Dados dos enteros positivos A y B y una string S de tamaño N, que denota un número en base A , la tarea es convertir la string S dada de base A a base B.
Ejemplos:
Entrada: S = “10B”, A = 16, B = 10
Salida: 267
Explicación: 10B en hexadecimal (base =16) cuando se convierte a decimal (base =10) es 267.Entrada: S = “10011”, A = 2, B = 8
Salida: 23
Explicación: 10011 en binario (base = 2) cuando se convierte a octal (base = 8) es 23.
Enfoque: Sistemas numéricos es la técnica para representar números en la arquitectura de sistemas informáticos . La arquitectura de la computadora admite los siguientes sistemas numéricos:
- Sistema numérico binario (Base 2): El sistema numérico binario solo consta de dos dígitos, 0 s y 1 s. La base de este sistema numérico es 2 .
- Sistema de numeración octal (base 8): El sistema de numeración octal consta de 8 dígitos que van del 0 al 7 .
- Sistema numérico decimal (base 10): El sistema numérico decimal consta de 10 dígitos que van del 0 al 9 .
- Sistema de numeración hexadecimal (Base 16): El sistema de numeración hexadecimal consta de 16 dígitos con 0 a 9 dígitos y alfabetos A a F. También se conoce como código alfanumérico, ya que consta de números y alfabetos.
Para convertir un número de base A a base B , la idea es convertirlo primero a su representación decimal y luego convertir el número decimal a base B.
Conversión de cualquier base a Decimal: El equivalente decimal del número “str” en base “base” es igual a 1 * str[len – 1] + base * str[len – 2] + (base) 2 * str[len – 3] + …
Conversión de decimal a cualquier base:
el número decimal «inputNum» se puede convertir en un número en base «base» dividiendo repetidamente inputNum por la base y almacenando el resto. Finalmente, invierta la string obtenida para obtener el resultado deseado.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to return ASCII
// value of a character
int val(char c)
{
if (c >= '0' && c <= '9')
return (int)c - '0';
else
return (int)c - 'A' + 10;
}
// Function to convert a number
// from given base to decimal number
int toDeci(string str, int base)
{
// Stores the length
// of the string
int len = str.size();
// Initialize power of base
int power = 1;
// Initialize result
int num = 0;
// Decimal equivalent is str[len-1]*1
// + str[len-2]*base + str[len-3]*(base^2) + ...
for (int i = len - 1; i >= 0; i--) {
// A digit in input number must
// be less than number's base
if (val(str[i]) >= base) {
printf("Invalid Number");
return -1;
}
// Update num
num += val(str[i]) * power;
// Update power
power = power * base;
}
return num;
}
// Function to return equivalent
// character of a given value
char reVal(int num)
{
if (num >= 0 && num <= 9)
return (char)(num + '0');
else
return (char)(num - 10 + 'A');
}
// Function to convert a given
// decimal number to a given base
string fromDeci(int base, int inputNum)
{
// Store the result
string res = "";
// Repeatedly divide inputNum
// by base and take remainder
while (inputNum > 0) {
// Update res
res += reVal(inputNum % base);
// Update inputNum
inputNum /= base;
}
// Reverse the result
reverse(res.begin(), res.end());
return res;
}
// Function to convert a given number
// from a base to another base
void convertBase(string s, int a, int b)
{
// Convert the number from
// base A to decimal
int num = toDeci(s, a);
// Convert the number from
// decimal to base B
string ans = fromDeci(b, num);
// Print the result
cout << ans;
}
// Driver Code
int main()
{
// Given input
string s = "10B";
int a = 16, b = 10;
// Function Call
convertBase(s, a, b);
return 0;
}
Java
// Java program for the above approach
import java.util.*;
class GFG{
// Function to return ASCII
// value of a character
static int val(char c)
{
if (c >= '0' && c <= '9')
return(int)c - '0';
else
return(int)c - 'A' + 10;
}
// Function to convert a number
// from given base to decimal number
static int toDeci(String str, int base)
{
// Stores the length
// of the String
int len = str.length();
// Initialize power of base
int power = 1;
// Initialize result
int num = 0;
// Decimal equivalent is str[len-1]*1
// + str[len-2]*base + str[len-3]*(base^2) + ...
