Add red black tree

Review URL: http://codereview.appspot.com/4184063



git-svn-id: http://skia.googlecode.com/svn/trunk@823 2bbb7eff-a529-9590-31e7-b0007b416f81

2 files changed, 1126 insertions, 1 deletions

diff --git a/gpu/src/GrRedBlackTree.h b/gpu/src/GrRedBlackTree.h
new file mode 100644
index 0000000000..310722a919
--- /dev/null
+++ b/gpu/src/GrRedBlackTree.h
@@ -0,0 +1,1123 @@
+/*
+    Copyright 2011 Google Inc.
+
+    Licensed under the Apache License, Version 2.0 (the "License");
+    you may not use this file except in compliance with the License.
+    You may obtain a copy of the License at
+
+         http://www.apache.org/licenses/LICENSE-2.0
+
+    Unless required by applicable law or agreed to in writing, software
+    distributed under the License is distributed on an "AS IS" BASIS,
+    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+    See the License for the specific language governing permissions and
+    limitations under the License.
+ */
+
+#ifndef GrRedBlackTree_DEFINED
+#define GrRedBlackTree_DEFINED
+
+#include "GrNoncopyable.h"
+
+template <typename T>
+class GrLess {
+public:
+    bool operator()(const T& a, const T& b) const { return a < b; }
+};
+
+template <typename T>
+class GrLess<T*> {
+public:
+    bool operator()(const T* a, const T* b) const { return *a < *b; }
+};
+
+/**
+ * In debug build this will cause full traversals of the tree when the validate
+ * is called on insert and remove. Useful for debugging but very slow.
+ */
+#define DEEP_VALIDATE 0
+
+/**
+ * A sorted tree that uses the red-black tree algorithm. Allows duplicate
+ * entries. Data is of type T and is compared using functor C. A single C object
+ * will be created and used for all comparisons.
+ */
+template <typename T, typename C = GrLess<T> >
+class GrRedBlackTree : public GrNoncopyable {
+public:
+    /**
+     * Creates an empty tree.
+     */
+    GrRedBlackTree();
+    virtual ~GrRedBlackTree();
+
+    /**
+     * Class used to iterater through the tree. The valid range of the tree
+     * is given by [begin(), end()). It is legal to dereference begin() but not
+     * end(). The iterator has preincrement and predecrement operators, it is
+     * legal to decerement end() if the tree is not empty to get the last
+     * element. However, a last() helper is provided.
+     */
+    class Iter;
+
+    /**
+     * Add an element to the tree. Duplicates are allowed.
+     * @param t     the item to add.
+     * @return  an iterator to the item.
+     */
+    Iter insert(const T& t);
+
+    /**
+     * Removes all items in the tree.
+     */
+    void reset();
+
+    /**
+     * @return true if there are no items in the tree, false otherwise.
+     */
+    bool empty() const {return 0 == fCount;}
+
+    /**
+     * @return the number of items in the tree.
+     */
+    int  count() const {return fCount;}
+
+    /**
+     * @return  an iterator to the first item in sorted order, or end() if empty
+     */
+    Iter begin();
+    /**
+     * Gets the last valid iterator. This is always valid, even on an empty.
+     * However, it can never be dereferenced. Useful as a loop terminator.
+     * @return  an iterator that is just beyond the last item in sorted order.
+     */
+    Iter end();
+    /**
+     * @return  an iterator that to the last item in sorted order, or end() if
+     * empty.
+     */
+    Iter last();
+
+    /**
+     * Finds an occurrence of an item.
+     * @param t     the item to find.
+     * @return an iterator to a tree element equal to t or end() if none exists.
+     */
+    Iter find(const T& t);
+    /**
+     * Finds the first of an item in iterator order.
+     * @param t     the item to find.
+     * @return  an iterator to the first element equal to t or end() if
+     *          none exists.
+     */
+    Iter findFirst(const T& t);
+    /**
+     * Finds the last of an item in iterator order.
