In Paulo Coelho's The Alchemist, the King of Salem, also known as Melchizedek, is the individual in the story who actually starts Santiago on the correct path to realize his Personal Legend.

When Santiago meets the King of Salem, the old man at first irritates the boy. Soon Santiago realizes that Melchizedek knows things about him that he shouldn't—they are strangers.

...the boy was able to read what the old man had written in the sand.

There, in the sand of the plaza of that small city, the boy read the names of his father and his mother and the name of the seminary he had attended...

Then the King of Salem introduces the topic of one's Personal Legend, something the boy has never heard of. Melchizedek explains:

It's what you have always wanted to accomplish. Everyone, when they are young, knows what their Personal Legend is.

At that point in their lives, everything is clear and everything is possible...

The king also explains that a mysterious force tries to stop people from realizing their Personal Legend, but that it is actually a force that "prepares your spirit and your will..."

And then, Melchizedek says...

And, when you want something, all the universe conspires in helping you to achieve it.

The King of Salem comes to Santiago because he realizes that Santiago is ready to give up searching for his Personal Legend. In fact, Melchizedek notes that he always appears in one way or another, as a "solution, or a good idea," to keep people going so they don't stop when they have come so close to realizing their Personal Legend.

When Santiago finally sells his sheep, the old man tells the boy about omens and how important they are, echoing words his grandfather had once told him. The old man also give Santiago two stones: Urim and Thummim, to help him make important decisions.

In essence, the King of Salem introduces Santiago to the most important concept: that of the Personal Legend and its oneness with all things. The king advises him to watch for omens, which will keep him on the correct path. And he gives Santiago knowledge and encouragement to carry with him to guide him along the way. Had it not been for the King of Salem, Santiago would never have realized his Personal Legend, which leads him to great happiness.

What does the King of Salem represent to Santiago in Coelho's The Alchemist?

The name of the King of Salem is Melchizedek and he acts as Santiago's first mentor, teacher, or spiritual guide. He is a person's introduction to learning about what a Personal Legend is and he helps them to make the choice to follow it. He actually shows up in a person's life when she or he is about to give up on their dreams and follow a life of "safety." Melchizedek reveals that he doesn't always show up in person form, either. Not everyone gets to seem him as the King of Salem. He tells the boy that he shows up as a good idea, sometimes, and makes decision making easier on people. Not only that, but most people don't even realize that he's visited them and helped them out. 

As Santiago decides to seek his Personal Legend, he looks back on his encounter with Melchizedek fondly. He remembers the advice and gifts he was given and they keep him motivated not to quit throughout the journey to Egypt.

In the Bible, Melchizedek was a high priest who actually collected tithing from Abraham, the father of the covenant in the Old Testament. For Coelho to select this high priest as Santiago's first mentor in the book is an allegorical choice in itself. He is a very old figure who dates far back in history. Coelho references this himself by saying the following:

"Melchizedek watched a small ship that was plowing its way out of the port. He would never again see the boy, just as he had never seen Abraham again after having charged him his one-tenth fee. That was his work"(33).

How does the King of Salem impact Santiago's journey in The Alchemist?

Melchizedek, also known as the King of Salem, contributes to Santiago's journey in The Alchemist by teaching the boy to learn about himself, to find the right path and to learn to be wise. The King of Salem helps Santiago understand that what people most want is to learn their personal Legends, the idea about themselves that is most true and to which they must stay attuned and committed. He also contributes to Santiago's journey by giving hints and clues as to where to find his treasure. In addition, he teaches Santiago to be wise by making a deal with him to trade one-tenth of his sheep for Malchizedek's clue to the treasure.