Given a number made of single digits, find its square. It may be assumed that the single digits are 3, 6 and 9. Numbers can be very large i.e. can exceed long long int.
Examples:
Input : 33 66 99 Output : Square of 33 is : 1089 Square of 66 is : 4356 Square of 99 is : 9801 Input : 333 666 999 Output : Square of 333 is : 110889 Square of 666 is : 443556 Square of 999 is : 998001
Method 1 (Writing as multiples of 1111…1)
An interesting fact is, every such number can be represented as a multiple of 1111…1. For example, 33333 = 3 * 11111. Squares of 11, 111, 1111, 11111 … are 121, 12321, 1234321, 123454321, … respectively. So a simple solution is find square of 111…11 then multiply the result with 3 or 6 or 9 (We can use multiplication with large number).
Method 2 (Using digit patterns)
For 333….333 Count the no. of digits and print in the below manner:
Suppose no. of digit is n then write the n-1 times 1 and then write one time 0 and then write n-1 time 8 and in last write 9.
Example :
{ 3333 } = 11108889
For 666….666 Count the no. of digits and print in the below manner:
Suppose no of digit is n then write the n-1 times 4 and then write one time 3 and then write n-1 time 5 and in last write 6.
Example :
{ 6666 } = 44435556
For 999….999 Count the no. of digits and print in the below manner:
Suppose no of digit is n then write the n-1 times 9 and then write one time 8 and then write n-1 time 0 and in last write 1.
Example :
{ 9999 } = 99980001
Below is the implementation of above approach:
C++
// C++ program to find square of // these large numbers#include <iostream>using namespace std;// Function to find the square of// 333...333, 666...666 and 999...999string find_Square_369(string num){ char a, b, c, d; // if the number is 333...333 if (num[0] == '3') a = '1', b = '0', c = '8', d = '9'; // if the number is 666...666 else if (num[0] == '6') a = '4', b = '3', c = '5', d = '6'; // if the number is 999...999 else a = '9', b = '8', c = '0', d = '1'; // variable for hold result string result = ""; // find the no of digit int size = num.size(); // add size-1 time a in result for (int i = 1; i < num.size(); i++) result += a; // add one time b in result result += b; // add size-1 time c in result for (int i = 1; i < num.size(); i++) result += c; // add one time d in result result += d; // return result return result;}// Drivers codeint main(){ string num_3, num_6, num_9; num_3 = "3333"; num_6 = "6666"; num_9 = "9999"; string result = ""; // find square of 33..33 result = find_Square_369(num_3); cout << "Square of " << num_3 << " is : " << result << endl; // find square of 66..66 result = find_Square_369(num_6); cout << "Square of " << num_6 << " is : " << result << endl; // find square of 66..66 result = find_Square_369(num_9); cout << "Square of " << num_9 << " is : " << result << endl; return 0;} |
Java
// Java program to find square of // these large numbersimport java.io.*;public class GFG { // Function to find the square of // 333...333, 666...666 and 999...999 static String find_Square_369(String num) { char a, b, c, d; // if the number is 333...333 if (num.charAt(0) == '3') {a = '1'; b = '0'; c = '8'; d = '9';} // if the number is 666...666 else if (num.charAt(0) == '6') {a = '4'; b = '3'; c = '5'; d = '6';} // if the number is 999...999 else {a = '9'; b = '8'; c = '0'; d = '1';} // variable for hold result String result = ""; // find the no of digit int size = num.length(); // add size-1 time a in result for (int i = 1; i < size; i++) result += a; // add one time b in result result += b; // add size-1 time c in result for (int i = 1; i < size; i++) result += c; // add one time d in result result += d; // return result return result; } // Drivers code public static void main(String[] args) { String num_3, num_6, num_9; num_3 = "3333"; num_6 = "6666"; num_9 = "9999"; String result = ""; // find square of 33..33 result = find_Square_369(num_3); System.out.println("Square of " + num_3 + " is : " + result); // find square of 66..66 result = find_Square_369(num_6); System.out.println("Square of " + num_6 + " is : " + result); // find square of 66..66 result = find_Square_369(num_9); System.out.println("Square of " + num_9 + " is : " + result); }}// This code is contributed by Smitha. |
Python 3
