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A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide (frequently flat) pieces along certain routes (usually on a board) to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a ...
Hacker's Delight is a software algorithm book by Henry S. Warren, Jr. first published in 2002. It presents fast bit-level and low-level arithmetic algorithms for common tasks such as counting bits or improving speed of division by using multiplication.
Named after the number of tiles in the frame, the 15 puzzle may also be called a "16 puzzle", alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle, which has 8 tiles in a 3×3 frame. The n puzzle is a classical problem for modeling algorithms involving heuristics.
The puzzle, unlit. The puzzle is based around a 3x3 grid of translucent panels, each panel being illuminated from below with red and blue LEDs. The bank of panels is mounted on a central spring-loaded pivot that can both slide a short distance in each of the four cardinal directions, as well as rotate or yaw slightly around the pivot.
A final two chapters provide brief hints and more detailed solutions to the puzzles, [2] with the solutions forming the majority of pages of the book. [3] Some of the puzzles are well known classics, some are variations of known puzzles making them more algorithmic, and some are new. [4] They include:
This slide rule is positioned to yield several values: From C scale to D scale (multiply by 2), from D scale to C scale (divide by 2), A and B scales (multiply and divide by 4), A and D scales (squares and square roots). In addition to the logarithmic scales, some slide rules have other mathematical functions encoded on other auxiliary scales.
⌈ x/3 ⌉ = ⌈ x′/3 ⌉ and ⌈ y/3 ⌉ = ⌈ y′/3 ⌉ (same 3×3 cell) The puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them. A Sudoku solution grid is also a Latin square. [9]
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.