Print symmetric double triangle pattern

Last Updated : 01 Mar, 2023

Given a value n, we need to print the following pattern accordingly, using only constant extra space.
Examples:

Input : n = 1
Output : x

Input : n = 2
Output :  
 x 
x x 
 x 

Input: n = 5
Output:
    x                                   
     x 
    o x 
     o x 
x o x o x 
 x o 
  x o 
   x 
    x 

Input: n = 6
Output:
     x 
      x 
     o x 
      o x 
     x o x 
x o x x o x 
 x o x 
  x o 
   x o 
    x 
     x

Input : n = 7;
Output :
      x 
       x 
      o x 
       o x 
      x o x 
       x o x 
x o x o x o x 
 x o x 
  x o x 
   x o 
    x o 
     x 
      x 

Input : n = 8;
Output : 
       x 
        x 
       o x 
        o x 
       x o x 
        x o x 
       o x o x 
x o x o o x o x 
 x o x o 
  x o x 
   x o x 
    x o 
     x o 
      x 
       x

We can divide this problem into 3 parts:
1) Print upper half with n-1 lines for odd n or n-2 lines for even n.
2) Print middle lines, 1 line for odd n or 3 lines for even n.
3) Print lower half, with n-1 lines for odd n or n-2 lines for even n.
For such complex patterns it may be easier if we can use 1-based indexing
and separate functions to print characters beginning with x or o.

C++

// Author:: Satish Srinivas
#include <iostream>

using namespace std;

// print alternate x o beginning with x
void printx(int n)
{
    for (int i = 1; i <= n; i++) {
        if (i % 2 != 0)
            cout << "x ";
        else
            cout << "o ";
    }
    return;
}

// print alternate x o beginning with o
void printo(int n)
{
    for (int i = 1; i <= n; i++) {
        if (i % 2 != 0)
            cout << "o ";
        else
            cout << "x ";
    }
    return;
}

// print the pattern for n
void printPattern(int n)
{
    // upper half
    // n-1 lines for odd, n-2 lines for even
    int x = n;

    if (n % 2 == 0)
        x = x - 1;

    // number of spaces to leave in each line
    int p = n - 1;

    // number of characters in each line
    int s = 1;

    // prints double lines in each iteration
    for (int i = 1; i <= (x - 1) / 2; i++) {
        for (int j = 1; j <= p; j++) {
            cout << " ";
        }

        if (i % 2 != 0)
            printx(s);
        else
            printo(s);

        cout << endl;
        p++;

        for (int j = 1; j <= p; j++) 
            cout << " ";        

        if (i % 2 != 0)
            printx(s);
        else
            printo(s);

        cout << endl;

        p--;
        s++;
    }

    // extra upper middle for even
    if (n % 2 == 0) {
        for (int i = 1; i <= p; i++)
            cout << " ";

        if (n % 4 != 0)
            printx(n / 2);
        else
            printo(n / 2);

        cout << endl;
    }

    // middle line
    if (n % 2 != 0) 
        printx(n);
    
    else {
        if (n % 4 != 0) {
            printx(n / 2);
            printx(n / 2);
        }
        else {
            printx(n / 2);
            printo(n / 2);
        }
    }

    cout << endl;

    // extra lower middle for even
    if (n % 2 == 0) {
        cout << " ";
        printx(n / 2);
        cout << endl;
    }

    // lower half
    p = 1;

    if (n % 2 == 0) {
        x--;
        p = 2;
    }

    int q = x / 2;

    // one line for each iteration
    for (int i = 1; i <= x; i++) {
        for (int j = 1; j <= p; j++)
            cout << " ";

        printx(q);

        if (i % 2 == 0)
            q--;

        cout << endl;

        p++;
    }

    cout << endl;
}

// Driver code
int main()
{
    int n = 7;
    printPattern(n);
    n = 8;
    printPattern(n);
    return 0;
}

Java

// java program to Print symmetric 
// double triangle pattern
class GFG
{
        
    // print alternate x o beginning with x
    static void printx(int n)
    {
        for (int i = 1; i <= n; i++) {
            if (i % 2 != 0)
                System.out.print("x ");
            else
                System.out.print("o ");
        }
        return;
    }
    
    // print alternate x o beginning with o
    static void printo(int n)
    {
        for (int i = 1; i <= n; i++) {
            if (i % 2 != 0)
                System.out.print("o ");
            else
                System.out.print("x ");
        }
        return;
    }
    
    // print the pattern for n
    static void printPattern(int n)
    {
        // upper half n-1 lines for
        // odd, n-2 lines for even
        int x = n;
    
        if (n % 2 == 0)
            x = x - 1;
    
        // number of spaces to leave in each line
        int p = n - 1;
    
        // number of characters in each line
        int s = 1;
    
        // prints double lines in each iteration
        for (int i = 1; i <= (x - 1) / 2; i++) {
            for (int j = 1; j <= p; j++) {
                System.out.print(" ");
            }
    
            if (i % 2 != 0)
                printx(s);
            else
                printo(s);
    
