A fib about ecosystems....
Ecosystems are made of cheese......
What is fun (12)?
Yes. We are part of an ecosystem. Without an ecosystem we would, nothing would, be able to survive. Hope that answered your question for ya!!
desert ecosystem in western punjab in pakistan is called thal e.g bukhar, mianwali In Sindh the desert ecosystem is called thar e.g khanpur,yazman
The non-living parts of an ecosystem are abiotic.
The coldeest land ecosystem is Tundra.
All living and non-living things in a given area that interact with one other, make up an ecosystem. The non-living part of an ecosystem includes water, rocks, air, light, and soil.
A recursive formula is one that references itself. The famous example is the Fibonacci function: fib(n) := fib(n-1) + fib(n-2), with the terminating proviso that fib(0) = 0 and fib(1) = 1.
Because the same calculations are done over and over again. Fib(n) - the nth. number in the sequence - is equal to fib(n-1) + fib(n-2). For example, fib(10) - the 10th. number in the sequence - is equal to fib(9) + fib(8). If you expand this, you get fib(8) + fib(7) + fib(7) + fib(6). If you expand again, you get fib(7) + fib(6) + fib(6) + fib(5) + fib(6) + fib(5) + fib(5) + fib(4). You can already see that some of the numbers have to be evaluated several times. In fact, the amount of calculations increases exponentially; whereas with a simple loop, to add numbers up to fib(n), this is not the case.
You don't actually need a program to prove this. Fib[n] is the sum of Fib[n-1] and Fib[n-2]. it therefore follows that Fib[n-2] must be the sum of Fib[n-3] and Fib[n-4]. That being the case, it stands to reason that Fib[n] must be the sum of Fib[n-1], Fib[n-3] and Fib[n-4]. The "not necessarily different" part of the problem is only required to cater for the first part of the sequence where either Fib[n-1], Fib[n-3] or Fib[n-4] do not exist. E.g.,: 0 = 0+0+0 1 = 1+0+0 2 = 1+1+0 or 2+0+0 3 = 1+1+1 or 2+1+0 or 3+0+0 5 = 2+2+1 or 3+1+1 or 3+2+0 or 5+0+0 From there onwards, there is always at least one solution where all three numbers are different and greater than zero. Note that every Fibonacci is the sum of itself, zero and zero, so there is always at least one solution for every Fibonacci number. int main (void) { /* Fact: there are only 44 Fibonacci numbers in the range 0:1,000,000,000 */ const int max=44; int fib[max]; int index; /* Note: the sequence begins 0, 1, 1, 2, 3, 5... The value 1 appears twice so we'll begin the sequence there and then replace the first 1 with a 0. */ fib[0]=1; fib[1]=1; index=2; while (index<max) { fib[index]=fib[index-1]+fib[index-2]; ++index; } fib[0]=0; /* Test each Fibonacci... */ for (index=0; index<max; ++index) { bool found = false; /* Toggle this when we find a solution */ int a, b, c; for (a=0; a<max; ++a) for (b=0; b<max; ++b) for (c=0; c<max; ++c) if (fib[index]==fib[a]+fib[b]+fib[c]) { found = true; printf ("%d = %d + %d + %d\n", fib[index], fib[a], fib[b], fib[c]); } if (!found) { printf ("I'm too stupid to solve this problem!\n"); return -1; } } return 0; }
public static int fib(int n) {return fib(n-1) + fib(n-2);}
You input an i, and the calculator will find Fibonacci(i) and Lucas(i) for i into the thousands. So if you input i=0 to i=12 the output is Computed values appear here. fib(0)=0 1 digit fib(1)=1 1 digit fib(2)=1 1 digit fib(3)=2 1 digit fib(4)=3 1 digit fib(5)=5 1 digit fib(6)=8 1 digit fib(7)=13 2 digits fib(8)=21 2 digits fib(9)=34 2 digits fib(10)=55 2 digits fib(11)=89 2 digits fib(12)=144 3 digits It will do the same thing for Lucas numbers. So say I input i=1 t0 i =10 Please enter a whole number into the 'From i=' box. luc(1)=1 1 digit luc(2)=3 1 digit luc(3)=4 1 digit luc(4)=7 1 digit luc(5)=11 2 digits luc(6)=18 2 digits luc(7)=29 2 digits luc(8)=47 2 digits luc(9)=76 2 digits luc(10)=123 3 digits Those are the corresponding Lucas numbers. I added a link to the calculator. It is a lot of fun to play with.
Me and My Monsters - 2010 The Big Fib 1-5 is rated/received certificates of: Australia:G
#include<iostream> unsigned fib (unsigned term, unsigned a=0, unsigned b=1) { if (term<1) return a; return fib (--term, a+b, a); } int main() { std::cout << "Fibonacci (1000th term): " << fib (1000) << std::endl; }
The only difference between dynamic programming and back tracking is DP allows overlapping of sub problems. (fib(n) = fib(n-1)+ fib (n-2)).
Fib as a noun "he told a fib about eating his spinach" fib as verb "Fibbing is not acceptable, even if you don't call it lying"
Round the Twist - 1989 The Cabbage Patch Fib 1-4 is rated/received certificates of: Australia:G
VeggieTales - 1993 LarryBoy and the Fib from Outer Space 1-16 is rated/received certificates of: Singapore:PG
No, it is not. The noun "fib" means a subjectively minor lie. The verb "to fib" means to tell a lie.