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CS6515 Exam 2 with correct answers, Exams of Insurance law

North Carolina Central University (NCCU)Insurance law

CS6515 Exam 2 with correct answers

Typology: Exams

2024/2025

Available from 02/11/2025

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CS6515 Exam 2 with correct answers
If |!|graph |!|G |!|has |!|more |!|than |!||V |!|| |!|โˆ’ |!|1 |!|edges, |!|and |!|there |!|is |!|a |!|unique |!|heaviest |!|edge, |!|then |!|this |!|
edge |!|cannot |!|be |!|part |!|of |!|a |!|minimum |!|spanning |!|tree |!|- |!|correct |!|answer |!|โœ”False, |!|because |!|the |!|
unique |!|heaviest |!|edge |!|may |!|not |!|be |!|part |!|of |!|a |!|cycle
If |!|G |!|has |!|a |!|cycle |!|with |!|a |!|unique |!|heaviest |!|edge |!|e, |!|then |!|e |!|cannot |!|be |!|part |!|of |!|any |!|MST. |!|- |!|
correct |!|answer |!|โœ”True, |!|if |!|the |!|unique |!|heaviest |!|edge |!|is |!|part |!|of |!|a |!|cycle |!|then |!|it |!|will |!|be |!|
removed |!|first.
Let |!|e |!|be |!|any |!|edge |!|of |!|minimum |!|weight |!|in |!|G. |!|Then |!|e |!|must |!|be |!|part |!|of |!|some |!|MST. |!|- |!|correct
|!|answer |!|โœ”True, |!|in |!|order |!|create |!|the |!|MST |!|we |!|use |!|the |!|edges |!|with |!|minimum |!|weight.
If |!|the |!|lightest |!|edge |!|in |!|a |!|graph |!|is |!|unique, |!|then |!|it |!|must |!|be |!|part |!|of |!|every |!|MST. |!|- |!|correct |!|
answer |!|โœ”True, |!|we |!|always |!|choose |!|the |!|lightest |!|edge |!|when |!|building |!|the |!|MST.
If |!|e |!|is |!|part |!|of |!|some |!|MST |!|of |!|G, |!|then |!|it |!|must |!|be |!|a |!|lightest |!|edge |!|across |!|some |!|cut |!|of |!|G. |!|- |!|
correct |!|answer |!|โœ”True, |!|due |!|to |!|cut |!|property
If |!|G |!|has |!|a |!|cycle |!|with |!|a |!|unique |!|lightest |!|edge |!|e, |!|then |!|e |!|must |!|part |!|of |!|every |!|MST. |!|- |!|correct |!|
answer |!|โœ”False, |!|lightest |!|edge |!|in |!|a |!|cycle |!|may |!|not |!|be |!|necessary |!|to |!|create |!|an |!|MST |!|because |!|
the |!|remaining |!|edges |!|may |!|be |!|necessary |!|to |!|connect |!|to |!|the |!|other |!|vertices
The |!|shortest-path |!|tree |!|computed |!|by |!|Dijkstra's |!|algorithm |!|is |!|necessarily |!|an |!|MST |!|- |!|correct |!|
answer |!|โœ”False, |!|the |!|shortest |!|path |!|may |!|not |!|visit |!|all |!|the |!|nodes |!|in |!|the |!|MST |!|tree
The |!|shortest |!|path |!|between |!|two |!|nodes |!|is |!|necessarily |!|an |!|MST |!|- |!|correct |!|answer |!|โœ”False, |!|the |!|
shortest |!|path |!|between |!|two |!|nodes |!|may |!|not |!|visit |!|all |!|the |!|nodes |!|in |!|that |!|make |!|up |!|an |!|MST
If |!|G |!|contains |!|an |!|r-path |!|from |!|node |!|s |!|to |!|t, |!|then |!|every |!|MST |!|of |!|G |!|must |!|also |!|contain |!|an |!|r-
path |!|from |!|node |!|s |!|to |!|node |!|t.
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CS6515 Exam 2 with correct answers

