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pp:tailend [2016/05/05 17:43] vrares [Fibonacci sequence] |
pp:tailend [2016/05/05 18:46] (current) vrares [Fibonacci sequence] |
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| ===== Fibonacci sequence ===== | ===== Fibonacci sequence ===== | ||
| - | Let us consider the following code: | + | Let us consider the following recursive function that computes the n-th Fibonacci number: |
| <code> | <code> | ||
| int fibo (int n) { | int fibo (int n) { | ||
| Line 11: | Line 12: | ||
| return n; | return n; | ||
| } | } | ||
| - | return f(n-1) + f(n-2); | + | return fibo(n-1) + fibo(n-2); |
| } | } | ||
| </code> | </code> | ||
| + | |||
| + | The code works well and behaves as expected, but let us discuss the above function in terms of efficiency. The function calls are shown below: | ||
| + | |||
| + | <code> | ||
| + | fibo(4) //ninth evaluation, fibo(4) = fibo(3) + fibo(2) = 2 + 1 = 3 | ||
| + | | | ||
| + | +->fibo(3) //fifth evaluation, fibo(3) = fibo(2) + fibo(1) = 1 + 1 = 2 | ||
| + | | | | ||
| + | | +->fibo(2) //third evaluation, fibo(2) = fibo(1) + fibo(0) = 1 + 0 = 1 | ||
| + | | | | | ||
| + | | | +->fibo(1) //first evaluation, fibo(1) = 1 | ||
| + | | | | | ||
| + | | | +->fibo(0) //second evaluation, fibo(0) = 0 | ||
| + | | | | ||
| + | | +->fibo(1) //fourth evaluation, fibo(1) = 1 | ||
| + | | | ||
| + | +->fibo(2) //eighth evaluation, fibo(2) = fibo(1) + fibo(0) = 1 + 0 = 1 | ||
| + | | | ||
| + | +->fibo(1) //sixth evaluation, fibo(1) = 1 | ||
| + | | | ||
| + | +->fibo(0) //seventh evaluation, fibo(0) = 0 | ||
| + | </code> | ||
| + | |||
| + | <stack diagram to be inserted here> | ||
| + | <work in progress> | ||