Je-li dané číslo n, najděte prvních k číslic nnkde k je hodnota menší než počet číslic v nn
Příklady:
10 procent ze 60
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
Problém lze vyřešit několika způsoby, z nichž dva jsou:
Metoda 1 (jednoduchá): Naivní metoda, která zahrnuje výpočet skutečné hodnoty a následné dělení 10, dokud nezískáme požadovanou odpověď. Tato metoda však nemůže mít vstup větší než n = 15, protože by to způsobilo přetečení.
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>
výstup:
4378
Metoda 2: Další metoda zahrnuje použití logaritmů k výpočtu prvních k číslic. Způsob a kroky jsou vysvětleny níže:
- Nechť součin = nn. Vezměte logaritmus se základem 10 na obou stranách rovnice. Dostáváme log10(produkt) = log10(nn), který můžeme také napsat jako n*log10(n)
- V tomto příkladu dostaneme log10(produkt) = 3871,137516. Můžeme rozdělit RHS jako 3871 + 0,137516, takže naši rovnici lze nyní zapsat jako log10(produkt) = 3871 + 0,137516
- Zvedněte obě strany se základnou 10 a pomocí výše uvedeného příkladu dostaneme součin = 103871x 100,137516. 103871nebude mít vliv na našich prvních k číslic, protože pouze posouvá desetinné čárky. Máme zájem o další díl 100,137516protože to určí prvních několik číslic.
V tomto případě hodnota 100,137516je 1,37251. - Našich požadovaných prvních 5 číslic by tedy bylo 13725.
//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>
výstup:
962948
Tento kód běží v konstantním čase a dokáže zpracovat velké vstupní hodnoty n
math.pow javaVytvořit kvíz