题目内容
Suppose we are given an instance of the $s-t$ shortest path problem on a directed graph $G$. We assume that all edge cost are positive and distinct. Let $P$ be a minimum-cost $s-t$ path for this instance.Now suppose we replace each edge cost $c_e $ by its square, $c_e^2 $, thereby creating a new instance of the problem with the same graph but different costs.\newlineDecide whether you think the following statement is true or false.\newline$P$ must still be a minimum-cost $s-t$ path for this new instance.
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