From 03250c0c1c3b0f1efaa651c9c166edb5cb1d0ca2 Mon Sep 17 00:00:00 2001
From: Eli Bendersky <eliben@gmail.com>
Date: Tue, 3 Sep 2024 06:53:09 -0700
Subject: [PATCH] Implemented verify

---
 btree/btree.go  | 19 ++++++++--------
 btree/verify.go | 60 ++++++++++++++++++++++++++++++++++++++++++++-----
 2 files changed, 64 insertions(+), 15 deletions(-)

diff --git a/btree/btree.go b/btree/btree.go
index 4afcbc6..4ee6d64 100644
--- a/btree/btree.go
+++ b/btree/btree.go
@@ -19,14 +19,16 @@ type BTree[K, V any] struct {
 
 const defaultTee = 10
 
+// node is a node in the BTree.
+//
+// Key ordering invariants (defining n=len(keys)):
+//
+// keys[i].key <= keys[i+1].key for each i in 0..n-2
+//
+// There are n+1 elements in children (0..n)
+// if kj is any key in children[j], then:  keys[j-1].key <= kj <= keys[j].key
+// Boundaries: k0 <= keys[0].key   and   keys[n-1].key <= kn
 type node[K, V any] struct {
-	// Key ordering invariants (defining n=len(keys)):
-	//
-	// keys[i].key <= keys[i+1].key for each i in 0..n-2
-	//
-	// There are n+1 elements in children (0..n)
-	// if kj is any key in children[j], then:  keys[j-1].key <= kj <= keys[j].key
-	// Boundaries: k0 <= keys[0].key   and   keys[n-1].key <= kn
 	keys     []nodeKey[K, V]
 	children []*node[K, V]
 	leaf     bool
@@ -187,9 +189,6 @@ func (bt *BTree[K, V]) nodeKeyCmp(a, b nodeKey[K, V]) int {
 	return bt.cmp(a.key, b.key)
 }
 
-// TODO: add "verify" method that verifies all invariants: min/max number
-// of keys per node, num keys vs. num children, height, and ordering invariants
-// of each node. use it in tests
 // TODO: add deletion
 
 // nodesPreOrder returns an iterator over the nodes of bt in pre-order.
diff --git a/btree/verify.go b/btree/verify.go
index 6377cae..f42c95c 100644
--- a/btree/verify.go
+++ b/btree/verify.go
@@ -3,6 +3,7 @@ package btree
 import (
 	"errors"
 	"fmt"
+	"slices"
 )
 
 // verify checks B-tree invariants on bt and returns an error combining all
@@ -10,28 +11,77 @@ import (
 func (bt *BTree[K, V]) verify() error {
 	var errs []error
 
+	// Verify invariants on each node separately
 	for n := range bt.nodesPreOrder() {
 		if err := bt.verifyNode(n); err != nil {
 			errs = append(errs, err)
 		}
 	}
-
 	if len(errs) > 0 {
 		return errors.Join(errs...)
 	}
+
+	// Recursive visit to calculate height of all leaf nodes in the tree.
+	var heights []int
+	var visit func(n *node[K, V], h int)
+	visit = func(n *node[K, V], h int) {
+		if n.leaf {
+			heights = append(heights, h)
+			return
+		}
+
+		for _, c := range n.children {
+			visit(c, h+1)
+		}
+	}
+	visit(bt.root, 0)
+
+	cp := slices.Compact(heights)
+	if len(cp) != 1 {
+		return fmt.Errorf("different leaf heights: %v", cp)
+	}
+
 	return nil
 }
 
 func (bt *BTree[K, V]) verifyNode(n *node[K, V]) error {
 	if len(n.keys) > 2*bt.tee-1 {
-		return fmt.Errorf("node %p has too many keys: %d", n, len(n.keys))
+		return fmt.Errorf("node %p: has too many keys: %d", n, len(n.keys))
 	}
 	if n != bt.root && len(n.keys) < bt.tee-1 {
-		return fmt.Errorf("node %p has too few keys: %d", n, len(n.keys))
+		return fmt.Errorf("node %p: has too few keys: %d", n, len(n.keys))
 	}
 
-	if !n.leaf && len(n.children) != len(n.keys)+1 {
-		return fmt.Errorf("internal node %p has %d keys but %d children", n, len(n.keys), len(n.children))
+	if n == bt.root && len(n.keys) < 1 {
+		return fmt.Errorf("node %p: root has 0 keys", n)
+	}
+
+	if !slices.IsSortedFunc(n.keys, bt.nodeKeyCmp) {
+		return fmt.Errorf("node %p: keys not sorted", n)
+	}
+
+	if !n.leaf {
+		if len(n.children) != len(n.keys)+1 {
+			return fmt.Errorf("internal node %p: %d keys but %d children", n, len(n.keys), len(n.children))
+		}
+
+		for j, k := range n.keys {
+			// Verify ordering invariant (see type node's comment).
+
+			// 1: ensure that kj <= keys[j].key
+			for ci, kj := range n.children[j].keys {
+				if bt.nodeKeyCmp(kj, k) > 0 {
+					return fmt.Errorf("node %p: key %v of child [%d] >= key %v of node[%d]", n, kj.key, j, k.key, ci)
+				}
+			}
+
+			// 2: ensure that keys[j-1].key <= kj
+			for ci, kj := range n.children[j+1].keys {
+				if bt.nodeKeyCmp(k, kj) > 0 {
+					return fmt.Errorf("node %p: key %v of child [%d] <= key %v of node[%d]", n, kj.key, j, k.key, ci)
+				}
+			}
+		}
 	}
 
 	return nil