Program to print Fibonacci Triangle

Given the value of n(n < 10), i.e, number of lines, print the Fibonacci triangle.

Examples:

Input : n = 5 
Output :
1 
1 2 
3 5 8 
13 21 34 55 
89 144 233 377 610 

Input : n = 7
Output :
1 
1 2 
3 5 8 
13 21 34 55 
89 144 233 377 610 
987 1597 2584 4181 6765 10946 
17711 28657 46368 75025 121393 196418 317811 

The Fibonacci numbers are the numbers in the following integer sequence.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..
In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation 

    Fn = Fn-1 + Fn-2

with seed values F₁ = 1 and F₂ = 1.

Below is the implementation of the above pattern :  

C++

// C++ Implementation for
// Fibonacci triangle
#include <bits/stdc++.h>
using namespace std;

// function to fill Fibonacci Numbers
// in f[]
void fib(int f[], int N)
{
    // 1st and 2nd number of the
    // series are 1 and 1
    f[1] = 1;
    f[2] = 1;

    for (int i = 3; i <= N; i++)

        // Add the previous 2 numbers
        // in the series and store it
        f[i] = f[i - 1] + f[i - 2];
}

void fiboTriangle(int n)
{
    // Fill Fibonacci numbers in f[] using
    // fib(). We need N = n*(n+1)/2 Fibonacci
    // numbers to make a triangle of height
    // n
    int N = n * (n + 1) / 2;
    int f[N + 1];
    fib(f, N);

    // To store next Fibonacci Number to print
    int fiboNum = 1;

    // for loop to keep track of
    // number of lines
    for (int i = 1; i <= n; i++) {
        // For loop to keep track of
        // numbers in each line
        for (int j = 1; j <= i; j++)
            cout << f[fiboNum++] << " ";

        cout << endl;
    }
}

// Driver code
int main()
{
    int n = 5;
    fiboTriangle(n);
    return 0;
}

Java

// Java Implementation for
// Fibonacci triangle
import java.io.*;

class GFG {

    // function to fill Fibonacci Numbers
    // in f[]
    static void fib(int f[], int N)
    {
        // 1st and 2nd number of the
        // series are 1 and 1
        f[1] = 1;
        f[2] = 1;

        for (int i = 3; i <= N; i++)

            // Add the previous 2 numbers
            // in the series and store it
            f[i] = f[i - 1] + f[i - 2];
    }

    static void fiboTriangle(int n)
    {
        // Fill Fibonacci numbers in f[] using
        // fib(). We need N = n*(n+1)/2 Fibonacci
        // numbers to make a triangle of height
        // n
        int N = n * (n + 1) / 2;
        int f[] = new int[N + 1];
        fib(f, N);

        // To store next Fibonacci
        // Number to print
        int fiboNum = 1;

        // for loop to keep track of
        // number of lines
        for (int i = 1; i <= n; i++) {
            // For loop to keep track of
            // numbers in each line
            for (int j = 1; j <= i; j++)
                System.out.print(f[fiboNum++] + " ");

            System.out.println();
        }
    }

    // Driver code
    public static void main(String args[])
    {
        int n = 5;
        fiboTriangle(n);
    }
}

/*This code is contributed by Nikita Tiwari.*/

Python3

# Python 3 Implementation for
# Fibonacci triangle


# function to fill Fibonacci
# Numbers in f[]
def fib(f, N):

    # 1st and 2nd number of
    # the series are 1 and 1
    f[1] = 1
    f[2] = 1

    for i in range(3, N + 1):

        # Add the previous 2 numbers
        # in the series and store it
        f[i] = f[i - 1] + f[i - 2]


def fiboTriangle(n):

    # Fill Fibonacci numbers in
    # f[] using fib(). We need
    # N = n*(n + 1)/2 Fibonacci
    # numbers to make a triangle
    # of height n
    N = n * (n + 1) // 2
    f = [0] * (N + 1)
    fib(f, N)

    # To store next Fibonacci
    # Number to print
    fiboNum = 1

    # for loop to keep track of
    # number of lines
    for i in range(1, n + 1):

        # For loop to keep track of
        # numbers in each line
        for j in range(1, i + 1):

            print(f[fiboNum], " ", end="")
            fiboNum = fiboNum + 1

        print()