+     * @param t     the item to find.
+     * @return  an iterator to the last element equal to t or end() if
+     *          none exists.
+     */
+    Iter findLast(const T& t);
+    /**
+     * Gets the number of items in the tree equal to t.
+     * @param t     the item to count.
+     * @return  number of items equal to t in the tree
+     */
+    int countOf(const T& t) const;
+
+    /**
+     * Removes the item indicated by an iterator. The iterator will not be valid
+     * afterwards.
+     *
+     * @param iter      iterator of item to remove. Must be valid (not end()).
+     */
+    void remove(const Iter& iter) { deleteAtNode(iter.fN); }
+
+    static void UnitTest();
+
+private:
+    enum Color {
+        kRed_Color,
+        kBlack_Color
+    };
+
+    enum Child {
+        kLeft_Child  = 0,
+        kRight_Child = 1
+    };
+
+    struct Node {
+        T       fItem;
+        Color   fColor;
+
+        Node*   fParent;
+        Node*   fChildren[2];
+    };
+
+    void rotateRight(Node* n);
+    void rotateLeft(Node* n);
+
+    static Node* SuccessorNode(Node* x);
+    static Node* PredecessorNode(Node* x);
+
+    void deleteAtNode(Node* x);
+    static void RecursiveDelete(Node* x);
+
+    int countOfHelper(const Node* n, const T& t) const;
+
+#if GR_DEBUG
+    void validate() const;
+    int checkNode(Node* n, int* blackHeight) const;
+    // checks relationship between a node and its children. allowRedRed means
+    // node may be in an intermediate state where a red parent has a red child.
+    bool validateChildRelations(const Node* n, bool allowRedRed) const;
+    // place to stick break point if validateChildRelations is failing.
+    bool validateChildRelationsFailed() const { return false; }
+#else
+    void validate() const {}
+#endif
+
+    int     fCount;
+    Node*   fRoot;
+    Node*   fFirst;
+    Node*   fLast;
+
+    const C fComp;
+};
+
+template <typename T, typename C>
+class GrRedBlackTree<T,C>::Iter {
+public:
+    Iter() {};
+    Iter(const Iter& i) {fN = i.fN; fTree = i.fTree;}
+    Iter& operator =(const Iter& i) {
+        fN = i.fN;
+        fTree = i.fTree;
+        return *this;
+    }
+    // altering the sort value of the item using this method will cause
+    // errors.
+    T& operator *() const { return fN->fItem; }
+    bool operator ==(const Iter& i) const {
+        return fN == i.fN && fTree == i.fTree;
+    }
+    bool operator !=(const Iter& i) const { return !(*this == i); }
+    Iter& operator ++() {
+        GrAssert(*this != fTree->end());
+        fN = SuccessorNode(fN);
+        return *this;
+    }
+    Iter& operator --() {
+        GrAssert(*this != fTree->begin());
+        if (NULL != fN) {
+            fN = PredecessorNode(fN);
+        } else {
+            *this = fTree->last();
+        }
+        return *this;
+    }
+
+private:
+    friend class GrRedBlackTree;
+    explicit Iter(Node* n, GrRedBlackTree* tree) {
+        fN = n;
+        fTree = tree;
+    }
+    Node* fN;
+    GrRedBlackTree* fTree;
+};
+
+template <typename T, typename C>
+GrRedBlackTree<T,C>::GrRedBlackTree() : fComp() {
+    fRoot = NULL;
+    fFirst = NULL;
+    fLast = NULL;
+    fCount = 0;
+    validate();
+}
+
+template <typename T, typename C>
+GrRedBlackTree<T,C>::~GrRedBlackTree() {
+    RecursiveDelete(fRoot);
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Iter GrRedBlackTree<T,C>::begin() {
+    return Iter(fFirst, this);
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Iter GrRedBlackTree<T,C>::end() {
+    return Iter(NULL, this);
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Iter GrRedBlackTree<T,C>::last() {
+    return Iter(fLast, this);
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Iter GrRedBlackTree<T,C>::find(const T& t) {
+    Node* n = fRoot;
+    while (NULL != n) {
+        if (fComp(t, n->fItem)) {
+            n = n->fChildren[kLeft_Child];
+        } else {
+            if (!fComp(n->fItem, t)) {
+                return Iter(n, this);
+            }
+            n = n->fChildren[kRight_Child];
+        }
+    }
+    return end();
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Iter GrRedBlackTree<T,C>::findFirst(const T& t) {
+    Node* n = fRoot;
+    Node* leftMost = NULL;
+    while (NULL != n) {
+        if (fComp(t, n->fItem)) {
+            n = n->fChildren[kLeft_Child];
+        } else {
+            if (!fComp(n->fItem, t)) {
+                // found one. check if another in left subtree.
