Dado un número hecho de un solo dígito, encuentre su cuadrado. Se puede suponer que los dígitos individuales son 3, 6 y 9. Los números pueden ser muy grandes, es decir, pueden exceder long long int.
Ejemplos:
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
Método 1 (Escribir como múltiplos de 1111…1)
Un hecho interesante es que cada uno de esos números se puede representar como un múltiplo de 1111…1. Por ejemplo, 33333 = 3 * 11111. Los cuadrados de 11, 111, 1111, 11111… son 121, 12321, 1234321, 123454321,… respectivamente. Entonces, una solución simple es encontrar el cuadrado de 111…11 y luego multiplicar el resultado por 3 o 6 o 9 (Podemos usar la multiplicación con un número grande ).
Método 2 (usando patrones de dígitos)
Para 333….333 Cuente el no. de dígitos e imprima de la siguiente manera:
Supongamos que no. del dígito es n, luego escriba n-1 veces 1 y luego escriba una vez 0 y luego escriba n-1 vez 8 y por último escriba 9.
Ejemplo:
{ 3333 } = 11108889
Para 666….666 Cuente el no. de dígitos e imprima de la siguiente manera:
Suponga que el número de dígitos es n, luego escriba n-1 por 4 y luego escriba una vez por 3 y luego escriba n-1 por 5 y por último escriba 6.
Ejemplo:
{ 6666 } = 44435556
Para 999….999 Cuente el no. de dígitos e imprímalos de la siguiente manera:
suponga que el número de dígitos es n, luego escriba n-1 veces 9 y luego escriba una vez 8 y luego escriba n-1 vez 0 y por último escriba 1.
Ejemplo:
{ 9999 } = 99980001
A continuación se muestra la implementación del enfoque anterior:
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...999
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.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 code
int 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 numbers
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_9
+ " 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...999
def 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 Code
num_3 = "3333"
num_6 = "6666"
num_9 = "9999"
result = ""
# find square of 33..33
result = find_Square_369(num_3)
print("Square of " + num_3 + " is : "
+ result);
# find square of 66..66
result = find_Square_369(num_6)
print("Square of " + num_6 + " is : "
+ result);
# find square of 66..66
result = 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 numbers
using 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_9
+ " 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...999
function 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>
Producción :
Square of 3333 is : 11108889 Square of 6666 is : 44435556 Square of 9999 is : 99980001