diff --git a/assignment2/csp.py b/assignment2/csp.py
index f01cc63..3ee6774 100644
--- a/assignment2/csp.py
+++ b/assignment2/csp.py
@@ -56,6 +56,20 @@ class CSP:
         bool
             False if a domain becomes empty, otherwise True
         """
+
+        def revise(csp, xi, xj) -> bool:
+            revised = False
+            for x in set(csp.domains[xi]):
+                if not any(
+                    [
+                        (x, y) in csp.binary_constraints[(xi, xj)]
+                        for y in csp.domains[xj]
+                    ]
+                ):
+                    csp.domains[xi].remove(x)
+                    revised = True
+            return revised
+
         queue = Queue()
         for edge in self.binary_constraints.keys():
             queue.put(edge)
@@ -63,7 +77,7 @@ class CSP:
         while not queue.empty():
             (xi, xj) = queue.get()
 
-            if self._revise(xi, xj):
+            if revise(self, xi, xj):
                 if len(self.domains[xi]) == 0:
                     return False
                 for neighboring_edge in [
@@ -74,53 +88,6 @@ class CSP:
                     queue.put(neighboring_edge)
         return True
 
-    def _revise(self, xi, xj) -> bool:
-        """Internal of ac_3
-        Makes an arc consistent by shrinking xi's domain.
-
-        Parameters
-        ----------
-        xi, xj
-            Nodes of the arc
-
-        Returns
-        -------
-        bool
-            True if a change was made to the domain of xi, False otherwise
-
-        """
-        revised = False
-        for x in set(self.domains[xi]):
-            if not any(
-                [(x, y) in self.binary_constraints[(xi, xj)] for y in self.domains[xj]]
-            ):
-                self.domains[xi].remove(x)
-                revised = True
-        return revised
-
-    def _consistent(self, var, value, assignment) -> bool:
-        for v in assignment:
-            if (var, v) in self.binary_constraints.keys():
-                if (value, assignment[v]) not in self.binary_constraints[(var, v)]:
-                    return False
-            if (v, var) in self.binary_constraints.keys():
-                if (value, assignment[v]) not in self.binary_constraints[(v, var)]:
-                    return False
-        return True
-
-    def _backtrack(self, assignment: dict[str, Any]) -> dict | None:
-        if len(assignment) == len(self.variables):
-            return assignment  # base-case
-        var = self._select_unassigned_variable(assignment)
-        for value in self._order_domain_values(var, assignment):
-            if not self._consistent(var, value, assignment):
-                continue
-            assignment[var] = value
-            if result := self._backtrack(assignment):
-                return result
-            assignment.pop(var)
-        return None  # failure
-
     def backtracking_search(self) -> None | dict[str, Any]:
         """Performs backtracking search on the CSP.
 
@@ -130,32 +97,53 @@ class CSP:
             A solution if any exists, otherwise None
         """
 
-        return self._backtrack({})
-
-    def _select_unassigned_variable(self, assignment) -> str:
-        for v in self.variables:
-            if v not in assignment.keys():
-                return v
-        return "this shouldn't happen"
-
-    # TODO: may be wrong
-    def _order_domain_values(self, var, assignment) -> list[Any]:
-        """least constrained value"""
-
-        def compare(value) -> int:
-            s = 0
-            for neighbor in [
-                b for (a, b) in self.binary_constraints.keys() if a == var
-            ]:
-                if neighbor in assignment.keys():
+        def backtrack(csp, assignment: dict[str, Any]) -> dict | None:
+            if len(assignment) == len(csp.variables):
+                return assignment  # base-case
+            var = select_unassigned_variable(csp, assignment)
+            for value in order_domain_values(csp, var, assignment):
+                if not consistent(csp, var, value, assignment):
                     continue
-                for neighbor_value in self.domains[neighbor]:
-                    s += (value, neighbor_value) not in self.binary_constraints[
-                        (var, neighbor)
-                    ]
-            return s
+                assignment[var] = value
+                if result := backtrack(csp, assignment):
+                    return result
+                assignment.pop(var)
+            return None  # failure
 
-        return sorted(list(self.domains[var]), key=compare)
+        def consistent(csp, var, value, assignment) -> bool:
+            for v in assignment:
+                if (var, v) in csp.binary_constraints.keys():
+                    if (value, assignment[v]) not in csp.binary_constraints[(var, v)]:
+                        return False
+                if (v, var) in csp.binary_constraints.keys():
+                    if (value, assignment[v]) not in csp.binary_constraints[(v, var)]:
+                        return False
+            return True
+
+        def select_unassigned_variable(csp, assignment) -> str:
+            for v in csp.variables:
+                if v not in assignment.keys():
+                    return v
+            return "this shouldn't happen"
+
+        # choose least constrained value
+        def order_domain_values(csp, var, assignment) -> list[Any]:
+            def compare(value) -> int:
+                s = 0
+                for neighbor in [
+                    b for (a, b) in csp.binary_constraints.keys() if a == var
+                ]:
+                    if neighbor in assignment.keys():
+                        continue
+                    for neighbor_value in csp.domains[neighbor]:
+                        s += (value, neighbor_value) not in csp.binary_constraints[
+                            (var, neighbor)
+                        ]
+                return s
+
+            return sorted(list(csp.domains[var]), key=compare)
+
+        return backtrack(self, {})
 
 
 def alldiff(variables: list[str]) -> list[tuple[str, str]]: