Topcoder 463 Div 2 1000

Topcoder 463 Div 2 1000

Problem Statement
	Taro and Hanako are playing a game called Nisoku, which is played as follows. Initially, there is a pile of cards. Each card contains a real number between 1.5 and 10.0, inclusive. You are given a vector <double> cards, the i-th element of which is the number written on the i-th card. Repeat the following step until there is only one card left in the pile: Remove any two cards from the pile, and add one new card to the pile. Write either a+b or a*b on the new card, where a and b are the numbers written on the two cards that were removed. Return the maximal possible number written on the final card in the pile.
Definition
	Class: Nisoku Method: theMax Parameters: vector <double> Returns: double Method signature: double theMax(vector <double> cards) (be sure your method is public)
Notes
-	Your return value must have an absolute or relative error less than 1e-9.
Constraints
-	cards will contain between 2 and 50 elements, inclusive.
-	Each element of cards will be between 1.5 and 10.0, inclusive.
Examples
0)
	{5, 8} Returns: 40.0 5 * 8 = 40.
1)
	{1.5, 1.8} Returns: 3.3 1.5 + 1.8 = 3.3.
2)
	{8.26, 7.54, 3.2567} Returns: 202.82857868
3)
	{1.5, 1.7, 1.6, 1.5} Returns: 9.920000000000002
4)
	{10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10} Returns: 1.0E50 The answer can be extremely big.

发现偶还是太水了。。。

#include < iostream >
#include < algorithm >
#include < vector >
using   namespace  std;



class  Nisoku
{
public:
    double theMax(vector<double>cards)
    {    
        int i,j;
        sort(cards.begin(),cards.end());
        double ans=0;
        for(i=0;i<=cards.size();i+=2)
        {
            double p=1;
            for(j=0;j<i/2;j++)
                p*=(cards[j]+cards[i-1-j]);
            for(j=i;j<cards.size();j++)
                p*=cards[j];
            ans=max(ans,p);
        }
        return ans;
    }
} ;

谁能证明下这份代码的正确性？