题目内容
We have a function $f(x)=2x^2-9x+3$. We want to get the minimize value of $f$ and define neighbors of $x$ are $x-1$ and $x+1$. We start at $x = 0$. The algorithm finds a local optimum at $x$ =_____.
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Decide whether you think the following statement is true or false. Let $G$ be an arbitrary flow network, with a source $s$, a sink $t$, and a positive integer capacity $c_e$ on every edge $e\ $. Let $(A, B) $ be a mimimum $s-t$ cut with respect to these capacities $\{c_e: e\in E\}$. Now suppose we add $1$ to every capacity, then $(A, B) $ is still a minimum $s-t$ cut with respect to these new capacities $\{1+c_e: e\in E\}$.
Coin is heads with probability 1/3 and tails with probability 2/3. The expectation of independent flips until first heads is _____.
Decide whether you think the following statement is true or false. Let $G$ be an arbitrary flow network, with a source $s$, a sink $t$, and a positive integer capacity $c_e$ on every edge $e\ $. If $f\ $ is a maximum $s-t$ flow in $G\ $, then $f$ saturates every edge out of $s$ with flow (i.e., for all edges $e$out of $s$, we have$ f (e) = c_e$).
Gale-Shapley algorithm finds a stable matching in _____ time.
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