, d, let f(a, b, c, d) be the minimum number of moves of a mission that ends up at (a, b, c, d). Compute the sum of f(a, b, c, d) over all points (with integer coordinates) such that -A < a < A-B < b

Programming Logic & Design Comprehensive

9th Edition

ISBN:9781337669405

Author:FARRELL

Publisher:FARRELL

Chapter2: Elements Of High-quality Programs

Section: Chapter Questions

Problem 1GZ

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