for(int i = len - 1; i >= 0; i--)
{
// A digit in input number must
// be less than number's base
if (val(str.charAt(i)) >= base)
{
System.out.printf("Invalid Number");
return -1;
}
// Update num
num += val(str.charAt(i)) * power;
// Update power
power = power * base;
}
return num;
}
// Function to return equivalent
// character of a given value
static char reVal(int num)
{
if (num >= 0 && num <= 9)
return(char)(num + '0');
else
return(char)(num - 10 + 'A');
}
// Function to convert a given
// decimal number to a given base
static String fromDeci(int base, int inputNum)
{
// Store the result
String res = "";
// Repeatedly divide inputNum
// by base and take remainder
while (inputNum > 0)
{
// Update res
res += reVal(inputNum % base);
// Update inputNum
inputNum /= base;
}
// Reverse the result
res = reverse(res);
return res;
}
// Function to convert a given number
// from a base to another base
static void convertBase(String s, int a, int b)
{
// Convert the number from
// base A to decimal
int num = toDeci(s, a);
// Convert the number from
// decimal to base B
String ans = fromDeci(b, num);
// Print the result
System.out.print(ans);
}
static String reverse(String input)
{
char[] a = input.toCharArray();
int l, r = a.length - 1;
for(l = 0; l < r; l++, r--)
{
char temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return String.valueOf(a);
}
// Driver Code
public static void main(String[] args)
{
// Given input
String s = "10B";
int a = 16, b = 10;
// Function Call
convertBase(s, a, b);
}
}
// This code is contributed by 29AjayKumar
Python3
# Python program for the above approach
# Function to return ASCII
# value of a character
def val(c):
if (c >= '0' and c <= '9'):
return ord(c) - 48
else:
return ord(c) - 65 + 10
# Function to convert a number
# from given base to decimal number
def toDeci(strr, base):
# Stores the length
# of the string
lenn = len(strr)
# Initialize power of base
power = 1
# Initialize result
num = 0
# Decimal equivalent is strr[len-1]*1
# + strr[len-2]*base + strr[len-3]*(base^2) + ...
for i in range(lenn - 1, -1, -1):
# A digit in input number must
# be less than number's base
if (val(strr[i]) >= base):
print("Invalid Number")
return -1
# Update num
num += val(strr[i]) * power
# Update power
power = power * base
return num
# Function to return equivalent
# character of a given value
def reVal(num):
if (num >= 0 and num <= 9):
return chr(num + 48)
else:
return chr(num - 10 + 65)
# Function to convert a given
# decimal number to a given base
def fromDeci(base, inputNum):
# Store the result
res = ""
# Repeatedly divide inputNum
# by base and take remainder
while (inputNum > 0):
# Update res
res += reVal(inputNum % base)
# Update inputNum
inputNum //= base
# Reverse the result
res = res[::-1]
return res
# Function to convert a given number
# from a base to another base
def convertBase(s, a, b):
# Convert the number from
# base A to decimal
num = toDeci(s, a)
# Convert the number from
# decimal to base B
ans = fromDeci(b, num)
# Print the result
print(ans)
# Driver Code
# Given input
s = "10B"
a = 16
b = 10
# Function Call
convertBase(s, a, b)
# This code is contributed by shubhamsingh10
C#
// C# program for the above approach
using System;
public class GFG{
// Function to return ASCII
// value of a character
static int val(char c)
{
if (c >= '0' && c <= '9')
return(int)c - '0';
else
return(int)c - 'A' + 10;
}
// Function to convert a number
// from given basse to decimal number
static int toDeci(string str, int basse)
{
// Stores the length
// of the string
int len = str.Length;
// Initialize power of basse
int power = 1;
// Initialize result
int num = 0;
// Decimal equivalent is str[len-1]*1
// + str[len-2]*basse + str[len-3]*(basse^2) + ...
