Nth Root Of Number

 

                Finding of Nth root can be done with following methods. Nth root is similar to find the
cube root of any Number, we can apply same methods with modification to find Nth root.

 

Calculate Cube Root Of any number

         
       For Calculating Cube root of N, We have straight forward method for checking all range like 0 to N with points with the difference of Accuracy we want. ISuppose we want to find Out Cube root of 3 with accuracy up to 5 decimal points, Then we have to check 0 to 3 with each time addition of 0.00001 (because we want 5 decimal accuracy) until we click right answer.

Analysis of Algorithm

                CubeRoot (3) = 1.44225

                                For click right answer loop must be run (1.44225 – 0)/0.00001 times which is  144225 times. For analysis purpose, let's assume loop go up to 3 So loop run 3/0.00001 times which is 300000 times.

                Implementation this algorithm in C/C++.

Efficient Method Of Calculating Cube root of any number

 

                If we apply binary search ( If you don’t know about Binary Search, Click here ) to the whole range of possible cubic root, then we can decrease significant loop count.

Analysis Of Algorithm with Binary Search

                CubeRoot(3) = 1.44225

                                For Analysis of this algorithm, let's take boundary case, which is whole range 0 to 3 with 0.00001 which means loop count range is 0 to 300000 times. BUT binary search has Time Complexity of log2 (N) here N=300000.

                So

                                Loop Count of CubeRootUsingBinarySearch(3) = log2 (300000)

                                                                                                                           = 18.19

                                                                                                                          ~ 19 (Because we want Upper limit)

                Now if we compare with former algorithm’s loop count which is 300000 and with binary search we make it 19.Implementation Of Cubic Root with Binary Search in C/C++. These function which is given here can be modified to find Nth root of any number.