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联系和发展的观点是( )的总观点和总特征。
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For any instance of 3-SAT, there exists a truth assignment that satisfies at least a 7/8 fraction of all clauses.
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.
Decide whether you think the following statements are true or false.Let [mathjaxinline]G[/mathjaxinline] be an arbitrary connected, undirected graph with a distinct cost on every edge. Suppose [mathjaxinline]e[/mathjaxinline] is the cheapest edge in [mathjaxinline]G[/mathjaxinline]. Then, there is a minimum spanning tree of [mathjaxinline]G[/mathjaxinline] that contains the edge [mathjaxinline]e[/mathjaxinline].
Given a MAX 3-SAT formula $\Phi$ with k clauses, we show that the expected number of clauses satisfied by a random assignment is 7k/8. Consider a random assignment for formula $\Phi \wedge \bar{\Phi}$, the expected number of clauses satisfied is _____.
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