If |!|graph |!|G |!|has |!|more |!|than |!||V |!|| |!|โˆ’ |!| 1 |!|edges, |!|and |!|there |!|is |!|a |!|unique |!|heaviest |!|edge, |!|then |!|this |!| edge |!|cannot |!|be |!|part |!|of |!|a |!|minimum |!|spanning |!|tree |!|- |!|correct |!|answer |!| โœ” False, |!|because |!|the |!| unique |!|heaviest |!|edge |!|may |!|not |!|be |!|part |!|of |!|a |!|cycle If |!|G |!|has |!|a |!|cycle |!|with |!|a |!|unique |!|heaviest |!|edge |!|e, |!|then |!|e |!|cannot |!|be |!|part |!|of |!|any |!|MST. |!|- |!| correct |!|answer |!| โœ” True, |!|if |!|the |!|unique |!|heaviest |!|edge |!|is |!|part |!|of |!|a |!|cycle |!|then |!|it |!|will |!|be |!| removed |!|first. Let |!|e |!|be |!|any |!|edge |!|of |!|minimum |!|weight |!|in |!|G. |!|Then |!|e |!|must |!|be |!|part |!|of |!|some |!|MST. |!|- |!|correct |!|answer |!| โœ” True, |!|in |!|order |!|create |!|the |!|MST |!|we |!|use |!|the |!|edges |!|with |!|minimum |!|weight. If |!|the |!|lightest |!|edge |!|in |!|a |!|graph |!|is |!|unique, |!|then |!|it |!|must |!|be |!|part |!|of |!|every |!|MST. |!|- |!|correct |!| answer |!| โœ” True, |!|we |!|always |!|choose |!|the |!|lightest |!|edge |!|when |!|building |!|the |!|MST. If |!|e |!|is |!|part |!|of |!|some |!|MST |!|of |!|G, |!|then |!|it |!|must |!|be |!|a |!|lightest |!|edge |!|across |!|some |!|cut |!|of |!|G. |!|- |!| correct |!|answer |!| โœ” True, |!|due |!|to |!|cut |!|property If |!|G |!|has |!|a |!|cycle |!|with |!|a |!|unique |!|lightest |!|edge |!|e, |!|then |!|e |!|must |!|part |!|of |!|every |!|MST. |!|- |!|correct |!| answer |!| โœ” False, |!|lightest |!|edge |!|in |!|a |!|cycle |!|may |!|not |!|be |!|necessary |!|to |!|create |!|an |!|MST |!|because |!| the |!|remaining |!|edges |!|may |!|be |!|necessary |!|to |!|connect |!|to |!|the |!|other |!|vertices The |!|shortest-path |!|tree |!|computed |!|by |!|Dijkstra's |!|algorithm |!|is |!|necessarily |!|an |!|MST |!|- |!|correct |!| answer |!| โœ” False, |!|the |!|shortest |!|path |!|may |!|not |!|visit |!|all |!|the |!|nodes |!|in |!|the |!|MST |!|tree The |!|shortest |!|path |!|between |!|two |!|nodes |!|is |!|necessarily |!|an |!|MST |!|- |!|correct |!|answer |!| โœ” False, |!|the |!| shortest |!|path |!|between |!|two |!|nodes |!|may |!|not |!|visit |!|all |!|the |!|nodes |!|in |!|that |!|make |!|up |!|an |!|MST If |!|G |!|contains |!|an |!|r-path |!|from |!|node |!|s |!|to |!|t, |!|then |!|every |!|MST |!|of |!|G |!|must |!|also |!|contain |!|an |!|r- path |!|from |!|node |!|s |!|to |!|node |!|t.

