Suppose you are given a source word and a target word. Your goal is to transform the source word to the target word in as few valid steps as possible. The valid steps are change one character of the word to a new character, add one character to the word, or remove one character from the word. After each step, the resulting string must be a valid word. For example, we could transform cat to hut in two steps:

cathathut

Model this problem as a graph. What algorithm can be used to solve this problem?