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 are positive integers.
for to m
for to k
for to j
[Statements in the body of the inner loop, none containing branching statements that lead outside loop]
To find the number of times that the 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 and similarly .
Observe that there is one iteration of the inner most loop for each column and there is one column of the table for each quadruples of integers .
The total number of quadruples is same as combinations with repetition allowed that can be formed from a set of elements
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