Two alternate packages A and B are available for processing a database having 10^k records. Package A requires 0.0001n² time units and package B requires $$10n.\log _{10}^n$$ time units to process n records. What is the smallest value of k for which package B will be preferred over A?

Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. $$$w = \left( {\matrix{ 0 & 1 & 8 & 1 & 4 \cr 1 & 0 & {12} & 4 & 9 \cr 8 & {12} & 0 & 7 & 3 \cr 1 & 4 & 7 & 0 & 2 \cr 4 & 9 & 3 & 2 & 0 \cr } } \right)$$$ What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T?

Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. $$$w = \left( {\matrix{ 0 & 1 & 8 & 1 & 4 \cr 1 & 0 & {12} & 4 & 9 \cr 8 & {12} & 0 & 7 & 3 \cr 1 & 4 & 7 & 0 & 2 \cr 4 & 9 & 3 & 2 & 0 \cr } } \right)$$$ What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?

Which data structure in a compiler is used for managing information about variables and their attributes?