+                leftMost = n;
+                n = n->fChildren[kLeft_Child];
+            } else {
+                n = n->fChildren[kRight_Child];
+            }
+        }
+    }
+    return Iter(leftMost, this);
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Iter GrRedBlackTree<T,C>::findLast(const T& t) {
+    Node* n = fRoot;
+    Node* rightMost = NULL;
+    while (NULL != n) {
+        if (fComp(t, n->fItem)) {
+            n = n->fChildren[kLeft_Child];
+        } else {
+            if (!fComp(n->fItem, t)) {
+                // found one. check if another in right subtree.
+                rightMost = n;
+            }
+            n = n->fChildren[kRight_Child];
+        }
+    }
+    return Iter(rightMost, this);
+}
+
+template <typename T, typename C>
+int GrRedBlackTree<T,C>::countOf(const T& t) const {
+    return countOfHelper(fRoot, t);
+}
+
+template <typename T, typename C>
+int GrRedBlackTree<T,C>::countOfHelper(const Node* n, const T& t) const {
+    // this is count*log(n) :(
+    while (NULL != n) {
+        if (fComp(t, n->fItem)) {
+            n = n->fChildren[kLeft_Child];
+        } else {
+            if (!fComp(n->fItem, t)) {
+                int count = 1;
+                count += countOfHelper(n->fChildren[kLeft_Child], t);
+                count += countOfHelper(n->fChildren[kRight_Child], t);
+                return count;
+            }
+            n = n->fChildren[kRight_Child];
+        }
+    }
+    return 0;
+
+}
+
+template <typename T, typename C>
+void GrRedBlackTree<T,C>::reset() {
+    RecursiveDelete(fRoot);
+    fRoot = NULL;
+    fFirst = NULL;
+    fLast = NULL;
+    fCount = 0;
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Iter GrRedBlackTree<T,C>::insert(const T& t) {
+    validate();
+
+    ++fCount;
+
+    Node* x = new Node;
+    x->fChildren[kLeft_Child] = NULL;
+    x->fChildren[kRight_Child] = NULL;
+    x->fItem = t;
+
+    Node* gp = NULL;
+    Node* p = NULL;
+    Node* n = fRoot;
+    Child pc;
+    Child gpc;
+
+    bool first = true;
+    bool last = true;
+    while (NULL != n) {
+        gpc = pc;
+        pc = fComp(x->fItem, n->fItem) ? kLeft_Child : kRight_Child;
+        first = first && kLeft_Child == pc;
+        last = last && kRight_Child == pc;
+        gp = p;
+        p = n;
+        n = p->fChildren[pc];
+
+    }
+    if (last) {
+        fLast = x;
+    }
+    if (first) {
+        fFirst = x;
+    }
+
+    if (NULL == p) {
+        fRoot = x;
+        x->fColor = kBlack_Color;
+        x->fParent = NULL;
+        GrAssert(1 == fCount);
+        return Iter(x, this);
+    }
+    p->fChildren[pc] = x;
+    x->fColor = kRed_Color;
+    x->fParent = p;
+
+    do {
+        // assumptions at loop start.
