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This lab will focus on populating and traversing a two-dimensional array (matrix). Consider a 3 by 3 square containing values Vị to V9 as shown below; conveniently, these values can be represented using a matrix (two-dimensional array). Vi V2 V3 V4 Vs V6 V7 Ve V9 A square is said to be row semi-magic if the values in each of the rows sum to the same value: (Vi + V2 + V3 = V4 + Vs + V6 = V7 + Ve + V9). A square is said to be column semi-magic if the values in each of the columns sum to the same value: (Vi + V4 + V7 = V2 + Vs + Ve = V3 + V6 + V9). A matrix is said to be magic if the matrix is semi-magic in terms of its rows and its columns. Complete the three corresponding methods that determine if the given matrix is column semi-magic, row semi- magic, and magic. You may not assume the input matrix has a particular number of sides. As a positive test example, use the following magic matrix. We verify that the matrix is magic by noting that 1 + 5 + 9 = 159 8 34 6 72 8 + 3 + 4 = 6 + 7 + 2 - 15 = 1 + 8 + 6 = 5 + 3 + 7 - 9 + 4 + 2 Implement a Matrix class with a matrix as an attribute and the necessary methods. The constructor should throw an exception if the input matrix is not square. Also implement a Tester class that constructs and initializes a Matrix object and tests whether the matrix is magic.

This lab will focus on populating and traversing a two-dimensional array (matrix). Consider a 3 by 3 square containing values Vị to V9 as shown below; conveniently, these values can be represented using a matrix (two-dimensional array). Vi V2 V3 V4 Vs V6 V7 Ve V9 A square is said to be row semi-magic if the values in each of the rows sum to the same value: (Vi + V2 + V3 = V4 + Vs + V6 = V7 + Ve + V9). A square is said to be column semi-magic if the values in each of the columns sum to the same value: (Vi + V4 + V7 = V2 + Vs + Ve = V3 + V6 + V9). A matrix is said to be magic if the matrix is semi-magic in terms of its rows and its columns. Complete the three corresponding methods that determine if the given matrix is column semi-magic, row semi- magic, and magic. You may not assume the input matrix has a particular number of sides. As a positive test example, use the following magic matrix. We verify that the matrix is magic by noting that 1 + 5 + 9 = 159 8 34 6 72 8 + 3 + 4 = 6 + 7 + 2 - 15 = 1 + 8 + 6 = 5 + 3 + 7 - 9 + 4 + 2 Implement a Matrix class with a matrix as an attribute and the necessary methods. The constructor should throw an exception if the input matrix is not square. Also implement a Tester class that constructs and initializes a Matrix object and tests whether the matrix is magic.

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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**CS101: Lab #17 - Arrays Part II** This lab will focus on populating and traversing a two-dimensional array (matrix). Consider a 3 by 3 square containing values \( V_1 \) to \( V_9 \) as shown below; conveniently, these values can be represented using a matrix (two-dimensional array). ``` | V1 | V2 | V3 | |----|----|----| | V4 | V5 | V6 | | V7 | V8 | V9 | ``` A square is said to be **row semi-magic** if the values in each of the rows sum to the same value: \[ (V_1 + V_2 + V_3 = V_4 + V_5 + V_6 = V_7 + V_8 + V_9) \] A square is said to be **column semi-magic** if the values in each of the columns sum to the same value: \[ (V_1 + V_4 + V_7 = V_2 + V_5 + V_8 = V_3 + V_6 + V_9) \] A matrix is said to be **magic** if the matrix is semi-magic in terms of its rows and its columns. Complete the three corresponding methods that determine if the given matrix is column semi-magic, row semi-magic, and magic. **You may not assume the input matrix has a particular number of sides.** As a positive test example, use the following magic matrix. ``` | 1 | 5 | 9 | | 8 | 3 | 4 | | 6 | 7 | 2 | ``` We verify that the matrix is magic by noting that: - \( 1 + 5 + 9 = 15 \) - \( 8 + 3 + 4 = 15 \) - \( 6 + 7 + 2 = 15 \) And for columns: - \( 1 + 8 + 6 = 15 \) - \( 5 + 3 + 7 = 15 \) - \( 9 + 4 + 2 = 15 \) **Implementation Tasks:** 1. Implement a `Matrix` class with a matrix as an attribute and the necessary methods. The constructor should throw an exception if the input matrix is not square. 2
Transcribed Image Text:**CS101: Lab #17 - Arrays Part II** This lab will focus on populating and traversing a two-dimensional array (matrix). Consider a 3 by 3 square containing values \( V_1 \) to \( V_9 \) as shown below; conveniently, these values can be represented using a matrix (two-dimensional array). ``` | V1 | V2 | V3 | |----|----|----| | V4 | V5 | V6 | | V7 | V8 | V9 | ``` A square is said to be **row semi-magic** if the values in each of the rows sum to the same value: \[ (V_1 + V_2 + V_3 = V_4 + V_5 + V_6 = V_7 + V_8 + V_9) \] A square is said to be **column semi-magic** if the values in each of the columns sum to the same value: \[ (V_1 + V_4 + V_7 = V_2 + V_5 + V_8 = V_3 + V_6 + V_9) \] A matrix is said to be **magic** if the matrix is semi-magic in terms of its rows and its columns. Complete the three corresponding methods that determine if the given matrix is column semi-magic, row semi-magic, and magic. **You may not assume the input matrix has a particular number of sides.** As a positive test example, use the following magic matrix. ``` | 1 | 5 | 9 | | 8 | 3 | 4 | | 6 | 7 | 2 | ``` We verify that the matrix is magic by noting that: - \( 1 + 5 + 9 = 15 \) - \( 8 + 3 + 4 = 15 \) - \( 6 + 7 + 2 = 15 \) And for columns: - \( 1 + 8 + 6 = 15 \) - \( 5 + 3 + 7 = 15 \) - \( 9 + 4 + 2 = 15 \) **Implementation Tasks:** 1. Implement a `Matrix` class with a matrix as an attribute and the necessary methods. The constructor should throw an exception if the input matrix is not square. 2
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