[LintCode] Backpack

Given n items with size A[i], an integer m denotes the size of a backpack. How full you can fill this backpack? 

Example

If we have 4 items with size [2, 3, 5, 7], the backpack size is 11, we can select 2, 3 and 5, so that the max size we can fill this backpack is 10. If the backpack size is 12. we can select [2, 3, 7] so that we can fulfill the backpack.

You function should return the max size we can fill in the given backpack.

Note

You can not divide any item into small pieces.

Analysis:
We can say all the possible sums that are smaller than m. The biggest one is the result.

class Solution {
public:
    int backPack(int m, vector<int> A) {
        // write your code here
        int len = A.size();
        vector<bool> size(m+1,false);
        size[0] = true;
        
        for (int i=0;i<len;i++)
        {
            for (int j=m;j>=A[i];j--)
            {
                if (size[j-A[i]])
                    size[j] = true;
            }
        }
        int i = m;
        while(!size[i]) i--;
        return i;
    }
};