1. Advanced Data Structure using C++

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MATRIX:‐ LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) SPARSE MATRIX An m*n (pronounced as m by n) matrix is a two‐dimensional array whose m.n elements are arranged in m rows and n columns. A matrix is denoted by capital letters such as A, B, C,….., and its elements are denoted by corresponding lower letters suffixed with row index and column index such as aij.,bij.,cij.,…..,respectively. Entries of a matrix are often denoted by a variable with two subscripts, as shown:‐ Example:‐ Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 120 ‐
LECTURE NOTES OF ADVANCED DATA STRUCTURE (MT-CSE 110) is a 4*4 matrix. An alternative notation uses large parenthesis instead of box brackets as shown:‐ Matrices are often used to organize data for business and scientific applications. It has been proved that many scientific & engg. Problems can be solved efficiently if they are expressed <strong>using</strong> matrices. NOTATIONS OF MATRIX:‐ The horizontal lines in a matrix are called rows and the vertical lines are called columns. A matrix with m rows and n columns is called an m‐by‐n matrix (or m×n matrix) and m and n are called its dimensions. We write to define an m × n matrix A with each entry in the matrix called aij for all 1 ≤ i ≤ m and 1 ≤ j ≤ n. In the above example, the element A [2, 3] or a23 =7. Some programming languages start the numbering of rows and columns at zero, in which case the entries of an m‐by‐n matrix are indexed by 0 ≤ i ≤ m − 1 and 0 ≤ j ≤ n − <strong>1.</strong> Prepared By : Er. Harvinder Singh Assist Prof., CSE, H.C.T.M (Kaithal) Page ‐ 121 ‐
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