# Driver code
n = 5
fiboTriangle(n)

# This code is contributed by Nikita Tiwari.

C#

// C# Implementation for
// Fibonacci triangle
using System;

class GFG {

    // function to fill Fibonacci Numbers
    // in f[]
    static void fib(int[] f, int N)
    {
        // 1st and 2nd number of the
        // series are 1 and 1
        f[1] = 1;
        f[2] = 1;

        for (int i = 3; i <= N; i++)

            // Add the previous 2 numbers
            // in the series and store it
            f[i] = f[i - 1] + f[i - 2];
    }

    static void fiboTriangle(int n)
    {
        // Fill Fibonacci numbers in f[] using
        // fib(). We need N = n*(n+1)/2 Fibonacci
        // numbers to make a triangle of height
        // n
        int N = n * (n + 1) / 2;
        int[] f = new int[N + 1];
        fib(f, N);

        // To store next Fibonacci
        // Number to print
        int fiboNum = 1;

        // for loop to keep track of
        // number of lines
        for (int i = 1; i <= n; i++) {
            // For loop to keep track of
            // numbers in each line
            for (int j = 1; j <= i; j++)
                Console.Write(f[fiboNum++] + " ");

            Console.WriteLine();
        }
    }

    // Driver code
    public static void Main()
    {
        int n = 5;
        fiboTriangle(n);
    }
}

/*This code is contributed by vt_m.*/

PHP

<?php
// PHP Implementation for
// Fibonacci triangle

// function to fill
// Fibonacci Numbers
// in f[]
function fib(&$f, $N)
{
    // 1st and 2nd number
    // of the series are
    // 1 and 1
    $f[1] = 1;
    $f[2] = 1;

    for ($i = 3;
         $i <= $N; $i++)

        // Add the previous
        // 2 numbers in the
        // series and store it
        $f[$i] = $f[$i - 1] +
                 $f[$i - 2];
}

function fiboTriangle($n)
{
    // Fill Fibonacci numbers
    // in f[] using fib(). We
    // need N = n*(n+1)/2
    // Fibonacci numbers to make
    // a triangle of height n
    $N = $n * ($n + 1) / 2;
    $f = array();
    fib($f, $N);

    // To store next
    // Fibonacci Number
    // to print
    $fiboNum = 1;

    // for loop to keep track
    // of number of lines
    for ($i = 1; $i <= $n; $i++)
    {
        // For loop to keep track
        // of numbers in each line
        for ($j = 1;$j <= $i; $j++)
            echo ($f[$fiboNum++] . " ");

        echo("\n");
    }
}

// Driver code
$n = 5;
fiboTriangle($n);

// This code is contributed by
// Manish Shaw(manishshaw1)
?>

Javascript

<script>

// JavaScript implementation for
// Fibonacci triangle

// Function to fill Fibonacci Numbers
// in f[]
function fib(f, N)
{

    // 1st and 2nd number of the
    // series are 1 and 1
    f[1] = 1;
    f[2] = 1;

    for(var i = 3; i <= N; i++)

        // Add the previous 2 numbers
        // in the series and store it
        f[i] = f[i - 1] + f[i - 2];
}

function fiboTriangle(n)
{

    // Fill Fibonacci numbers in f[] using
    // fib(). We need N = n*(n+1)/2 Fibonacci
    // numbers to make a triangle of height
    // n
    var N = (n * (n + 1)) / 2;
    var f = [...Array(N + 1)];
    fib(f, N);

    // To store next Fibonacci Number to print
    var fiboNum = 1;

    // for loop to keep track of
    // number of lines
    for(var i = 1; i <= n; i++)
    {
        // For loop to keep track of
        // numbers in each line
        for(var j = 1; j <= i; j++)
            document.write(f[fiboNum++] + " ");

        document.write("<br>");
    }
}

// Driver code
var n = 5;

fiboTriangle(n);

// This code is contributed by rdtank

</script>

Output:

1 
1 2 
3 5 8 
13 21 34 55 
89 144 233 377 610 

Time complexity: O(n*n)

Auxiliary Space: O(n)