            System.out.println();
            p++;
    
            for (int j = 1; j <= p; j++) 
                System.out.print(" ");     
    
            if (i % 2 != 0)
                printx(s);
            else
                printo(s);
    
            System.out.println();
    
            p--;
            s++;
        }
    
        // extra upper middle for even
        if (n % 2 == 0) {
            for (int i = 1; i <= p; i++)
                System.out.print(" ");
    
            if (n % 4 != 0)
                printx(n / 2);
            else
                printo(n / 2);
    
            System.out.println();
        }
    
        // middle line
        if (n % 2 != 0) 
            printx(n);
        
        else {
            if (n % 4 != 0) {
                printx(n / 2);
                printx(n / 2);
            }
            else {
                printx(n / 2);
                printo(n / 2);
            }
        }
    
        System.out.println();
    
        // extra lower middle for even
        if (n % 2 == 0) {
            System.out.print(" ");
            printx(n / 2);
            System.out.println();
        }
    
        // lower half
        p = 1;
    
        if (n % 2 == 0) {
            x--;
            p = 2;
        }
    
        int q = x / 2;
    
        // one line for each iteration
        for (int i = 1; i <= x; i++) {
            for (int j = 1; j <= p; j++)
                System.out.print(" ");
    
            printx(q);
    
            if (i % 2 == 0)
                q--;
    
            System.out.println();
    
            p++;
        }
    
        System.out.println();
    } 
    
    // Driver code
    public static void main (String[] args)
    {
        int n = 7;
        printPattern(n);
        
        n = 8;
        printPattern(n);
    }
}


// This code is contributed by Anant Agarwal.

Python3

# Python3 program to Print symmetric 
# double triangle pattern

# Print alternate x o beginning with x
def printx(n):

    for i in range(1, n + 1):
        if (i % 2 != 0):
            print("x ", end = "")
        else:
            print("o ", end = "")

    return

# Print alternate x o beginning with o
def printo(n):

    for i in range(1, n + 1):
        if (i % 2 != 0):
            print("o ", end = "")
        else:
            print("x ", end = "")

    return

# Print the pattern for n
def printPattern(n):

    # upper half
    # n-1 lines for odd,
    # n-2 lines for even
    x = n

    if (n % 2 == 0):
        x = x - 1

    # number of spaces to leave
    # in each line
    p = n - 1

    # number of characters in each line
    s = 1

    # prints double lines in each iteration
    for i in range(1, (x - 1) // 2 + 1):
        for j in range(1, p + 1):
            print(" ", end = "")

        if (i % 2 != 0):
            printx(s)
        else:
            printo(s)

        print()
        p += 1

        for j in range(1, p + 1):
            print(" ", end = "")

        if (i % 2 != 0):
            printx(s)
        else:
            printo(s)

        print()

        p -= 1
        s += 1

    # extra upper middle for even
    if (n % 2 == 0):
        for i in range(1, p + 1):
            print(" ", end = "")

        if (n % 4 != 0):
            printx(n // 2)
        else:
            printo(n // 2)

        print()

    # middle line
    if (n % 2 != 0):
        printx(n)
    else:
        if (n % 4 != 0):
            printx(n // 2)
            printx(n // 2)
        else:
            printx(n // 2)
            printo(n // 2)

    print()

    # extra lower middle for even
    if (n % 2 == 0):
        print(" ", end = "")
        printx(n // 2)
        print()

    # lower half
    p = 1

    if (n % 2 == 0):
        x-=1
        p = 2

    q = x // 2

    # one line for each iteration
    for i in range(1, x + 1):
        for j in range(1, p + 1):
            print(" ", end = "")

        printx(q)

        if (i % 2 == 0):
            q -= 1

        print()

        p += 1

    print()

# Driver code
n = 7
printPattern(n)
n = 8
printPattern(n)

# This code is contributed by mohit kumar

JavaScript

<script>
      // JavaScript program to Print symmetric
      // double triangle pattern
      // print alternate x o beginning with x
      function printx(n) {
        for (var i = 1; i <= n; i++) {
          if (i % 2 !== 0) document.write("x&nbsp;&nbsp;");
          else document.write("o&nbsp;&nbsp;");
        }
        return;
      }

      // print alternate x o beginning with o
      function printo(n) {
        for (var i = 1; i <= n; i++) {
          if (i % 2 !== 0) document.write("o&nbsp;&nbsp;");
          else document.write("x&nbsp;&nbsp;");
        }
        return;
      }

      // print the pattern for n
      function printPattern(n) {
        // upper half n-1 lines for
        // odd, n-2 lines for even
        var x = n;

        if (n % 2 === 0) x = x - 1;

        // number of spaces to leave in each line
        var p = n - 1;

        // number of characters in each line
        var s = 1;

