$[$ TRUE$/$FALSE $]$

Let T be a complete binary tree with n nodes. Finding a path from the root of T to a

given vertex v in T using breadth$-$first search takes O$($log n$).$

$[$ TRUE$/$FALSE $]$

A binary max heap can be converted to a binary min heap in O$($n$)$ time.

$[$ TRUE$/$FALSE $]$

The runtime complexity of merge sort can be improved asymptotically by recursively

splitting the array into three parts rather than two parts.

$[$ TRUE$/$FALSE $]$

A graph G with non$-$unique edge weights can have a unique minimum spanning tree.

$[$ TRUE$/$FALSE $]$

A Fibonacci Heap extract$-$min operation has a worst case runtime of O$($log n$)$

$[$ TRUE$/$FALSE $]$

Prim's algorithm can be used to find the minimum spanning tree of a graph with negative

edge weights.

$[$ TRUE$/$FALSE $]$

When using the accounting method, if a sequence of n operations involves different

operations, it is possible for all operations to end up with the same amortized cost even if

their worst case costs are different.

$[$ TRUE$/$FALSE $]$

For the recurrence relation T$($n$)=2$T$($n$/4)+$n$,$ the time complexity is $\backslash$theta $($n log n$)$

$[$ TRUE$/$FALSE $]$

Every directed acyclic graph $($DAG$)$ has a unique topological ordering of its vertices.

$[$ TRUE$/$FALSE $]$

If all edge weights in a connected, undirected graph are distinct, the heaviest edge in the

graph cannot be part of any minimum spanning tree.