The decision tree algorithm involves recursive programming because it solves the problem of constructing a decision tree by breaking it down into smaller sub-problems of the same type, and then solving those sub-problems in a similar way until a base case is reached.

At each step of the recursion, the algorithm selects the best attribute to split the data based on a criterion such as information gain or Gini impurity. The data is then divided into subsets based on the selected attribute, and the process is repeated on each subset until a stopping criterion is met.

The stopping criterion may be a maximum tree depth, a minimum number of samples per leaf, or a minimum improvement in the objective function. When the stopping criterion is met, the recursion stops and a leaf node is created that represents the final decision or prediction.

This recursive approach allows the algorithm to efficiently explore the possible splits and select the optimal one, leading to a tree that accurately captures the underlying relationships in the data. Without recursive programming, the decision tree algorithm would not be able to recursively partition the data and construct the decision tree.