# Binary Search Trees Related to [Binary Trees](Binary%20Trees.md), **binary search trees** are trees that satisfy the **binary search tree (BST) invariant**, which states that for every node `x`: ``` x.left.value <= x.value <= x.right.value ```  This property allows us to quickly search through the tree to retrieve values that we want. It is often useful to require *uniqueness* on the node values in our tree. So, this would change the invariant structure to be strictly lt;$ rather than $\leq$: ``` x.left.value < x.value < x.right.value ``` --- Links to: [Trees](Trees.md) References: