给定一个以十进制为基数的数 N，求其任意基数(基数 b)的位数

原文:https://www . geesforgeks . org/给定-number-n-十进制-base-find-number-digits-base-b/

给定一个以 10 为底的数 n，求其以 b 为底的数。 约束:N \in \mathbb{W} 整体 T3】举例:T5】

Input : Number = 48 
        Base = 4
Output: 3
Explanation : (48)10 = (300)4

Input : Number = 1446
        Base = 7
Output: 4
Explanation : (446)10 = (4134)7

A 简单方法:将十进制数转换成给定的基数 r，然后计算位数。 一种有效的方法:它基于数字的基数和该数字的位数之间的关系。 通常:让 n 为正整数。如果是b^{d-1}\leq n < b^d ，则n 的基础b 表示有d 位数字，如果是d-1 \leq \log_b n < d 或\lfloor log_b n \rfloor = d-1 就是这种情况。因此，n 的基数 b 表示中的位数是 \lfloor log_b N \rfloor + 1 = \left \lfloor \dfrac {ln N}{ln b} \right \rfloor + 1 = \left \lfloor \dfrac {log N}{log b} \right \rfloor + 1 在上面的等式中，使用了基数变化对数特性。所以我们计算基数的对数，我们想计算位数。取其地板值，然后加 1。 这个思路还可以进一步用于求基数 r 中给定的基数 b 的数字 n 的位数，所要做的就是将基数 10 中的数字进行转换，然后应用上面的求位数公式。当数字以 10 为基数时，计算任何基数的对数会更容易。

C++

// C++ program to Find Number of digits
// in base b.
#include <iostream>
#include <math.h>
using namespace std;

// function to print number of
// digits
void findNumberOfDigits(long n, int base)
{
    // Calculating log using base
    // changing property and then
    // taking it floor and then
    // adding 1.
    int dig = (int)(floor( log(n) /
                         log(base)) + 1);

    // printing output
    cout << "The Number of digits of "
         << "Number " << n << " in base "
         << base << " is " << dig;
}

// Driver method
int main()
{
    // taking inputs
    long n = 1446;
    int base = 7;

    // calling the method
    findNumberOfDigits(n, base);
    return 0;
}

// This code is contributed by Manish Shaw
// (manishshaw1)

Java 语言(一种计算机语言，尤用于创建网站)

// Java program to Find Number
// of digits in base b.
class GFG {

    // function to print number of digits
    static void findNumberOfDigits(long n, int base)
    {

        // Calculating log using base changing
        // property and then taking it
        // floor and then adding 1.
        int dig = (int)(Math.floor(
                        Math.log(n) / Math.log(base))
                        + 1);

        // printing output
        System.out.println("The Number of digits of Number "
                            + n + " in base " + base
                            + " is " + dig);
    }

    // Driver method   
    public static void main(String[] args)
    {
        // taking inputs
        long n = 1446;
        int base = 7;

        // calling the method
        findNumberOfDigits(n, base);
    }
}

Python 3

# Python3 program to Find Number of digits
# in base b.

import math

# function to print number of
# digits
def findNumberOfDigits(n, base):

    # Calculating log using base
    # changing property and then
    # taking it floor and then
    # adding 1.
    dig = (math.floor(math.log(n) /
                 math.log(base)) + 1)

    # printing output
    print ("The Number of digits of"
      " Number {} in base {} is {}"
            . format(n, base, dig))

# Driver method

# taking inputs
n = 1446
base = 7

# calling the method
findNumberOfDigits(n, base)

# This code is contributed by
# Manish Shaw (manishshaw1)

C

// C# program to Find Number of digits
// in base b.
using System;

class GFG {

    // function to print number of
    // digits
    static void findNumberOfDigits(long n,
                                    int b)
    {
        // Calculating log using base
        // changing property and then
        // taking it floor and then
        // adding 1.
        int dig = (int)(Math.Floor(
          Math.Log(n) / Math.Log(b)) + 1);

        // printing output
        Console.Write("The Number of digits"
           + " of Number " + n + " in base "
                        + b + " is " + dig);
    }

    // Driver method
    public static void Main()
    {
        // taking inputs
        long n = 1446;
        int b = 7;

        // calling the method
        findNumberOfDigits(n, b);
    }
}

// This code is contributed by Manish Shaw
// (manishshaw1)

服务器端编程语言（Professional Hypertext Preprocessor 的缩写）

<?php
// PHP program to Find Number
// of digits in base b.

// function to print
// number of digits
function findNumberOfDigits($n, $b)
{
    // Calculating log using base
    // changing property and then
    // taking it floor and then
    // adding 1.
    $dig = (int)(floor(log($n) /
                       log($b)) + 1);

    // printing output
    echo ("The Number of digits".
               " of Number ". $n.
                  " in base ".$b.
                    " is ".$dig);
}

// Driver Code
$n = 1446;
$b = 7;

// calling the method
findNumberOfDigits($n, $b);

// This code is contributed by
// Manish Shaw (manishshaw1)
?>

java 描述语言

<script>

// Javascript program to Find Number of digits
// in base b.

// function to print number of
// digits
function findNumberOfDigits(n, base)
{
    // Calculating log using base
    // changing property and then
    // taking it floor and then
    // adding 1.
    var dig = parseInt(Math.floor( Math.log(n) /
                        Math.log(base)) + 1);

    // printing output
    document.write("The Number of digits of "
        + "Number " + n + " in base "
        + base + " is " + dig);
}

// Driver method

// taking inputs
var n = 1446;
var base = 7;

// calling the method
findNumberOfDigits(n, base);

</script>

输出:

The Number of digits of Number 1446 in base 7 is 4

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