solver: make results of `poetry update` more deterministic and similar to results of `poetry lock`

When running `poetry lock`, dependencies with less candidates are chosen first.
Prior to this change when running `poetry update`, all whitelisted dependencies (aka `use_latest`) got the same priority which results in a more or less random resolution order.

src/poetry/mixology/version_solver.py

@@ -362,31 +362,50 @@ class VersionSolver:
         if not unsatisfied:
         if not unsatisfied:
             return None
             return None
 
 
+        class Preference:
+            """
+            Preference is one of the criteria for choosing which dependency to solve
+            first. A higher value means that there are "more options" to satisfy
+            a dependency. A lower value takes precedence.
+            """
+
+            DIRECT_ORIGIN = 0
+            NO_CHOICE = 1
+            USE_LATEST = 2
+            LOCKED = 3
+            DEFAULT = 4
+
         # Prefer packages with as few remaining versions as possible,
         # Prefer packages with as few remaining versions as possible,
         # so that if a conflict is necessary it's forced quickly.
         # so that if a conflict is necessary it's forced quickly.
-        def _get_min(dependency: Dependency) -> tuple[bool, int]:
+        # In order to provide results that are as deterministic as possible
+        # and consistent between `poetry lock` and `poetry update`, the return value
+        # of two different dependencies should not be equal if possible.
+        def _get_min(dependency: Dependency) -> tuple[bool, int, int]:
             # Direct origin dependencies must be handled first: we don't want to resolve
             # Direct origin dependencies must be handled first: we don't want to resolve
             # a regular dependency for some package only to find later that we had a
             # a regular dependency for some package only to find later that we had a
             # direct-origin dependency.
             # direct-origin dependency.
             if dependency.is_direct_origin():
             if dependency.is_direct_origin():
-                return False, -1
+                return False, Preference.DIRECT_ORIGIN, 1
 
 
-            if dependency.name in self._provider.use_latest:
-                # If we're forced to use the latest version of a package, it effectively
-                # only has one version to choose from.
-                return not dependency.marker.is_any(), 1
+            is_specific_marker = not dependency.marker.is_any()
 
 
-            locked = self._provider.get_locked(dependency)
-            if locked:
-                return not dependency.marker.is_any(), 1
+            use_latest = dependency.name in self._provider.use_latest
+            if not use_latest:
+                locked = self._provider.get_locked(dependency)
+                if locked:
+                    return is_specific_marker, Preference.LOCKED, 1
 
 
             try:
             try:
-                return (
-                    not dependency.marker.is_any(),
-                    len(self._dependency_cache.search_for(dependency)),
-                )
+                num_packages = len(self._dependency_cache.search_for(dependency))
             except ValueError:
             except ValueError:
-                return not dependency.marker.is_any(), 0
+                num_packages = 0
+            if num_packages < 2:
+                preference = Preference.NO_CHOICE
+            elif use_latest:
+                preference = Preference.USE_LATEST
+            else:
+                preference = Preference.DEFAULT
+            return is_specific_marker, preference, num_packages
 
 
         if len(unsatisfied) == 1:
         if len(unsatisfied) == 1:
             dependency = unsatisfied[0]
             dependency = unsatisfied[0]

tests/puzzle/test_solver.py

@@ -3716,3 +3716,72 @@ def test_solver_yanked_warning(
     )
     )
     assert error.count("is a yanked version") == 2
     assert error.count("is a yanked version") == 2
     assert error.count("Reason for being yanked") == 1
     assert error.count("Reason for being yanked") == 1
+
+
+@pytest.mark.parametrize("is_locked", [False, True])
+def test_update_with_use_latest_vs_lock(
+    package: ProjectPackage, repo: Repository, pool: Pool, io: NullIO, is_locked: bool
+):
+    """
+    A1 depends on B2, A2 and A3 depend on B1. Same for C.
+    B1 depends on A2/C2, B2 depends on A1/C1.
+
+    Because there are fewer versions B than of A and C, B is resolved first
+    so that latest version of B is used.
+    There shouldn't be a difference between `poetry lock` (not is_locked)
+    and `poetry update` (is_locked + use_latest)
+    """
+    # B added between A and C (and also alphabetically between)
+    # to ensure that neither the first nor the last one is resolved first
+    package.add_dependency(Factory.create_dependency("A", "*"))
+    package.add_dependency(Factory.create_dependency("B", "*"))
+    package.add_dependency(Factory.create_dependency("C", "*"))
+
+    package_a1 = get_package("A", "1")
+    package_a1.add_dependency(Factory.create_dependency("B", "2"))
+    package_a2 = get_package("A", "2")
+    package_a2.add_dependency(Factory.create_dependency("B", "1"))
+    package_a3 = get_package("A", "3")
+    package_a3.add_dependency(Factory.create_dependency("B", "1"))
+
+    package_c1 = get_package("C", "1")
+    package_c1.add_dependency(Factory.create_dependency("B", "2"))
+    package_c2 = get_package("C", "2")
+    package_c2.add_dependency(Factory.create_dependency("B", "1"))
+    package_c3 = get_package("C", "3")
+    package_c3.add_dependency(Factory.create_dependency("B", "1"))
+
+    package_b1 = get_package("B", "1")
+    package_b1.add_dependency(Factory.create_dependency("A", "2"))
+    package_b1.add_dependency(Factory.create_dependency("C", "2"))
+    package_b2 = get_package("B", "2")
+    package_b2.add_dependency(Factory.create_dependency("A", "1"))
+    package_b2.add_dependency(Factory.create_dependency("C", "1"))
+
+    repo.add_package(package_a1)
+    repo.add_package(package_a2)
+    repo.add_package(package_a3)
+    repo.add_package(package_b1)
+    repo.add_package(package_b2)
+    repo.add_package(package_c1)
+    repo.add_package(package_c2)
+    repo.add_package(package_c3)
+
+    if is_locked:
+        locked = [package_a1, package_b2, package_c1]
+        use_latest = [package.name for package in locked]
+    else:
+        locked = []
+        use_latest = []
+
+    solver = Solver(package, pool, [], locked, io)
+    transaction = solver.solve(use_latest)
+
+    check_solver_result(
+        transaction,
+        [
+            {"job": "install", "package": package_c1},
+            {"job": "install", "package": package_b2},
+            {"job": "install", "package": package_a1},
+        ],
+    )