        // prints double lines in each iteration
        for (var i = 1; i <= (x - 1) / 2; i++) {
          for (var j = 1; j <= p; j++) {
            document.write("&nbsp;&nbsp;");
          }

          if (i % 2 !== 0) printx(s);
          else printo(s);

          document.write("<br>");
          p++;

          for (var j = 1; j <= p; j++) document.write("&nbsp;&nbsp;");

          if (i % 2 != 0) printx(s);
          else printo(s);

          document.write("<br>");

          p--;
          s++;
        }

        // extra upper middle for even
        if (n % 2 === 0) {
          for (var i = 1; i <= p; i++) document.write("&nbsp;&nbsp;");

          if (n % 4 !== 0) printx(n / 2);
          else printo(n / 2);

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

        // middle line
        if (n % 2 !== 0) printx(n);
        else {
          if (n % 4 !== 0) {
            printx(n / 2);
            printx(n / 2);
          } else {
            printx(n / 2);
            printo(n / 2);
          }
        }

        document.write("<br>");

        // extra lower middle for even
        if (n % 2 === 0) {
          document.write("&nbsp;&nbsp;");
          printx(n / 2);
          document.write("<br>");
        }

        // lower half
        p = 1;

        if (n % 2 === 0) {
          x--;
          p = 2;
        }

        var q = x / 2;

        // one line for each iteration
        for (var i = 1; i <= x; i++) {
          for (var j = 1; j <= p; j++) document.write("&nbsp;&nbsp;");

          printx(q);

          if (i % 2 === 0) q--;

          document.write("<br>");

          p++;
        }

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

      // Driver code
      var n = 7;
      printPattern(n);

      n = 8;
      printPattern(n);
    </script>

// c# equivalent of above java code
using System;
 
class GFG
{ 
    // print alternate x o beginning with x
    static void PrintX(int n)
    {
        for (int i = 1; i <= n; i++) 
        {
            if (i % 2 != 0)
                Console.Write("x ");
            else
                Console.Write("o ");
        }
        return;
    }
    
    // print alternate x o beginning with o
    static void PrintO(int n)
    {
        for (int i = 1; i <= n; i++) 
        {
            if (i % 2 != 0)
                Console.Write("o ");
            else
                Console.Write("x ");
        }
        return;
    }
    
    // print the pattern for n
    static void PrintPattern(int n)
    {
        // upper half n-1 lines for
        // odd, n-2 lines for even
        int x = n;
    
        if (n % 2 == 0)
            x = x - 1;
    
        // number of spaces to leave in each line
        int p = n - 1;
    
        // number of characters in each line
        int s = 1;
    
        // prints double lines in each iteration
        for (int i = 1; i <= (x - 1) / 2; i++) 
        {
            for (int j = 1; j <= p; j++) 
            {
                Console.Write(" ");
            }
    
            if (i % 2 != 0)
                PrintX(s);
            else
                PrintO(s);
    
            Console.WriteLine();
            p++;
    
            for (int j = 1; j <= p; j++) 
                Console.Write(" ");     
    
            if (i % 2 != 0)
                PrintX(s);
            else
                PrintO(s);
    
            Console.WriteLine();
    
            p--;
            s++;
        }
    
        // extra upper middle for even
        if (n % 2 == 0) 
        {
            for (int i = 1; i <= p; i++)
                Console.Write(" ");
    
            if (n % 4 != 0)
                PrintX(n / 2);
            else
                PrintO(n / 2);
    
            Console.WriteLine();
        }
    
        // middle line
        if (n % 2 != 0) 
            PrintX(n);
        
        else 
        {
            if (n % 4 != 0) 
            {
                PrintX(n / 2);
                PrintX(n / 2);
            }
            else 
            {
                PrintX(n / 2);
                PrintO(n / 2);
            }
        }
    
        Console.WriteLine();
    
        // extra lower middle for even
        if (n % 2 == 0) 
        {
            Console.Write(" ");
            PrintX(n / 2);
            Console.WriteLine();
        }
    
        // lower half
        p = 1;
    
        if (n % 2 == 0) 
        {
            x--;
            p = 2;
        }
    
        int q = x / 2;
    
        // one line for each iteration
        for (int i = 1; i <= x; i++) 
        {
            for (int j = 1; j <= p; j++)
                Console.Write(" ");
    
            PrintX(q);
    
            if (i % 2 == 0)
                q--;
    
            Console.WriteLine();
    
            p++;
        }
    
        Console.WriteLine();
    } 
    
    // Driver code
    public static void Main (String[] args)
    {
        int n = 7;
        PrintPattern(n);
        
        n = 8;
        PrintPattern(n);
    }
}

Output:

      x 
       x 
      o x 
       o x 
      x o x 
       x o x 
x o x o x o x 
 x o x 
  x o x 
   x o 
    x o 
     x 
      x 

       x 
        x 
       o x 
        o x 
       x o x 
        x o x 
       o x o x 
x o x o o x o x 
 x o x o 
  x o x 
   x o x 
    x o 
     x o 
      x 
       x

Time Complexity: O(N^2) .

Auxiliary Space: O(1) because it is using constant space for variables

Analysis of Algorithms

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Print symmetric double triangle pattern

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