检查b基中的数字N是否以1开头-yiteyi-C++库

给定一个数字N和基数b，如果基数b表示中的N以1开头，则打印是，否则打印否

null

例如：

Input : n = 6, b = 4Output : Yes6 can be written as  in base 4so answer is Yes as it starts with 1Input : n = 24, b = 2Output : Yes24 can be written as  in base 2so answer is Yes as it starts with 1Input :  n = 24, b = 7Output : No24 can be written as  in base 7so answer is No as it starts with 3

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

当一个数字N以基数“b”表示时，它会被转换为m+1长度序列 $b_{m}$ [Tex]b_{m-1}[/Tex]…。。 $b_0$ 这意味着 $b_{m}$ * $b^{m}$ + $b_{m-1}$ * $b^{m-1}$ …..+ $b_0$ * $b^0$ =N

以b为基数，以“1”开头的最小数字，即100。。00和m+1数字的基数为 $b^{m}$ 最大的数字是2* $b^{m}$ -1.所以N应该在这个范围内。 $b^{m}$ <=N<=2* $b^{m}$ -1 另一件需要注意的事情是，m不能超过地板( $log_2$ （N））因为当我们用基数2表示任何数字时，它会被转换成一个只有1和0的序列，所以这个序列的长度总是大于任何其他基数表示，它的长度将等于0( $log_2$ （N））+1。

所以，为了检查给定的基数“b”，如果N以1开头，我们将从m=1遍历到m=floor( $log_2$ （N））并检查是否有MN在该范围内 $b^{m}$ <=N<=2* $b^{m}$ -1或否，并相应地打印“是”或“否”。

C++

                         // C++ program to check if number starts with                       
                         // one in base b representation                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Returns true if n starts with  1 in                       
                         // base b representation                       
                         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 representation                       
                                                 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 representation                       
                         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;                       
           
                         class                                     GFG{                       
                                   
                         // Returns true if n starts with 1 in                       
                         // base b representation                       
                         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 code                       
                         public                                     static                                     void                                     Main(String []args)                       
                         {                       
                                                 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 Princi Singh                       

PHP

                         <?php                       
                         // PHP program to check if                       
                         // number starts with one                       
                         // in base b representation                       
           
                         // Returns true if n starts                       
                         // with 1 in base b representation                       
                         function                                     CheckIfstartsWithOne(                                     $n                                     ,                                     $b                                     )                       
                         {                       
                                                 // highest m can be log2(n)                       
                                                 $m                                     = log(                                     $n                                     , 2);                       
                                                 for                                     (                                     $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                       
                         function                                     printYesORno(                                     $n                                     ,                                     $b                                     )                       
                         {                       
                                                 if                                     (CheckIfstartsWithOne(                                     $n                                     ,                                     $b                                     ) == true)                       
                                                 echo                                     "Yes"                                     ,                                     ""                                     ;                       
                                                 else                                     if                                     (CheckIfstartsWithOne(                                     $n                                     ,                                     $b                                     ) == false)                       
                                                 echo                                     "No"                                     ,                                     ""                                     ;                       
                         }                       
           
                         // Driver Code                       
                         printYesORno(6, 4);                       
                         printYesORno(24, 2);                       
                         printYesORno(24, 7);                       
                         printYesORno(24, 15);                       
           
                         // This code is contributed by ajit                       
                         ?>                       

Javascript

                         <script>                       
                                                 // Javascript program to check if number starts                       
                                                 // with one in base b representation                       
                                   
                                                 // Returns true if n starts with                       
                                                 // 1 in base b representation                       
                                                 function                                     CheckIfstartsWithOne(n, b)                       
                                                 {                       
                                   
                                                 // highest m can be log2(n)                       
                                                 let m = parseInt(Math.log10(n) / Math.log10(2), 10);                       
                                   
                                                 for                                     (let i = 1; i <= m; i++)                       
                                                 {                       
                                   
                                                 // if b^m <= N <= 2*b^m - 1,                       
                                                 // return true                       
                                                 if                                     (n >= Math.pow(b, i) && n <= 2 * Math.pow(b, i) - 1)                       
                                                 return                                     true                                     ;                       
                                                 }                       
                                   
                                                 return                                     false                                     ;                       
                                                 }                       
                                   
                                                 document.write(CheckIfstartsWithOne(6, 4) ?                                     "Yes"                                     +                                     "</br>"                                     :                                     "No"                                     +                                     "</br>"                                     );                       
                                   
                                                 document.write(CheckIfstartsWithOne(24, 2) ?                                     "Yes"                                     +                                     "</br>"                                     :                                     "No"                                     +                                     "</br>"                                     );                       
           
                                                 document.write(CheckIfstartsWithOne(24, 7) ?                                     "Yes"                                     +                                     "</br>"                                     :                                     "No"                                     +                                     "</br>"                                     );                       
           
                                                 document.write(CheckIfstartsWithOne(24, 15) ?                                     "Yes"                                     :                                     "No"                                     );                       
                                   
                         </script>                       

输出：

YesYesNoYes

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