GATE & PSUs - Computer Science & Information Technology (CS & IT)

Asymptotic Analysis & Recurrences question bank (Data Structures & Algorithms)

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Q1.
Consider an undirected graph $G = (V, E)$ with $n$ vertices and $m$ edges having distinct positive edge weights. Which of the following statements is ALWAYS TRUE?

(A)
The edge with the minimum weight in any cycle of $G$ must belong to the minimum spanning tree (MST).
(B)
The edge with the maximum weight in any cycle of $G$ cannot belong to the minimum spanning tree (MST).
(C)
The shortest path between any two vertices $u$ and $v$ is always composed of edges belonging to the MST.
(D)
If all edge weights are squared, the minimum spanning tree of $G$ may change.
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Q2.
[Asymptotic Analysis & Recurrences Concept 7] Consider an undirected graph $G = (V, E)$ with $n$ vertices and $m$ edges having distinct positive edge weights. Which of the following statements is ALWAYS TRUE?

(A)
The edge with the minimum weight in any cycle of $G$ must belong to the minimum spanning tree (MST).
(B)
The edge with the maximum weight in any cycle of $G$ cannot belong to the minimum spanning tree (MST).
(C)
The shortest path between any two vertices $u$ and $v$ is always composed of edges belonging to the MST.
(D)
If all edge weights are squared, the minimum spanning tree of $G$ may change.
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