Greedy Algorithm$-$ Muddy City problem.

Muddy City Problem.

$1.$ Discuss how the MST $($Minimum spanning Tree $)$ can be used to solve the Muddy City problem.

$2.$ Can we use the Dijkstra algorithm to solve the problem? why $?$

$3.$ What other algorithms were used to solve this problem?

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Getting around the city was particularly difficult after rainstorms because the ground became very muddy$$cars got stuck in the mud and people got their boots dirty. The mayor of the city decided that some of the streets must be paved, but didn$$t want to spend more money than necessary because the city also wanted to build a swimming pool.

The mayor therefore specified two conditions:

Enough streets must be paved so that it is possible for everyone to travel from their house to anyone else$$s house only along paved roads, and

The paving should cost as little as possible.