Consider the square grid networks with n=px p vertices and the edges directed to the right and downwards. The top- left vertex is the source vertex and the bottom-right vertex is the sink vertex. The edge capacities may be any non- negative numbers. The number of edges is m = 2p(p-1) = O(n). (There are 2p rows/columns of edges and each row/column has p-1 edges.) An example of such a network is given below. S. Complete the sentences below using the provided choices. (a) For each such grid network, the paths in this network from s to t (counted as the number of edges). (b) For each such grid network and for a flow in this network, the augmenting paths in the residual network (counted as the number of edges). (c) For such square grid networks, it happen that an augmenting path in a residual network has length (n) (exactly of the order of n). have the same length may have different lengths may cannot Consider the square grid networks with n=px p vertices and the edges directed to the right and downwards. The top- left vertex is the source vertex and the bottom-right vertex is the sink vertex. The edge capacities may be any non- negative numbers. The number of edges is m = 2p(p-1) = O(n). (There are 2p rows/columns of edges and each row/column has p-1 edges.) An example of such a network is given below. S. Complete the sentences below using the provided choices. (a) For each such grid network, the paths in this network from s to t (counted as the number of edges). (b) For each such grid network and for a flow in this network, the augmenting paths in the residual network (counted as the number of edges). (c) For such square grid networks, it happen that an augmenting path in a residual network has length (n) (exactly of the order of n). have the same length may have different lengths may cannot