# Python 3 program to find square of # these large numbers# Function to find the square of# 333...333, 666...666 and 999...999def find_Square_369(num): # if the number is 333...333 if (num[0] == '3'): a = '1' b = '0' c = '8' d = '9' # if the number is 666...666 elif (num[0] == '6'): a = '4' b = '3' c = '5' d = '6' # if the number is 999...999 else: a = '9' b = '8' c = '0' d = '1' # variable for hold result result = "" # find the no of digit size = len(num) # add size-1 time a in result for i in range(1, size): result += a # add one time b in result result += b # add size-1 time c in result for i in range(1, size): result += c # add one time d in result result += d # return result return result# Drivers code# Your Python 3 Codenum_3 = "3333"num_6 = "6666"num_9 = "9999"result = ""# find square of 33..33result = find_Square_369(num_3)print("Square of " + num_3 + " is : " + result);# find square of 66..66result = find_Square_369(num_6)print("Square of " + num_6 + " is : " + result);# find square of 66..66result = find_Square_369(num_9)print("Square of " + num_9 + " is : " + result);# This code is contributed by Smitha |
C#
// C# program to find square of // these large numbersusing System;class GFG { // Function to find the square of // 333...333, 666...666 and 999...999 static string find_Square_369(string num) { char a, b, c, d; // if the number is 333...333 if (num[0] == '3') {a = '1'; b = '0'; c = '8'; d = '9';} // if the number is 666...666 else if (num[0] == '6') {a = '4'; b = '3'; c = '5'; d = '6';} // if the number is 999...999 else {a = '9'; b = '8'; c = '0'; d = '1';} // variable for hold result string result = ""; // find the no of digit int size = num.Length; // add size-1 time a in result for (int i = 1; i < size; i++) result += a; // add one time b in result result += b; // add size-1 time c in result for (int i = 1; i < size; i++) result += c; // add one time d in result result += d; // return result return result; } // Drivers code public static void Main() { string num_3, num_6, num_9; num_3 = "3333"; num_6 = "6666"; num_9 = "9999"; string result = ""; // find square of 33..33 result = find_Square_369(num_3); Console.Write("Square of " + num_3 + " is : " + result + "\n"); // find square of 66..66 result = find_Square_369(num_6); Console.Write("Square of " + num_6 + " is : " + result + "\n"); // find square of 66..66 result = find_Square_369(num_9); Console.Write("Square of " + num_9 + " is : " + result + "\n"); }}// This code is contributed by Smitha |
PHP
<?php // PHP program to find square of // these large numbers // Function to find the square of// 333...333, 666...666 and 999...999function find_Square_369($num){ // if the number is 333...333 if ($num[0] == '3') { $a = '1'; $b = '0'; $c = '8'; $d = '9'; } // if the number is 666...666 else if ($num[0] == '6') { $a = '4'; $b = '3'; $c = '5'; $d = '6'; } // if the number is 999...999 else { $a = '9'; $b = '8'; $c = '0'; $d = '1'; } // variable for hold result $result = ""; // find the no of digit $size = strlen($num); // add size-1 time a in result for ($i = 1; $i < $size; $i++) $result = $result.$a; // add one time b in result $result = $result.$b; // add size-1 time c in result for ($i = 1; $i < $size; $i++) $result = $result.$c; // add one time d in result $result = $result.$d; // return result return $result;} // Drivers code$num_3 = "3333";$num_6 = "6666";$num_9 = "9999";$result = "";// find square of 33..33$result = find_Square_369($num_3);echo "Square of " . $num_3 . " is : " . $result ."\n" ;// find square of 66..66$result = find_Square_369($num_6);echo "Square of " . $num_6 . " is : " .$result ."\n";// find square of 66..66$result = find_Square_369($num_9);echo "Square of " . $num_9 . " is : ".$result ."\n";return 0;?> |
Javascript
<script>// Javascript program to find square of // these large numbers // Function to find the square of // 333...333, 666...666 and 999...999 function find_Square_369(num) { let a, b, c, d; // if the number is 333...333 if (num[0] == '3') {a = '1'; b = '0'; c = '8'; d = '9';} // if the number is 666...666 else if (num[0] == '6') {a = '4'; b = '3'; c = '5'; d = '6';} // if the number is 999...999 else {a = '9'; b = '8'; c = '0'; d = '1';} // variable for hold result let result = ""; // find the no of digit let size = num.length; // add size-1 time a in result for (let i = 1; i < size; i++) result += a; // add one time b in result result += b; // add size-1 time c in result for (let i = 1; i < size; i++) result += c; // add one time d in result result += d; // return result return result; } // Drivers code let num_3, num_6, num_9; num_3 = "3333"; num_6 = "6666"; num_9 = "9999"; let result = ""; // find square of 33..33 result = find_Square_369(num_3); document.write("Square of " + num_3 + " is : " + result+"<br>"); // find square of 66..66 result = find_Square_369(num_6); document.write("Square of " + num_9 + " is : " + result+"<br>"); // find square of 66..66 result = find_Square_369(num_9); document.write("Square of " + num_9 + " is : " + result+"<br>"); // This code is contributed by avanitrachhadiya2155</script> |
Output :
Square of 3333 is : 11108889 Square of 6666 is : 44435556 Square of 9999 is : 99980001
Time complexity : O(n)
Space complexity : O(n)
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