Match the algorithms with their time complexities:

Let us match each algorithm to its time complexity:

• (P) Towers of Hanoi with $n$ disks: The recurrence relation for Towers of Hanoi is $T(n) = 2T(n-1) + 1$, which gives $T(n) = 2^n - 1 = \Theta(2^n)$. Thus, P $\rightarrow$ (iii).

• (Q) Binary search given $n$ sorted numbers: Binary search divides the search space in half at each step, yielding a recurrence $T(n) = T(n/2) + O(1)$, so the time complexity is $\Theta(\log n)$. Thus, Q $\rightarrow$ (iv).

• (R) Heap sort given $n$ numbers at the worst case: Heap sort takes $O(n)$ to build the heap and performs $n$ extractions each taking $O(\log n)$, leading to a worst-case time complexity of $\Theta(n \log n)$. Thus, R $\rightarrow$ (ii).

• (S) Addition of two $n \times n$ matrices: Adding two matrices of size $n \times n$ requires performing element-wise addition for all $n^2$ elements, giving a time complexity of $\Theta(n^2)$. Thus, S $\rightarrow$ (i).

Matching combination: P $\rightarrow$ (iii), Q $\rightarrow$ (iv), R $\rightarrow$ (ii), S $\rightarrow$ (i), which corresponds to option C.