Dados dos números enteros L y R que denotan los valores inicial y final de un rango, la tarea es contar todos los números en ese rango cuyos dígitos sean todos iguales, como 1, 22, 444, 3333, etc.
Ejemplo:
Entrada: L = 12, R = 68
Salida: 5
Explicación:
{ 22, 33, 44, 55, 66} son los números con los mismos dígitos en el rango dado.
Entrada: L = 1, R = 32
Salida: 11
Enfoque ingenuo: iterar a través de todos los números de L a R y para cada número, verificar si tiene todos sus dígitos iguales. En caso afirmativo, aumente el recuento requerido. Imprime este conteo al final.
Enfoque Eficiente: La idea se basa en el hecho de que los múltiplos (1 a 9) de 1, 11, 111, etc. tienen todos sus dígitos iguales.
Por ejemplo:
1 times 1 = 1 (All digits are same) 2 times 1 = 2 (All digits are same) 3 times 1 = 3 (All digits are same) . . 9 times 1 = 9 (All digits are same) Similarly 1 times 11 = 11 (All digits are same) 2 times 11 = 22 (All digits are same) 3 times 11 = 33 (All digits are same) . . 9 times 11 = 99 (All digits are same) Same is the case for 111, 1111, etc.
Por lo tanto, los pasos se pueden definir como:
- Encuentre la cantidad de dígitos en R. Esto decidirá la longitud de los 1 consecutivos que se crearán, hasta los cuales debemos verificar.
Por ejemplo, si R = 100, entonces length(R) = 3. Por lo tanto, solo debemos verificar los múltiplos de 1, 11 y 111.
- Para cada longitud de 1s consecutivos de 1 a longitud(R):
- Multiplícalos con todos los valores del 2 al 9
- Compruebe si se encuentra dentro del rango [L, R] o no.
- Si es así, entonces incremente el conteo de números requeridos.
- Imprime el conteo requerido de números.
C++
// C++ program to count the
// total numbers in the range
// L and R which have all the
// digit same
#include <bits/stdc++.h>
using namespace std;
// Function that count the
// total numbersProgram between L
// and R which have all the
// digit same
int count_same_digit(int L, int R)
{
int tmp = 0, ans = 0;
// length of R
int n = log10(R) + 1;
for (int i = 0; i < n; i++) {
// tmp has all digits as 1
tmp = tmp * 10 + 1;
// For each multiple
// of tmp in range 1 to 9,
// check if it present
// in range [L, R]
for (int j = 1; j <= 9; j++) {
if (L <= (tmp * j)
&& (tmp * j) <= R) {
// Increment the required count
ans++;
}
}
}
return ans;
}
// Driver Program
int main()
{
int L = 12, R = 68;
cout << count_same_digit(L, R)
<< endl;
return 0;
}
Java
// Java program to count the
// total numbers in the range
// L and R which have all the
// digit same
import java.util.*;
class GFG{
// Function that count the total
// numbersProgram between L and
// R which have all the digit same
static int count_same_digit(int L, int R)
{
int tmp = 0, ans = 0;
// Length of R
int n = (int)Math.log10(R) + 1;
for(int i = 0; i < n; i++)
{
// tmp has all digits as 1
tmp = tmp * 10 + 1;
// For each multiple of tmp
// in range 1 to 9, check if
// it present in range [L, R]
for(int j = 1; j <= 9; j++)
{
if (L <= (tmp * j) && (tmp * j) <= R)
{
// Increment the required count
ans++;
}
}
}
return ans;
}
// Driver code
public static void main(String[] args)
{
int L = 12, R = 68;
System.out.println(count_same_digit(L, R));
}
}
// This code is contributed by offbeat
Python3
# Python3 program to count the # total numbers in the range # L and R which have all the # digit same import math # Function that count the # total numbersProgram between L # and R which have all the # digit same def count_same_digit(L, R): tmp = 0; ans = 0; # length of R n = int(math.log10(R) + 1); for i in range(0, n): # tmp has all digits as 1 tmp = tmp * 10 + 1; # For each multiple # of tmp in range 1 to 9, # check if it present # in range [L, R] for j in range(1, 9): if (L <= (tmp * j) and (tmp * j) <= R): # Increment the required count ans += 1; return ans; # Driver Code L = 12; R = 68; print(count_same_digit(L, R)) # This code is contributed by Nidhi_biet
C#
// C# program to count the
// total numbers in the range
// L and R which have all the
// digit same
using System;
class GFG{
// Function that count the total
// numbersProgram between L and
// R which have all the digit same
static int count_same_digit(int L, int R)
{
int tmp = 0, ans = 0;
// Length of R
int n = (int)Math.Log10(R) + 1;
for(int i = 0; i < n; i++)
{
// tmp has all digits as 1
tmp = tmp * 10 + 1;
// For each multiple of tmp
// in range 1 to 9, check if
// it present in range [L, R]
for(int j = 1; j <= 9; j++)
{
if (L <= (tmp * j) && (tmp * j) <= R)
{
// Increment the required count
ans++;
}
}
}
return ans;
}
// Driver code
public static void Main()
{
int L = 12, R = 68;
Console.Write(count_same_digit(L, R));
}
}
// This code is contributed by Code_Mech
Javascript
<script>
// JavaScript program to count the
// total numbers in the range
// L and R which have all the
// digit same
// Function that count the
// total numbersProgram between L
// and R which have all the
// digit same
function count_same_digit( L, R)
{
var tmp = 0, ans = 0;
// length of R
var n = Math.log10(R) + 1;
for (let i = 0; i < n; i++) {
// tmp has all digits as 1
tmp = tmp * 10 + 1;
// For each multiple
// of tmp in range 1 to 9,
// check if it present
// in range [L, R]
for (let j = 1; j <= 9; j++) {
if (L <= (tmp * j)
&& (tmp * j) <= R) {
// Increment the required count
ans++;
}
}
}
return ans;
}
// Driver Program
var L = 12, R = 68;
document.write( count_same_digit(L, R));
// This code is contributed by ukasp.
</script>