单选题：In the bin packing problem, suppose that the maximum size of the

In the bin packing problem, suppose that the maximum size of the items is bounded from above by $$\alpha < 1$$. Now let's apply the Next Fit algorithm to pack a set of items $$L$$ into bins with capacity 1. Let $$NF(L)$$ and $$OPT(L)$$ denote the numbers of bins used by algorithms Next Fit and the optimal solution. Then for all $$L$$, we have $$ NF(L) < \rho \cdot OPT(L) + 1$$ for some $$ \rho$$. Which one of the following statements is FALSE? @[D](3)

A. $$\rho = \frac{1}{1- \alpha} $$, if $$ 0 \leq \alpha \leq 1/2$$.
B. $$\rho = 2 $$, if $$ \alpha > 1/2$$.
C. If $$L$$ = (0.5, 0.3, 0.4, 0.8, 0.2, 0.3), then $$NF(L) = 4$$.
D. $$ \rho= 2 \alpha$$ if $$ 0 \leq \alpha \leq 1$$





A.$$\rho = \frac{1}{1- \alpha} $$, if $$ 0 \leq \alpha \leq 1/2$$.
B.$$\rho = 2 $$, if $$ \alpha > 1/2$$.
C.If $$L$$ = (0.5, 0.3, 0.4, 0.8, 0.2, 0.3), then $$NF(L) = 4$$.
D.$$ \rho= 2 \alpha$$ if $$ 0 \leq \alpha \leq 1$$


答案：D