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Problem: N-Queens We would like to place n queens on an n x n chessboard, therefore no queen could ever take any of the other n queens. The brute-force algorithm has poor characteristics, so we want you to design a more efficient one. Input: you are given the size n such that n > 4 Output: return a 2D binary matrix whose dimension is n × n that represents the chessboard. A value of 1 means there is a queen in such position. Example: [o 1 0 0] 0 0 0 1 1 0 0 0 0 0 1 0 Requirements: i) develop a python function that implements your efficient, correct algorithm ii) empirically, test your function while varying the chessboard size, n, to have an intuition over the complexity of your algorithm. iii) show the complexity analysis of your algorithm, theoretically, from the perspective of space and time. iv) write a function to visualize your solution, graphically.

Problem: N-Queens We would like to place n queens on an n x n chessboard, therefore no queen could ever take any of the other n queens. The brute-force algorithm has poor characteristics, so we want you to design a more efficient one. Input: you are given the size n such that n > 4 Output: return a 2D binary matrix whose dimension is n × n that represents the chessboard. A value of 1 means there is a queen in such position. Example: [o 1 0 0] 0 0 0 1 1 0 0 0 0 0 1 0 Requirements: i) develop a python function that implements your efficient, correct algorithm ii) empirically, test your function while varying the chessboard size, n, to have an intuition over the complexity of your algorithm. iii) show the complexity analysis of your algorithm, theoretically, from the perspective of space and time. iv) write a function to visualize your solution, graphically.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Problem: N-Queens We would like to place n queens on an n x n chessboard, therefore no queen could ever take any of the other n queens. The brute-force algorithm has poor characteristics, so we want you to design a more efficient one. Input: you are given the size n such that n > 4 Output: return a 2D binary matrix whose dimension is n xn that represents the chessboard. A value of 1 means there is a queen in such position. Example: 0 1 0 0] 0 0 0 1 1 0 0 0 0 0 1 0 Requirements: i) develop a python function that implements your efficient, correct algorithm ii) empirically, test your function while varying the chessboard size, n, to have an intuition over the complexity of your algorithm. iii) show the complexity analysis of your algorithm, theoretically, from the perspective of space and time. iv) write a function to visualize your solution, graphically.
Transcribed Image Text:Problem: N-Queens We would like to place n queens on an n x n chessboard, therefore no queen could ever take any of the other n queens. The brute-force algorithm has poor characteristics, so we want you to design a more efficient one. Input: you are given the size n such that n > 4 Output: return a 2D binary matrix whose dimension is n xn that represents the chessboard. A value of 1 means there is a queen in such position. Example: 0 1 0 0] 0 0 0 1 1 0 0 0 0 0 1 0 Requirements: i) develop a python function that implements your efficient, correct algorithm ii) empirically, test your function while varying the chessboard size, n, to have an intuition over the complexity of your algorithm. iii) show the complexity analysis of your algorithm, theoretically, from the perspective of space and time. iv) write a function to visualize your solution, graphically.
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