Question

Recursive definition for factorial: a0 = 1, an = n * an-1

procedure factorial(n: nonnegative integer)

if n = 0 then return 1

else return n * factorial( n - 1 )

Trace the execution of the factorial algorithm described above for input 7. Track the number of times factorial is invoked (with the first invocation with input 7 as invocation 0) and the value returned by each invocation.

Answer 1

`Hey,

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TRACE

factorial(7) returns 7 * factorial(6)

factorial(6) returns 6 * factorial(5)

factorial(5) returns 5 * factorial(4)
factorial(4) returns 4 * factorial(3)
factorial(3) returns 3 * factorial(2)
factorial(2) returns 2 * factorial(1)
factorial(1) returns 1 * factorial(0)
factorial(0) returns 1

Once factorial(0) executes and returns 1 that value can be substituted back into the previous method call, starting at the top of the stack (shown at the bottom here) and working our way back to the bottom of the stack (shown at the top here).

factorial(7) returns 7 * factorial(6) = 7 * 720 = 5040

factorial(6) returns 6 * factorial(5) = 6 * 120= 720

factorial(5) returns 5 * factorial(4) = 5 * 24 = 120
factorial(4) returns 4 * factorial(3) = 4 * 6 = 24
factorial(3) returns 3 * factorial(2) = 2 so 3 * 2 = 6
factorial(2) returns 2 * factorial(1) = 1 so 2 * 1 = 2
factorial(1) returns 1 * factorial(0) = 1 so 1 * 1 = 1
factorial(0) returns 1

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