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8ea50b59a3
Implemented an easier to implement and faster algorithm than the already present matrix exponentiation method. This is faster than matrix exponentiation method as it is a DP form of matrix exponentiation.
48 lines
1.1 KiB
C++
48 lines
1.1 KiB
C++
//An efficient way to calculate nth fibonacci number faster and simpler than O(nlogn) method of matrix exponentiation
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//This works by using both recursion and dynamic programming.
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//as 93rd fibonacci exceeds 19 digits, which cannot be stored in a single long long variable, we can only use it till 92nd fibonacci
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//we can use it for 10000th fibonacci etc, if we implement bigintegers.
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//This algorithm works with the fact that nth fibonacci can easily found if we have already found n/2th or (n+1)/2th fibonacci
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//It is a property of fibonacci similar to matrix exponentiation.
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#include <iostream>
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#include<cstdio>
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using namespace std;
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const long long MAX = 93;
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long long f[MAX] = {0};
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long long fib(long long n)
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{
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if (n == 0)
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return 0;
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if (n == 1 || n == 2)
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return (f[n] = 1);
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if (f[n])
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return f[n];
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long long k = (n%2!=0)? (n+1)/2 : n/2;
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f[n] = (n%2!=0)? (fib(k)*fib(k) + fib(k-1)*fib(k-1))
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: (2*fib(k-1) + fib(k))*fib(k);
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return f[n];
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}
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int main()
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{
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//Main Function
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for(long long i=1;i<93;i++)
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{
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cout << i << " th fibonacci number is " << fib(i) << "\n";
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}
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return 0;
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}
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