for(int i = len - 1; i >= 0; i--)
{
// A digit in input number must
// be less than number's basse
if (val(str[i]) >= basse)
{
Console.Write("Invalid Number");
return -1;
}
// Update num
num += val(str[i]) * power;
// Update power
power = power * basse;
}
return num;
}
// Function to return equivalent
// character of a given value
static char reVal(int num)
{
if (num >= 0 && num <= 9)
return(char)(num + '0');
else
return(char)(num - 10 + 'A');
}
// Function to convert a given
// decimal number to a given basse
static string fromDeci(int basse, int inputNum)
{
// Store the result
string res = "";
// Repeatedly divide inputNum
// by basse and take remainder
while (inputNum > 0)
{
// Update res
res += reVal(inputNum % basse);
// Update inputNum
inputNum /= basse;
}
// Reverse the result
res = reverse(res);
return res;
}
// Function to convert a given number
// from a basse to another basse
static void convertbasse(string s, int a, int b)
{
// Convert the number from
// basse A to decimal
int num = toDeci(s, a);
// Convert the number from
// decimal to basse B
string ans = fromDeci(b, num);
// Print the result
Console.Write(ans);
}
static string reverse(string input)
{
char[] a = input.ToCharArray();
int l, r = a.Length - 1;
for(l = 0; l < r; l++, r--)
{
char temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return new string(a);
}
// Driver Code
static public void Main (){
// Given input
string s = "10B";
int a = 16, b = 10;
// Function Call
convertbasse(s, a, b);
}
}
// This code is contributed by shubhamsingh10
Javascript
<script>
// Javascript program for the above approach
// Function to return ASCII
// value of a character
function val(c)
{
if (c >= '0' && c <= '9')
return c.charCodeAt(0) - 48;
else
return c.charCodeAt(0) - 65 + 10;
}
// Function to convert a number
// from given base to decimal number
function toDeci(str, base)
{
// Stores the length
// of the var
var len = str.length;
// Initialize power of base
var power = 1;
// Initialize result
var num = 0;
// Decimal equivalent is str[len-1]*1
// + str[len-2]*base + str[len-3]*(base^2) + ...
for (var i = len - 1; i >= 0; i--) {
// A digit in input number must
// be less than number's base
if (val(str[i]) >= base) {
document.write("Invalid Number");
return -1;
}
// Update num
num += val(str[i]) * power;
// Update power
power = power * base;
}
return num;
}
// Function to return equivalent
// character of a given valueString.fromCharCode
function reVal(num)
{
if (num >= 0 && num <= 9)
return String.fromCharCode(num + 48);
else
return String.fromCharCode(num - 10 + 65);
}
// Function to convert a given
// decimal number to a given base
function fromDeci(base, inputNum)
{
// Store the result
var res = "";
// Repeatedly divide inputNum
// by base and take remainder
while (inputNum > 0) {
// Update res
res += reVal(inputNum % base);
// Update inputNum
inputNum = Math.floor(inputNum/base);
}
// Reverse the result
res = res.split("").reverse().join("");
return res;
}
// Function to convert a given number
// from a base to another base
function convertBase(s, a, b)
{
// Convert the number from
// base A to decimal
var num = toDeci(s, a);
// Convert the number from
// decimal to base B
var ans = fromDeci(b, num);
// Print the result
document.write(ans);
}
// Driver Code
// Given input
var s = "10B";
var a = 16
var b = 10;
// Function Call
convertBase(s, a, b);
// This code is contributed by ShubhamSingh10
</script>
Producción:
267
Complejidad temporal: O(N)
Espacio auxiliar: O(N)