blob: 20f7769e08bf91641560135b327550181a9dcfc8 (
plain) (
blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
|
#include <iostream>
#include <string>
#include <vector>
const double RATIO_THRESHOLD = 0.000001;
const unsigned int DISPLAY_ITERATIONS = 20;
/*
@param series: unsigned int, the n-bonacci series "degree" (2 -> fib, 3 -> trib)
@param n: unsigned int, the term to find
@return long: the nth term of the series-degree n-bonacci series
*/
long nbonacci(unsigned int series, unsigned int n)
{
if (n <= series)
return 1;
long sum = 0;
for (unsigned int i = 1; i <= series; ++i)
sum += nbonacci(series, n - i);
return sum;
}
/*
@param title: std::string, the name of the series
@param series: unsigned int, the degree of the n-bonacci series
@return void: print the ratio of the series to stdout
*/
void computeNbonacciRatio(std::string title, unsigned int series)
{
unsigned int i = series+1;
long prev = 1;
long curr = nbonacci(series, i); // The first series numbers are one's
double currRatio = static_cast<double>(curr) / static_cast<double>(prev);
double prevRatio;
do
{
prevRatio = currRatio;
prev = curr;
curr = nbonacci(series, ++i);
currRatio = static_cast<double>(curr) / static_cast<double>(prev);
} while (std::abs(currRatio - prevRatio) > RATIO_THRESHOLD);
// i-1 because the nth number in the sequence corresponds with the (n-1)'th iteration
std::cout << title << " ratio approches " << currRatio << " after " << i-1 << " iterations." << std::endl;
}
int main()
{
std::vector<std::string> names;
names.push_back("Fibonacci");
names.push_back("Tribonacci");
names.push_back("Fourbonacci");
names.push_back("Fivebonacci");
unsigned int i;
for (i = 0; i < names.size(); i++)
{
std::cout << "--- " << names.at(i) << " ---" << std::endl;
for (unsigned int n = 1; n < i+2; n++)
std::cout << "1 ";
for (unsigned int n = i+2; n <= DISPLAY_ITERATIONS; n++)
std::cout << nbonacci(i+2, n) << " ";
std::cout << std::endl;
}
std::cout << std::endl;
for (i = 0; i < names.size(); i++)
computeNbonacciRatio(names.at(i), i+2);
return 0;
}
|
