Simplify graph in get_topological_weights. (#10574)

Fixes #10557 where the resolver spends too much time calculating the weights.

Also, do not let `get_installation_order` calculate these weights at all when there is nothing left to install.

Co-authored-by: Tzu-ping Chung <uranusjr@gmail.com>

news/10557.bugfix.rst

@@ -0,0 +1 @@
+Optimize installation order calculation to improve performance when installing requirements that form a complex dependency graph with a large amount of edges.

src/pip/_internal/resolution/resolvelib/resolver.py

@@ -171,12 +171,17 @@ def get_installation_order(
         get installed one-by-one.
 
         The current implementation creates a topological ordering of the
-        dependency graph, while breaking any cycles in the graph at arbitrary
-        points. We make no guarantees about where the cycle would be broken,
-        other than they would be broken.
+        dependency graph, giving more weight to packages with less
+        or no dependencies, while breaking any cycles in the graph at
+        arbitrary points. We make no guarantees about where the cycle
+        would be broken, other than it *would* be broken.
         """
         assert self._result is not None, "must call resolve() first"
 
+        if not req_set.requirements:
+            # Nothing is left to install, so we do not need an order.
+            return []
+
         graph = self._result.graph
         weights = get_topological_weights(
             graph,
@@ -199,13 +204,19 @@ def get_topological_weights(
     This implementation may change at any point in the future without prior
     notice.
 
-    We take the length for the longest path to any node from root, ignoring any
-    paths that contain a single node twice (i.e. cycles). This is done through
-    a depth-first search through the graph, while keeping track of the path to
-    the node.
+    We first simplify the dependency graph by pruning any leaves and giving them
+    the highest weight: a package without any dependencies should be installed
+    first. This is done again and again in the same way, giving ever less weight
+    to the newly found leaves. The loop stops when no leaves are left: all
+    remaining packages have at least one dependency left in the graph.
+
+    Then we continue with the remaining graph, by taking the length for the
+    longest path to any node from root, ignoring any paths that contain a single
+    node twice (i.e. cycles). This is done through a depth-first search through
+    the graph, while keeping track of the path to the node.
 
     Cycles in the graph result would result in node being revisited while also
-    being it's own path. In this case, take no action. This helps ensure we
+    being on its own path. In this case, take no action. This helps ensure we
     don't get stuck in a cycle.
 
     When assigning weight, the longer path (i.e. larger length) is preferred.
@@ -227,6 +238,34 @@ def visit(node: Optional[str]) -> None:
         last_known_parent_count = weights.get(node, 0)
         weights[node] = max(last_known_parent_count, len(path))
 
+    # Simplify the graph, pruning leaves that have no dependencies.
+    # This is needed for large graphs (say over 200 packages) because the
+    # `visit` function is exponentially slower then, taking minutes.
+    # See https://github.com/pypa/pip/issues/10557
+    # We will loop until we explicitly break the loop.
+    while True:
+        leaves = set()
+        for key in graph:
+            if key is None:
+                continue
+            for _child in graph.iter_children(key):
+                # This means we have at least one child
+                break
+            else:
+                # No child.
+                leaves.add(key)
+        if not leaves:
+            # We are done simplifying.
+            break
+        # Calculate the weight for the leaves.
+        weight = len(graph) - 1
+        for leaf in leaves:
+            weights[leaf] = weight
+        # Remove the leaves from the graph, making it simpler.
+        for leaf in leaves:
+            graph.remove(leaf)
+
+    # Visit the remaining graph.
     # `None` is guaranteed to be the root node by resolvelib.
     visit(None)
 

tests/unit/resolution_resolvelib/test_resolver.py

@@ -115,7 +115,7 @@ def test_new_resolver_get_installation_order(
                 ("three", "four"),
                 ("four", "five"),
             ],
-            {None: 0, "one": 1, "two": 1, "three": 2, "four": 3, "five": 4},
+            {None: 0, "five": 5, "four": 4, "one": 4, "three": 2, "two": 1},
         ),
         (
             "linear",