
Adva egy n számot, keresse meg az n kocka gyökerét.
Példák:
Input: n = 3 Output: Cubic Root is 1.442250 Input: n = 8 Output: Cubic Root is 2.000000
Ajánlott gyakorlat Egy szám kocka gyökere Próbáld ki!
Használhatunk bináris keresés - Először definiáljuk az E hibát. Tegyük fel, hogy a mi esetünkben 0,0000001. Algoritmusunk fő lépései az n szám köbös gyökérének kiszámításához:
- Inicializálja a start = 0 és a vég = n
- Számítsa ki a közepét = (Start + End)/2
- Ellenőrizze, hogy a (n - közepe*közepén*közepén) abszolút értéke< e. If this condition holds true then mid is our answer so return mid.
- If (közepén*közepén*közepén)> n Ezután állítsa be a végét = közepe
- If (*közepén**közepén)
Az alábbiakban bemutatjuk a fenti ötlet megvalósítását.
// C++ program to find cubic root of a number // using Binary Search #include using namespace std; // Returns the absolute value of n-mid*mid*mid double diff(double ndouble mid) { if (n > (mid*mid*mid)) return (n-(mid*mid*mid)); else return ((mid*mid*mid) - n); } // Returns cube root of a no n double cubicRoot(double n) { // Set start and end for binary search double start = 0 end = n; // Set precision double e = 0.0000001; while (true) { double mid = (start + end)/2; double error = diff(n mid); // If error is less than e then mid is // our answer so return mid if (error <= e) return mid; // If mid*mid*mid is greater than n set // end = mid if ((mid*mid*mid) > n) end = mid; // If mid*mid*mid is less than n set // start = mid else start = mid; } } // Driver code int main() { double n = 3; printf('Cubic root of %lf is %lfn' n cubicRoot(n)); return 0; }
Java // Java program to find cubic root of a number // using Binary Search import java.io.*; class GFG { // Returns the absolute value of n-mid*mid*mid static double diff(double ndouble mid) { if (n > (mid*mid*mid)) return (n-(mid*mid*mid)); else return ((mid*mid*mid) - n); } // Returns cube root of a no n static double cubicRoot(double n) { // Set start and end for binary search double start = 0 end = n; // Set precision double e = 0.0000001; while (true) { double mid = (start + end)/2; double error = diff(n mid); // If error is less than e then mid is // our answer so return mid if (error <= e) return mid; // If mid*mid*mid is greater than n set // end = mid if ((mid*mid*mid) > n) end = mid; // If mid*mid*mid is less than n set // start = mid else start = mid; } } // Driver program to test above function public static void main (String[] args) { double n = 3; System.out.println('Cube root of '+n+' is '+cubicRoot(n)); } } // This code is contributed by Pramod Kumar
Python3 # Python 3 program to find cubic root # of a number using Binary Search # Returns the absolute value of # n-mid*mid*mid def diff(n mid) : if (n > (mid * mid * mid)) : return (n - (mid * mid * mid)) else : return ((mid * mid * mid) - n) # Returns cube root of a no n def cubicRoot(n) : # Set start and end for binary # search start = 0 end = n # Set precision e = 0.0000001 while (True) : mid = (start + end) / 2 error = diff(n mid) # If error is less than e # then mid is our answer # so return mid if (error <= e) : return mid # If mid*mid*mid is greater # than n set end = mid if ((mid * mid * mid) > n) : end = mid # If mid*mid*mid is less # than n set start = mid else : start = mid # Driver code n = 3 print('Cubic root of' n 'is' round(cubicRoot(n)6)) # This code is contributed by Nikita Tiwari.
C# // C# program to find cubic root // of a number using Binary Search using System; class GFG { // Returns the absolute value // of n - mid * mid * mid static double diff(double n double mid) { if (n > (mid * mid * mid)) return (n-(mid * mid * mid)); else return ((mid * mid * mid) - n); } // Returns cube root of a no. n static double cubicRoot(double n) { // Set start and end for // binary search double start = 0 end = n; // Set precision double e = 0.0000001; while (true) { double mid = (start + end) / 2; double error = diff(n mid); // If error is less than e then // mid is our answer so return mid if (error <= e) return mid; // If mid * mid * mid is greater // than n set end = mid if ((mid * mid * mid) > n) end = mid; // If mid*mid*mid is less than // n set start = mid else start = mid; } } // Driver Code public static void Main () { double n = 3; Console.Write('Cube root of '+ n + ' is '+cubicRoot(n)); } } // This code is contributed by nitin mittal.
PHP // PHP program to find cubic root // of a number using Binary Search // Returns the absolute value // of n - mid * mid * mid function diff($n$mid) { if ($n > ($mid * $mid * $mid)) return ($n - ($mid * $mid * $mid)); else return (($mid * $mid * $mid) - $n); } // Returns cube root of a no n function cubicRoot($n) { // Set start and end // for binary search $start = 0; $end = $n; // Set precision $e = 0.0000001; while (true) { $mid = (($start + $end)/2); $error = diff($n $mid); // If error is less // than e then mid is // our answer so return mid if ($error <= $e) return $mid; // If mid*mid*mid is // greater than n set // end = mid if (($mid * $mid * $mid) > $n) $end = $mid; // If mid*mid*mid is // less than n set // start = mid else $start = $mid; } } // Driver Code $n = 3; echo('Cubic root of $n is '); echo(cubicRoot($n)); // This code is contributed by nitin mittal. ?>
JavaScript <script> // Javascript program to find cubic root of a number // using Binary Search // Returns the absolute value of n-mid*mid*mid function diff(n mid) { if (n > (mid*mid*mid)) return (n-(mid*mid*mid)); else return ((mid*mid*mid) - n); } // Returns cube root of a no n function cubicRoot(n) { // Set start and end for binary search let start = 0 end = n; // Set precision let e = 0.0000001; while (true) { let mid = (start + end)/2; let error = diff(n mid); // If error is less than e then mid is // our answer so return mid if (error <= e) return mid; // If mid*mid*mid is greater than n set // end = mid if ((mid*mid*mid) > n) end = mid; // If mid*mid*mid is less than n set // start = mid else start = mid; } } // Driver Code let n = 3; document.write('Cube root of '+n+' is '+cubicRoot(n)); </script>
Kimenet:
Cubic root of 3.000000 is 1.442250
Idő bonyolultsága: O (napló)
Kiegészítő hely: O (1)