For an algorithm with a running time of N * n, the algorithm with a running time of 2 ^ n runs very fast on the same machine. What is the minimum value of n?

In 《AlgorithmIn the first part of the introduction, there is an algorithm question:

 
1.2-3 for an algorithm with a running time of N x N, the algorithm with a running time of 2 ^ n needs to run quickly on the same machine, what is the minimum value of n?
 

The following provides my own solutions:

 
For the comparison between 100n ^ 2 and 2 ^ n algorithms, we can do this: for the 100n ^ 2-2 ^ n operation, if the result is less than 0, then, n is the value we want.
 

The following algorithm implementation is provided for this idea:

 1   /**  2   *  3    */  4   Package  Com. b510.algorithms;  5  6   /**  7   * Introduction to algorithms Part 1: Exercise 1.2-3: For an algorithm with a running time of 100n ^ 2, make it on the same machine, returns the result of a 2 ^ n running time.  8   * The method runs faster. What is the minimum value of n?  9   *  10   *  @ Author  Hong (hongtenzone@foxmail.com) <br>  11   * @ Date 2013-6-6  12    */ 13   Public   Class  Partoneofalgorithms {  14   15       Public   Static   Void  Main (string [] ARGs ){  16   Getsum ();  17   }  18   19       /** 20   * To compare the 100n ^ 2 and 2 ^ n algorithms, we can perform the 100n ^ 2-2 ^ n operation. If the result is smaller than 0, then, n is the value we want.  21   * In Java, evaluate the N power of a number by using math. Pow (x, y), that is, the y power of X.  22        */  23       Public   Static   Void  Getsum (){  24           Int N = 1 ;  25          Long Sum = 0 ;  26           Boolean Flag = True  ;  27           While  (FLAG ){  28 Sum = ( Long ) (100 * (math. Pow (n, 2)-math. Pow (2 , N ));  29 System. Out. println ("nth" + N + "Calculation Result:" + Sum ); 30               If (Sum <0 ){  31 Flag = False  ;  32                   Break  ;  33   }  34 N = n + 1 ;  35   }  36  System. Out. println (N );  37   }  38 }

Running effect:

1st calculation results: 98The 2nd calculation result is:396The 3rd calculation result is:892The 4th calculation result is:1584The 5th calculation result is:2468The 6th calculation result is:3536The 7th calculation result is:4772The 8th calculation result is:6144The 9th calculation result is:7588The 10th calculation result is:8976The 11th calculation result is:10052The 12th calculation result is:10304The 13th calculation result is:8708The 14th calculation result is:3216The 15th calculation result is:-1026815