Describe an array of size n = 32 such that if it is the initial input to HeapSort in the order presented, no other permutation of the input will cause the algorithm to use more comparisons to sort the array. Explain why it does this. You do not (and should not) write out the entire array, but rather describe the order. You may wish to split your explanation for why so many comparisons happen into phases (heapify and then extract-Min phases).

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[a] create a class called “cycle” which has two instance integer variables as properties, “numberofwheels” and “weight.” create a constructor with two parameters, using the same variable names in the parameter list. assign each variable to numberofwheels” and “weight” respectively. write a separate application to test the class and display its properties. note: do not change the names of the instance variables or the variables listed in the constructor’s parameter list. [b] edit your class cycle by adding a default constructor which will assign the default values of 100 to represent the numberofwheels, and 1000 to represent the weight, by invoking a call to the other constructor. modify your application created in [a] to test the class.

All of the following are characteristics that must be contained in any knowledge representation scheme except