# Chapter 45: Prim’s Algorithm Challenges

> Challenge 1
>
> Given the graph and minimum spanning tree below, what can you say about the value of x?

![](https://2630101043-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LfMpyG53TWtxqHbRTtR%2F-LrqBwmAQ2jiC4L9q9mD%2F-LrqC1bZ9GgmChJB-gZn%2F278.png?generation=1571793678143041\&alt=media)

The value of x is less than

> Challenge 2
>
> Given the graph below, step through Prim’s algorithm to produce a minimum spanning tree, and provide the total cost. Start at vertex B. If two edges share the same weight, prioritize them alphabetically.

![](https://2630101043-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LfMpyG53TWtxqHbRTtR%2F-LrqBwmAQ2jiC4L9q9mD%2F-LrqC1bau_v09EWFN2W2%2F279.png?generation=1571793678247251\&alt=media)

![](https://2630101043-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LfMpyG53TWtxqHbRTtR%2F-LrqBwmAQ2jiC4L9q9mD%2F-LrqC1bgi1VcsuvuTB1T%2F280.png?generation=1571793678278442\&alt=media)

![](https://2630101043-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LfMpyG53TWtxqHbRTtR%2F-LrqBwmAQ2jiC4L9q9mD%2F-LrqC1biiFBtueDgxYyn%2F281.png?generation=1571793678280400\&alt=media)

![](https://2630101043-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LfMpyG53TWtxqHbRTtR%2F-LrqBwmAQ2jiC4L9q9mD%2F-LrqC1bkQJEY_wKN-IkF%2F282.png?generation=1571793678316493\&alt=media)
