Proficiency Assignment: Network Flow in a Tree

$($not a programming problem$)$

Topic: Network Flow.

Design and describe an algorithm to calculate the maximum flow through a tree, with a specified root as the source and all of its leaves as valid sinks$.($That is$,$ units of flow can "stop" at any leaf.$)$

Show that your algorithm is correct, and show its runtime.

Hint: This is a flow problem, not a pathfinding problem. So if your solution consists of a single path, back up and review the textbook material on network flow problems!

Once you have written and submitted your solution via Canvas, schedule a $10$ minute meeting with me to present it$.$

I will ask you about:

$-$ How your algorithm works $($in enough detail that I could follow it on a new tree$)$

$-$ Your algorithm's runtime