Program to print Fibonacci Triangle (original) (raw)

Last Updated : 10 Aug, 2022

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

JavaScript

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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)