## Fibonacci Series without recursion

Program Description

Program in C++ to calculate the series upto the N'th fibonacci number. The program demonstrates a fast and efficient implementation(for small purposes), for calculating fibonacci series.

The program also demonstrates the use of memoization technique to calculate fibonacci series in almost no time. Memoization helps reduce redundant computation by storing the previously calculated results in memory temporarily,so that they can be used later to speed up the total computation. This program does not use recursion.

In this example we've used a "long long int" type array to store the fibonacci series.You can get fibonacci series correct upto 92'nd fibonacci number,after which the overflow occurs as the size of the numbers exceed the limit which "long long int" data type can hold can hold.

Program
```/**************************************
*   Fibonacci Series without recursion
*
*	code.cheraus.com
*
**************************************/

#include<iostream>
using namespace std;

int main()
{
int n;    // series upto "n'th" fibonacci number
int i;    //loop variable

//take user input
cout<<"\nEnter the number upto which you want fibonaccie series : ";
cin>>n;

//declaring an array of appropriate size, to fit in all the numbers
long long int a[n];

//initializing the first two fibonacci numbers
a[0]=0;
a[1]=1;

// calculates and stores all the fibonacci numbers in the array
for(i=2;i<n;i++)
{
a[i] = a[i-1] + a[i-2];
}

//printing out the results
cout<<"\nThe Fibonacci series is : \n";
for(i=0;i<n;i++)
{
cout<<i<<": "<<a[i]<<"\n";
}

return 0;
}
```

Output

Enter the number upto which you want fibonaccie series :93
The Fibonacci Series is :
0: 0
1: 1
2: 1
3: 2
4: 3
5: 5
6: 8
7: 13
8: 21
9: 34
10: 55
11: 89
12: 144
13: 233
14: 377
15: 610
16: 987
17: 1597
18: 2584
19: 4181
20: 6765
21: 10946
22: 17711
23: 28657
24: 46368
25: 75025
26: 121393
27: 196418
28: 317811
29: 514229
30: 832040
31: 1346269
32: 2178309
33: 3524578
34: 5702887
35: 9227465
36: 14930352
37: 24157817
38: 39088169
39: 63245986
40: 102334155
41: 165580141
42: 267914296
43: 433494437
44: 701408733
45: 1134903170
46: 1836311903
47: 2971215073
48: 4807526976
49: 7778742049
50: 12586269025
51: 20365011074
52: 32951280099
53: 53316291173
54: 86267571272
55: 139583862445
56: 225851433717
57: 365435296162
58: 591286729879
59: 956722026041
60: 1548008755920
61: 2504730781961
62: 4052739537881
63: 6557470319842
64: 10610209857723
65: 17167680177565
66: 27777890035288
67: 44945570212853
68: 72723460248141
69: 117669030460994
70: 190392490709135
71: 308061521170129
72: 498454011879264
73: 806515533049393
74: 1304969544928657
75: 2111485077978050
76: 3416454622906707
77: 5527939700884757
78: 8944394323791464
79: 14472334024676221
80: 23416728348467685
81: 37889062373143906
82: 61305790721611591
83: 99194853094755497
84: 160500643816367088
85: 259695496911122585
86: 420196140727489673
87: 679891637638612258
88: 1100087778366101931
89: 1779979416004714189
90: 2880067194370816120
91: 4660046610375530309
92: 7540113804746346429