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Donat un nombre n, trobeu els primers k dígits de n^n

Donat un nombre n, trobeu els primers k dígits de nnon k és un valor menor que el nombre de dígits en nn 
Exemples:
 

   Input :    n = 10 k = 2    Output :   10 The first 2 digits in 1010 are 10.    Input :    n = 144 k = 6    Output :   637087    Input:    n = 1250 k = 5    Output:    13725 


 


El problema es pot resoldre de diverses maneres, de les quals dues són:
Mètode 1 (simple): Un mètode ingenu que consisteix a calcular el valor real i després dividir per 10 fins a obtenir la resposta requerida. No obstant això, aquest mètode no pot prendre una entrada superior a n = 15, ja que provocaria un desbordament. 
 



C++
// C++ program to find the first k digits of n^n #include    using namespace std; // function that manually calculates n^n and then // removes digits until k digits remain unsigned long long firstkdigits(int n int k) {  unsigned long long product = 1;  for (int i = 0 ; i < n ; i++)  product *= n;  // loop will terminate when there are only  // k digits left  while ((int)(product / pow(10 k)) != 0)  product = product / 10;  return product; } //driver function int main() {  int n = 15;  int k = 4;  cout << firstkdigits(n k);  return 0; } 
Java
// Java program to find the first k digits of n^n public class Digits {  // function that manually calculates n^n and then  // removes digits until k digits remain  static long firstkdigits(int n int k)  {  long product = 1;  for (int i = 0 ; i < n ; i++)  product *= n;    // loop will terminate when there are only  // k digits left  while ((int)(product / Math.pow(10 k)) != 0)  product = product / 10;  return product;  }    public static void main(String[] args)  {  int n = 15;  int k = 4;  System.out.println(firstkdigits(n k));  } } //This code is contributed by Saket Kumar 
Python 3
# Python 3 program to find the  # first k digits of n^n # function that manually calculates  # n^n and then removes digits until # k digits remain def firstkdigits(n k): product = 1 for i in range(n ): product *= n # loop will terminate when there  # are only k digits left while ((product // pow(10 k)) != 0): product = product // 10 return product # Driver Code n = 15 k = 4 print(firstkdigits(n k)) # This code is contributed  # by ChitraNayal 
C#
// C# program to find the // first k digits of n^n using System; class Digits {  // function that manually calculates  // n^n and then removes digits until  // k digits remain  static long firstkdigits(int n int k)  {  long product = 1;  for (int i = 0 ; i < n ; i++)  product *= n;    // loop will terminate when there   // are only k digits left  while ((int)(product / Math.Pow(10 k)) != 0)  product = product / 10;    return product;  }    // Driver code  public static void Main()  {  int n = 15;  int k = 4;  Console.Write(firstkdigits(n k));  } } // This code is contributed by nitin mittal. 
PHP
 // PHP program to find the // first k digits of n^n // function that manually  // calculates n^n and then // removes digits until k // digits remain function firstkdigits($n $k) { $product = 1; for ($i = 0 ; $i < $n ; $i++) $product *= $n; // loop will terminate when  // there are only k digits left while ((int)($product / pow(10 $k)) != 0) $product = (int) $product / 10; return floor($product); } // Driver Code $n = 15; $k = 4; echo firstkdigits($n $k); // This code is contributed by aj_36 ?> 
JavaScript
<script> // Javascript program to find the first k digits of n^n    // function that manually calculates n^n and then  // removes digits until k digits remain  function firstkdigits(nk)  {  let product = 1;  for (let i = 0 ; i < n ; i++)  product *= n;    // loop will terminate when there are only  // k digits left  while (Math.floor(product / Math.pow(10 k)) != 0)  product = Math.floor(product / 10);  return product;  }    let n = 15;  let k = 4;  document.write(firstkdigits(n k));    // This code is contributed by avanitrachhadiya2155 </script> 

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Mètode 2: El següent mètode consisteix a utilitzar logaritmes per calcular els primers k dígits. El mètode i els passos s'expliquen a continuació:
 

  1. Sigui producte = nn. Prengui el logaritme de base 10 a ambdós costats de l'equació. Rebem el registre10(producte) = registre10(nn) que també podem escriure com a n*log10(n)
  2. En aquest exemple obtenim el registre10(producte) = 3871,137516. Podem dividir el RHS com a 3871 + 0,137516, de manera que la nostra equació ara es pot escriure com a log10(producte) = 3871 + 0,137516
  3. Aixequeu els dos costats amb base 10 i utilitzant l'exemple anterior obtenim producte = 103871x 100,137516. 103871no marcarà cap diferència amb els nostres primers k dígits, ja que només desplaça els punts decimals. Ens interessa la següent part 100,137516ja que això determinarà els primers dígits. 
    En aquest cas el valor de 100,137516és 1,37251.
  4. Per tant, els nostres primers 5 dígits necessaris serien 13725.


