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For binary strings a and b the Hamming distance is equal to the number of ones (population count) in a XOR b. [3] The metric space of length-n binary strings, with the Hamming distance, is known as the Hamming cube; it is equivalent as a metric space to the set of distances between vertices in a hypercube graph.
A = round (rand (3, 4, 5) * 10) % 3x4x5 three-dimensional or cubic array > A (:,:, 3) % 3x4 two-dimensional array along first and second dimensions ans = 8 3 5 7 8 9 1 4 4 4 2 5 > A (:, 2: 3, 3) % 3x2 two-dimensional array along first and second dimensions ans = 3 5 9 1 4 2 > A (2: end,:, 3) % 2x4 two-dimensional array using the 'end' keyword ...
Another somewhat contrived special case of this is string concatenation of a list of strings. In C, for example, the cost of concatenating two strings of length m and n using strcat is O(m + n), since we need O(m) time to find the end of the first string and O(n) time to copy the second string onto the end of it. Using this cost function, we ...
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
As mentioned above, rows 1, 2, and 4 of G should look familiar as they map the data bits to their parity bits: p 1 covers d 1, d 2, d 4; p 2 covers d 1, d 3, d 4; p 3 covers d 2, d 3, d 4; The remaining rows (3, 5, 6, 7) map the data to their position in encoded form and there is only 1 in that row so it is an identical copy.
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
This has the convenient implication for 2 × 2 and 3 × 3 rotation matrices that the trace reveals the angle of rotation, θ, in the two-dimensional space (or subspace). For a 2 × 2 matrix the trace is 2 cos θ, and for a 3 × 3 matrix it is 1 + 2 cos θ. In the three-dimensional case, the subspace consists of all vectors perpendicular to the ...