For |!|any |!|r |!|> |!|0, |!|an |!|r-path |!|is |!|a |!|path |!|whose |!|edges |!|all |!|have |!|weight |!|< |!|r. |!|- |!|correct |!|answer |!| โœ” True, |!|if |!|an |!|r-path |!|exists |!|between |!|s |!|and |!|t |!|then |!|we |!|are |!|guaranteed |!|to |!|get |!|either |!|this |!|path |!|or |!|another |!|r-path |!|with |!|weight |!|< |!|this |!|r-path |!|in |!|the |!|MST What |!|is |!|the |!|input |!|for |!|DFS? |!|- |!|correct |!|answer |!| โœ” Directed |!|or |!|undirected |!|graph What |!|is |!|the |!|output |!|for |!|DFS? |!|- |!|correct |!|answer |!| โœ” Pre/post/ccnum What |!|information |!|can |!|you |!|get |!|from |!|post |!|numbers? |!|- |!|correct |!|answer |!| โœ” In |!|a |!|directed |!|graph, |!| highest |!|post |!|numbers |!|are |!|sinks |!|and |!|lowest |!|post |!|numbers |!|are |!|sources What |!|information |!|can |!|you |!|get |!|from |!|ccnum? |!|- |!|correct |!|answer |!| โœ” Connected |!|components |!| (undirected) |!|or |!|SCCs |!|(directed) What |!|is |!|the |!|input |!|for |!|Explore? |!|- |!|correct |!|answer |!| โœ” Directed |!|or |!|undirected |!|graph, |!|start |!|vertex |!|v What |!|is |!|the |!|output |!|for |!|Explore? |!|- |!|correct |!|answer |!| โœ” Pre/post/ccnum visited What |!|is |!|the |!|runtime |!|for |!|DFS? |!|- |!|correct |!|answer |!| โœ” O(n+m) What |!|is |!|the |!|runtime |!|for |!|Explore? |!|- |!|correct |!|answer |!| โœ” O(n+m) What |!|is |!|the |!|input |!|for |!|topo |!|sort? |!|- |!|correct |!|answer |!| โœ” Graph, |!|DAG What |!|is |!|the |!|output |!|for |!|topo |!|sort? |!|- |!|correct |!|answer |!| โœ” Vertices |!|sorted |!|in |!|descending |!|post |!| order |!|number |!|(source |!|to |!|sink) What |!|is |!|the |!|runtime |!|for |!|topo |!|sort? |!|- |!|correct |!|answer |!| โœ” O(n+m)

What |!|is |!|the |!|runtime |!|for |!|reversing |!|a |!|graph? |!|- |!|correct |!|answer |!| โœ” O(n+m) What |!|is |!|the |!|runtime |!|for |!|building |!|a |!|residual |!|graph? |!|- |!|correct |!|answer |!| โœ” O(n+m) What |!|is |!|the |!|input |!|for |!|building |!|a |!|residual |!|graph? |!|- |!|correct |!|answer |!| โœ” Flow |!|network |!|f What |!|is |!|the |!|input |!|to |!|the |!|Ford-Fulkerson |!|algorithm? |!|- |!|correct |!|answer |!| โœ” Flow |!|network |!|f, |!|only |!|positive |!|integer |!|capacities What |!|is |!|the |!|output |!|to |!|the |!|Ford-Fulkerson |!|algorithm? |!|- |!|correct |!|answer |!| โœ” Max |!|flow |!|network |!| f* What |!|is |!|the |!|input |!|to |!|the |!|Edmonds-Karp |!|algorithm? |!|- |!|correct |!|answer |!| โœ” Flow |!|network |!|f, |!|any |!| positive |!|number |!|capacities What |!|is |!|the |!|output |!|to |!|the |!|Edmonds-Karp |!|algorithm? |!|- |!|correct |!|answer |!| โœ” Max |!|flow |!|network |!| f* What |!|algorithm |!|does |!|Edmonds-Karp |!|use |!|to |!|search? |!|- |!|correct |!|answer |!| โœ” BFS What |!|is |!|the |!|runtime |!|of |!|the |!|Ford-Fulkerson |!|algo? |!|- |!|correct |!|answer |!| โœ” O(mC) What |!|is |!|the |!|runtime |!|of |!|the |!|Edmonds-Karp |!|algo? |!|- |!|correct |!|answer |!| โœ” O(m^2n) What |!|is |!|min |!|cut |!|- |!|max |!|flow? |!|- |!|correct |!|answer |!| โœ” The |!|min |!|s-t |!|cut |!|of |!|f |!|will |!|give |!|you |!|the |!| max |!|flow |!|of |!|f