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Explanation:
Algorithm for solving flood condition:
We suggest an algorithm to resolve the flood condition by creating a flow network graph.
Let us assume for every patient "p" there is a node "2" and for every hospital "h" there is a node "uh" and there is an edge ()T, uh) exist between patient "p" and hospital "h" with flow capacity of 1 iff patient "p" is reachable to hospital "h" within a half-hour.
Then source node "s" is made between all the patient-nodes by an edge with flow capacity of 1 and then the sink "t" is made by linking all the hospital nodes by an edge with capacity "[n/k]".
There is an approach to send patients to hospitals: when there is a source "s" to sink "t" flow of "n". We can send 1 flow-unit from source "s" to sink "t" along the paths (s, yp, uh, t) whenever a probable approach is available to send patients.
This approach of sending patients to hospitals doesn't break the capacity limitation of edges. Hence we can send patient "p" to hospital "h" with 1 flow- unit if edge(m uh) permits at least 1 flow- unit.
The running-time of this algorithm is found by finding the time needed to solve max-flow graph with nodes O(n+k) and edges O() edges.