+        GrAssert(NULL != x);
+        GrAssert(kRed_Color == x->fColor);
+        // can't have a grandparent but no parent.
+        GrAssert(!(NULL != gp && NULL == p));
+        // make sure pc and gpc are correct
+        GrAssert(NULL == p  || p->fChildren[pc] == x);
+        GrAssert(NULL == gp || gp->fChildren[gpc] == p);
+
+        // if x's parent is black then we didn't violate any of the
+        // red/black properties when we added x as red.
+        if (kBlack_Color == p->fColor) {
+            return Iter(x, this);
+        }
+        // gp must be valid because if p was the root then it is black
+        GrAssert(NULL != gp);
+        // gp must be black since it's child, p, is red.
+        GrAssert(kBlack_Color == gp->fColor);
+
+
+        // x and its parent are red, violating red-black property.
+        Node* u = gp->fChildren[1-gpc];
+        // if x's uncle (p's sibling) is also red then we can flip
+        // p and u to black and make gp red. But then we have to recurse
+        // up to gp since it's parent may also be red.
+        if (NULL != u && kRed_Color == u->fColor) {
+            p->fColor = kBlack_Color;
+            u->fColor = kBlack_Color;
+            gp->fColor = kRed_Color;
+            x = gp;
+            p = x->fParent;
+            if (NULL == p) {
+                // x (prev gp) is the root, color it black and be done.
+                GrAssert(fRoot == x);
+                x->fColor = kBlack_Color;
+                validate();
+                return Iter(x, this);
+            }
+            gp = p->fParent;
+            pc = (p->fChildren[kLeft_Child] == x) ? kLeft_Child :
+                                                    kRight_Child;
+            if (NULL != gp) {
+                gpc = (gp->fChildren[kLeft_Child] == p) ? kLeft_Child :
+                                                          kRight_Child;
+            }
+            continue;
+        } break;
+    } while (true);
+    // Here p is red but u is black and we still have to resolve the fact
+    // that x and p are both red.
+    GrAssert(NULL == gp->fChildren[1-gpc] || kBlack_Color == gp->fChildren[1-gpc]->fColor);
+    GrAssert(kRed_Color == x->fColor);
+    GrAssert(kRed_Color == p->fColor);
+    GrAssert(kBlack_Color == gp->fColor);
+
+    // make x be on the same side of p as p is of gp. If it isn't already
+    // the case then rotate x up to p and swap their labels.
+    if (pc != gpc) {
+        if (kRight_Child == pc) {
+            rotateLeft(p);
+            Node* temp = p;
+            p = x;
+            x = temp;
+            pc = kLeft_Child;
+        } else {
+            rotateRight(p);
+            Node* temp = p;
+            p = x;
+            x = temp;
+            pc = kRight_Child;
+        }
+    }
+    // we now rotate gp down, pulling up p to be it's new parent.
+    // gp's child, u, that is not affected we know to be black. gp's new
+    // child is p's previous child (x's pre-rotation sibling) which must be
+    // black since p is red.
+    GrAssert(NULL == p->fChildren[1-pc] ||
+             kBlack_Color == p->fChildren[1-pc]->fColor);
+    // Since gp's two children are black it can become red if p is made
+    // black. This leaves the black-height of both of p's new subtrees
+    // preserved and removes the red/red parent child relationship.
+    p->fColor = kBlack_Color;
+    gp->fColor = kRed_Color;
+    if (kLeft_Child == pc) {
+        rotateRight(gp);
+    } else {
+        rotateLeft(gp);
+    }
+    validate();
+    return Iter(x, this);
+}
+
+
+template <typename T, typename C>
+void GrRedBlackTree<T,C>::rotateRight(Node* n) {
+    /*            d?              d?
+     *           /               /
+     *          n               s
+     *         / \     --->    / \
+     *        s   a?          c?  n
+     *       / \                 / \
+     *      c?  b?              b?  a?
