A hospital is attempting to schedule their doctors for night shifts over the next n nights. There are d doctors. Each doctor specifies a set of nights they are available for the night shift; let S_i denote the set of nights that the i^th doctor is available, 1≤i≤d. The hospital has determined its exact need for each night; for the j^th night, 1≤j≤n, the hospital needs exactly p_j doctors to do the night shift. There is one further constraint. To be fair, the hospital does not want any doctor to do more than k night shifts. Give a network flow algorithm to determine an assignment of the d doctors to the n nights so that all relevant constraints are met, that is, every night that the i^th doctor is assigned to is in S_i ; exactly p_j doctors are assigned on night j; and no doctor is assigned to more than k nights. If no such assignment is possible, then your algorithm should indicate so. Provide running time analysis.