Match the following algorithm with its time complexity recurrence equation.

Algorithms:

Algorithm A: Binary Search

Algorithm B: Merge Sort

Algorithm C: Quick Sort

Algorithm D: Tower of Hanoi

Recurrence equation:

equation #$1$: T$($n$)=2$T$($n$-1)+$ O$(1)$

equation #$2$: T$($n$)=$ T$($n$/2)+$ O$(1)$

equation #$3$: T$($n$)=2$T$($n$/2)+$ O$($n$)$

equation #$4$: T$($n$)=$ T$($n$-$k$)+$ T$($k$)+$ O$($n$)$