检查数字N是否以b为基础以1开头

给定数字N和基数b，如果基数b表示中的N以1打印开始，则为其他，打印否
例子 ：

输入：n = 6，b = 4输出：是6可以写成$12_4$在基数4中，所以答案是肯定的，因为它以1开头输入：n = 24，b = 2输出：是，可以将24表示为$11000_2$在基数2中，所以答案是肯定的，因为它以1开头输入：n = 24，b = 7输出：否24可以写为$33_7$在基数7中，所以答案是“否”，因为它以3开头

当数字N以基数’b’表示时，它将转换为m + 1个长度序列$b_{m}$$b_{m-1}$ ….. $b_0$这意味着$b_{m}$ * $b^{m}$ + $b_{m-1}$ * $b^{m-1}$ ….. + $b_0$ * $b^0$ = N
基数b中最小的数字，以’1’开头，即基数为100..00和m + 1个数字为$b^{m}$
最大数量是2 * $b^{m}$ -1。因此N应该在此范围内。
$b^{m}$ <= N <= 2 * $b^{m}$ -1
现在要注意的另一点是，m不能超过楼板数( $log_2$ (N))因为当我们在base-2中表示任何数字时，它将转换为仅1和0的序列，因此此序列的长度将始终大于任何其他基本表示形式，并且其长度将等于floor( $log_2$ ((N))+ 1。
因此，要检查给定的基数“ b”(如果N开头不是1)，我们将从m = 1遍历到m = floor( $log_2$ (N))，并检查是否有m N处于该范围内$b^{m}$ <= N <= 2 * $b^{m}$ -1或否，并因此打印“是”或“否”。

C++

// C++ program to check if number starts with
// one in base b representation
#include 
using namespace std;
  
// Returns true if n starts with  1 in
// base b represenation
bool CheckIfstartsWithOne(int n, int b)
{
    // highest m can be log2(n)
    int m = log2(n);
    for (int i = 1; i <= m; i++) {
        // if b^m <= N <= 2*b^m - 1,
        // return true
        if (n >= pow(b, i) && n <= 2 * pow(b, i) - 1)
            return true;
    }
    return false;
}
  
// printing yes or no
void printYesORno(int n, int b)
{
    if (CheckIfstartsWithOne(n, b) == true)
        cout << "Yes" << endl;
    else if (CheckIfstartsWithOne(n, b) == false)
        cout << "No" << endl;
}
  
// driver function
int main()
{
    printYesORno(6, 4);
    printYesORno(24, 2);
    printYesORno(24, 7);
    printYesORno(24, 15);
}

Java

// Java program to check if number starts with
// one in base b representation
  
class GFG {
      
    // Returns true if n starts with 1 in
    // base b represenation
    static boolean CheckIfstartsWithOne(int n, int b)
    {
          
        // highest m can be log2(n)
        int m = (int)(Math.log10(n) / Math.log10(2));
        for (int i = 1; i <= m; i++) {
              
            // if b^m <= N <= 2*b^m - 1,
            // return true
            if (n >= (int)Math.pow(b, i) &&
                n <= 2 * (int)Math.pow(b, i) - 1)
                return true;
        }
          
        return false;
    }
  
    // Driver method
    public static void main(String args[])
    {
        System.out.println(
           CheckIfstartsWithOne(6, 4) ? "Yes" : "No");
             
        System.out.println(
           CheckIfstartsWithOne(24, 2) ? "Yes" : "No");
             
        System.out.println(
           CheckIfstartsWithOne(24, 7) ? "Yes" : "No");
             
        System.out.println(
           CheckIfstartsWithOne(24, 15) ? "Yes" : "No");
    }
}

Python3

# Python3 program to check 
# if number starts with one
# in base b representation
import math
  
# Returns true if n 
# starts with 1 in 
# base b represenation
def CheckIfstartsWithOne(n, b):
      
    # highest m can be log2(n)
    m = (int)(math.log2(n));
    for i in range (1, m + 1):
          
        # if b^m <= N <= 2*b^m - 1,
        #return true
        x = (int)(math.pow(b, i));
        if n >= x and n <= 2 * x - 1:
            return 1;
    return 0;
  
# printing yes or no
def printYesORno(n, b):
    if CheckIfstartsWithOne(n, b) == 1:
        print("Yes");
    if CheckIfstartsWithOne(n, b) == 0:
        print("No");
          
# Driver Code
printYesORno(6, 4);
printYesORno(24, 2);
printYesORno(24, 7);
printYesORno(24, 15);
  
# This code is contributed by mits.

C#

// C# program to check if number starts
// with one in base b representation
using System;
  
public class GFG {
      
    // Returns true if n starts with
    // 1 in base b represenation
    static bool CheckIfstartsWithOne(int n, int b)
    {
          
        // highest m can be log2(n)
        int m = (int)(Math.Log10(n) / Math.Log10(2));
          
        for (int i = 1; i <= m; i++)
        {
              
            // if b^m <= N <= 2*b^m - 1,
            // return true
            if (n >= (int)Math.Pow(b, i) && 
                   n <= 2 * (int)Math.Pow(b, i) - 1)
                return true;
        }
          
        return false;
    }
  
    // Driver method
    public static void Main()
    {
        Console.WriteLine(
           CheckIfstartsWithOne(6, 4) ? "Yes" : "No");
             
        Console.WriteLine(
           CheckIfstartsWithOne(24, 2) ? "Yes" : "No");
             
        Console.WriteLine(
           CheckIfstartsWithOne(24, 7) ? "Yes" : "No");
             
        Console.WriteLine(
           CheckIfstartsWithOne(24, 15) ? "Yes" : "No");
    }
}
  
// This code is contributed by Sam007.

PHP

= pow($b, $i) && 
                $n <= 2 * pow($b, $i) - 1)
            return true;
    }
    return false;
}
  
// printing yes or no
function printYesORno($n, $b)
{
    if (CheckIfstartsWithOne($n, $b) == true)
        echo "Yes" ,"\n";
    else if (CheckIfstartsWithOne($n, $b) == false)
        echo "No" ,"\n";
}
  
// Driver Code
printYesORno(6, 4);
printYesORno(24, 2);
printYesORno(24, 7);
printYesORno(24, 15);
  
// This code is contributed by ajit 
?>

输出 ：

Yes
Yes
No
Yes