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A matrix is a 2-dimensional array. To access an element of a matrix, you look at a row position and a column position. (Ex. matrix[i][j] )
Matrices are useful data structures, but representing elements with two distinct keys (i, j) makes it trickier for using certain algorithms together with matrices. Being able to represent a position in a matrix with one value would be useful for situations like:
Encoding Matrix Positions
It's possible to encode a position (i,j) in a matrix into a single value. We can do this because we know the number of columns in the matrix, and can basically think of each cell in the matrix as a number, incrementing while going left to right, continuing for each row (like reading a book).
Encoding a position (i,J) into an encoded value h can be done by multiplying i by the number of columns and adding j.
h = i * num_cols + j
Decoding an encoded value can be done by dividing/modulusing the value h by the number of columns.
i = h / num_cols
j = h % num_cols
We can write some code to test this out.
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