 

C++
//C++ program to generate first k digits of // n ^ n #include    using namespace std; // function to calculate first k digits // of n^n long long firstkdigits(int nint k) {  //take log10 of n^n. log10(n^n) = n*log10(n)  long double product = n * log10(n);  // We now try to separate the decimal and  // integral part of the /product. The floor  // function returns the smallest integer  // less than or equal to the argument. So in  // this case product - floor(product) will  // give us the decimal part of product  long double decimal_part = product - floor(product);  // we now exponentiate this back by raising 10  // to the power of decimal part  decimal_part = pow(10 decimal_part);  // We now try to find the power of 10 by which  // we will have to multiply the decimal part to  // obtain our final answer  long long digits = pow(10 k - 1) i = 0;  return decimal_part * digits; } // driver function int main() {  int n = 1450;  int k = 6;  cout << firstkdigits(n k);  return 0; } 
Java
// Java program to find the first k digits of n^n import java.util.*; import java.lang.*; import java.io.*; class KDigitSquare {  /* function that manually calculates   n^n and then removes digits until   k digits remain */  public static long firstkdigits(int n int k)  {  //take log10 of n^n.   // log10(n^n) = n*log10(n)  double product = n * Math.log10(n);    /* We will now try to separate the decimal   and integral part of the /product. The   floor function returns the smallest integer  less than or equal to the argument. So in  this case product - floor(product) will  give us the decimal part of product */  double decimal_part = product - Math.floor(product);    // we will now exponentiate this back by   // raising 10 to the power of decimal part  decimal_part = Math.pow(10 decimal_part);    /* We now try to find the power of 10 by   which we will have to multiply the decimal   part to obtain our final answer*/  double digits = Math.pow(10 k - 1) i = 0;    return ((long)(decimal_part * digits));  }  // driver function  public static void main (String[] args)  {  int n = 1450;  int k = 6;  System.out.println(firstkdigits(nk));  } } /* This code is contributed by Mr. Somesh Awasthi */ 
Python3
# Python3 program to generate k digits of n ^ n  import math # function to calculate first k digits of n^n  def firstkdigits(n k): # take log10 of n^n. # log10(n^n) = n*log10(n) product = n * math.log(n 10); # We now try to separate the decimal  # and integral part of the /product. # The floor function returns the smallest  # integer less than or equal to the argument.  # So in this case product - floor(product)  # will give us the decimal part of product decimal_part = product - math.floor(product); # we now exponentiate this back # by raising 10 to the power of # decimal part decimal_part = pow(10 decimal_part); # We now try to find the power of 10 by  # which we will have to multiply the  # decimal part to obtain our final answer digits = pow(10 k - 1); return math.floor(decimal_part * digits); # Driver Code  n = 1450; k = 6; print(firstkdigits(n k)); # This code is contributed by mits 
C#
// C# program to find the first k digits of n^n using System; class GFG {    /* function that manually calculates   n^n and then removes digits until   k digits remain */  public static long firstkdigits(int n int k)  {    // take log10 of n^n.   // log10(n^n) = n*log10(n)  double product = n * Math.Log10(n);    /* We will now try to separate the decimal   and integral part of the /product. The   floor function returns the smallest integer  less than or equal to the argument. So in  this case product - floor(product) will  give us the decimal part of product */  double decimal_part = product -  Math.Floor(product);    // we will now exponentiate this back by   // raising 10 to the power of decimal part  decimal_part = Math.Pow(10 decimal_part);    /* We now try to find the power of 10 by   which we will have to multiply the decimal   part to obtain our final answer*/  double digits = Math.Pow(10 k - 1);    return ((long)(decimal_part * digits));  }  // driver function  public static void Main ()  {  int n = 1450;  int k = 6;  Console.Write(firstkdigits(nk));  } } // This code is contributed by nitin mittal 
PHP
 // PHP program to generate  // k digits of n ^ n // function to calculate  // first k digits of n^n function firstkdigits($n $k) { // take log10 of n^n.  // log10(n^n) = n*log10(n) $product = $n * log10($n); // We now try to separate the  // decimal and integral part  // of the /product. The floor  // function returns the smallest  // integer less than or equal to  // the argument. So in this case // product - floor(product) will  // give us the decimal part of product $decimal_part = $product - floor($product); // we now exponentiate this back  // by raising 10 to the power of // decimal part $decimal_part = pow(10 $decimal_part); // We now try to find the power  // of 10 by which we will have  // to multiply the decimal part  // to obtain our final answer $digits = pow(10 $k - 1); $i = 0; return floor($decimal_part * $digits); } // Driver Code $n = 1450; $k = 6; echo firstkdigits($n $k); // This code is contributed by m_kit ?> 
JavaScript
<script> // Javascript program to find the first k digits of n^n    /* function that manually calculates   n^n and then removes digits until   k digits remain */  function firstkdigits(nk)  {  //take log10 of n^n.   // log10(n^n) = n*log10(n)  let product = n * Math.log10(n);    /* We will now try to separate the decimal   and integral part of the /product. The   floor function returns the smallest integer  less than or equal to the argument. So in  this case product - floor(product) will  give us the decimal part of product */  let decimal_part = product - Math.floor(product);    // we will now exponentiate this back by   // raising 10 to the power of decimal part  decimal_part = Math.pow(10 decimal_part);    /* We now try to find the power of 10 by   which we will have to multiply the decimal   part to obtain our final answer*/  let digits = Math.pow(10 k - 1) i = 0;    return (Math.floor(decimal_part * digits));  }    // Driver code  let n = 1450;  let k = 6;  document.write(firstkdigits(n k));    // This code is contributed by rag2127 </script> 

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Aquest codi s'executa en temps constant i pot gestionar grans valors d'entrada de n
 

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