Priority queues and heaps

A priority queue is basically a type of queue that will always return items in order of priority. This priority could be, for example, that the lowest item is always popped off first. Although it is called a queue, priority queues are often implemented using a heap, since it is very efficient for this purpose.

Consider that, in a store, customers queue in a line where service is only rendered at the front of the queue. Each customer will spend some time in the queue to get served. If the waiting times for the customers in the queue are 4, 30, 2, and 1, then the average time spent in the queue becomes (4 + 34 + 36 + 37)/4, which is 27.75. However, if we change the order of service such that customers with the least amount of waiting time are served first, then we obtain a different average waiting time. In doing so, we calculate our new average waiting time by (1 + 3 + 7 + 37)/4, which now equals 12, a better average waiting time. Clearly, there is merit to serving...