In 8 and 9, how many times will the innermost loop be iterated when the algorithm segment is implemented and run? Assume n,m,k and j positive integers.
To find the number of times that innermost loop be iterated when the algorithm segment is implemented and run. Assume are positive integers.
Construct a trace table for the values of for which the statement in the body of the inner most loop are executed.
Observe that goes from . It is always the case that . Similarly, because goes from , it is always the case that .
Observe that there is one iteration of the inner most loop for each column and there is one column of the table for each triples of integers .
The total number of triples is same as combinations with repetition allowed that can be formed from a set of elements
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