Translate a large computer game consisting of n program units. We have a directed acyclic graph G$=($V$,$E$)$ describing how units depend on each other. Nodes in the graph correspond to program units, and an edge from v to w indicates that v must be translated before w can begin translation. It takes exactly one minute to translate each unit. We want to translate the computer game in the shortest time possible, and to do so$,$ we can use a cloud service to translate as many units as we want simultaneously, as long as we consider how units are dependent on each other.

Present an efficient algorithm that runs in linear time to determine the minimum possible time to translate the computer game.

Guidelines: In this problem you should solve the task by transferring it into "classical" network task. Describe the network G $=($V$,$ E$)$ that "encodes" the original task, which $($classical$)$ network algorithm is used, and how the solution to the original task is found subsequently. Use the following framework:

i$)$ What do the nodes in the network represent and how many are there?

ii$)$ What do the edges represent and how many are there?

iii$)$ What property of the network corresponds to the original task?

iv$)$ Which network algorithm should be executed?

v$)$ What is the time complexity in terms of the size of the original task? Here, consider the time it takes to construct the network, execute the network algorithm, and $($if necessary$)$ transfer the solution to the original task.