What is the worst-case space complexity of storing a Sparse Matrix with K non-zero elements using the Coordinate Format (COO / Triplet representation)?
COO represents a sparse matrix using 3 arrays of length K (row index, column index, value), consuming O(K) space instead of O(M*N).
How many total elements are present in a Tridiagonal Matrix of size N x N?
A Tridiagonal matrix has non-zero elements only on the main diagonal (N elements), the superdiagonal (N-1 elements), and the subdiagonal (N-1 elements), totaling N + (N-1) + (N-1) = 3N - 2.
According to Big O notation properties, what is the asymptotic simplification of the function f(n) = 5n^3 + 100n^2 + 5000?
In asymptotic analysis, constant coefficients are dropped and only the highest-order dominant term determines growth rate: O($n^3)$.
Which statements correctly characterize little-o notation f(n) = o(g(n))?
Little-o means the ratio tends to zero, so f grows strictly slower than g. A function that is o(g) is also O(g). Hence all three statements are correct.
In little-o notation (o), what does f(n) = o(g(n)) mathematically signify?
Little-o notation denotes a strict upper bound where f(n) grows strictly slower than g(n) as n approaches infinity (lim f(n)/g(n) = 0).