a$.$ Implement the Shortest Augmenting Path algorithm to find the maximum flow from s to t$.$ Show the iterations.

b$.$ Implement the Push Relabel algorithm to the same problem. In the algorithm when there are more than one active nodes, pick the node with the largest label. List all the push and relabel operations.

c$.$ Find a minimum capacity cut starting from the flow in part a or b$.$ What is the complexity of finding a min cut after finding the max flow?