Match the following:

List 1

(P) Prim’s algorithm for minimum spanning tree
(Q) Floyd-Warshall algorithm for all pairs shortest paths
(R) Mergesort
(S) Hamiltonian circuit

List 2

(i) Backtracking
(ii) Greedy method
(iii) Dynamic programming
(iv) Divide and conquer

Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n ( $$ \ge 2$$ ) numbers? In the recurrence equations given in the options below, c is a constant.

The least number of temporary variables required to create a three-address code in static single assignment form for the expression $$q + r / 3 + s - t * 5 + u * v/w$$ is _______________.

A variable x is said to be live at a statement $${S_i}$$ in a programif the following three conditions hold simultaneously:

i. There exists a statement $${S_j}$$ that uses x
ii. There is a path from $${S_i}$$ to $${S_j}$$ in the flow graph corresponding to the program
iii. The path has no intervening assignment to x including at $${S_i}$$ and $${S_j}$$

The variables which are live both at the statement in basic block 2 and at the statement in basic block 3 of the above control flow graph are