+     */
+    Node* d = n->fParent;
+    Node* s = n->fChildren[kLeft_Child];
+    GrAssert(NULL != s);
+    Node* b = s->fChildren[kRight_Child];
+
+    if (NULL != d) {
+        Child c = d->fChildren[kLeft_Child] == n ? kLeft_Child :
+                                             kRight_Child;
+        d->fChildren[c] = s;
+    } else {
+        GrAssert(fRoot == n);
+        fRoot = s;
+    }
+    s->fParent = d;
+    s->fChildren[kRight_Child] = n;
+    n->fParent = s;
+    n->fChildren[kLeft_Child] = b;
+    if (NULL != b) {
+        b->fParent = n;
+    }
+
+    GR_DEBUGASSERT(validateChildRelations(d, true));
+    GR_DEBUGASSERT(validateChildRelations(s, true));
+    GR_DEBUGASSERT(validateChildRelations(n, false));
+    GR_DEBUGASSERT(validateChildRelations(n->fChildren[kRight_Child], true));
+    GR_DEBUGASSERT(validateChildRelations(b, true));
+    GR_DEBUGASSERT(validateChildRelations(s->fChildren[kLeft_Child], true));
+}
+
+template <typename T, typename C>
+void GrRedBlackTree<T,C>::rotateLeft(Node* n) {
+
+    Node* d = n->fParent;
+    Node* s = n->fChildren[kRight_Child];
+    GrAssert(NULL != s);
+    Node* b = s->fChildren[kLeft_Child];
+
+    if (NULL != d) {
+        Child c = d->fChildren[kRight_Child] == n ? kRight_Child :
+                                                   kLeft_Child;
+        d->fChildren[c] = s;
+    } else {
+        GrAssert(fRoot == n);
+        fRoot = s;
+    }
+    s->fParent = d;
+    s->fChildren[kLeft_Child] = n;
+    n->fParent = s;
+    n->fChildren[kRight_Child] = b;
+    if (NULL != b) {
+        b->fParent = n;
+    }
+
+    GR_DEBUGASSERT(validateChildRelations(d, true));
+    GR_DEBUGASSERT(validateChildRelations(s, true));
+    GR_DEBUGASSERT(validateChildRelations(n, true));
+    GR_DEBUGASSERT(validateChildRelations(n->fChildren[kLeft_Child], true));
+    GR_DEBUGASSERT(validateChildRelations(b, true));
+    GR_DEBUGASSERT(validateChildRelations(s->fChildren[kRight_Child], true));
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Node* GrRedBlackTree<T,C>::SuccessorNode(Node* x) {
+    GrAssert(NULL != x);
+    if (NULL != x->fChildren[kRight_Child]) {
+        x = x->fChildren[kRight_Child];
+        while (NULL != x->fChildren[kLeft_Child]) {
+            x = x->fChildren[kLeft_Child];
+        }
+        return x;
+    }
+    while (NULL != x->fParent && x == x->fParent->fChildren[kRight_Child]) {
+        x = x->fParent;
+    }
+    return x->fParent;
+}
+
+template <typename T, typename C>
+typename GrRedBlackTree<T,C>::Node* GrRedBlackTree<T,C>::PredecessorNode(Node* x) {
+    GrAssert(NULL != x);
+    if (NULL != x->fChildren[kLeft_Child]) {
+        x = x->fChildren[kLeft_Child];
+        while (NULL != x->fChildren[kRight_Child]) {
+            x = x->fChildren[kRight_Child];
+        }
+        return x;
+    }
+    while (NULL != x->fParent && x == x->fParent->fChildren[kLeft_Child]) {
+        x = x->fParent;
+    }
+    return x->fParent;
+}
+
+template <typename T, typename C>
+void GrRedBlackTree<T,C>::deleteAtNode(Node* x) {
+    GrAssert(NULL != x);
+    validate();
+    --fCount;
+
+    bool hasLeft =  NULL != x->fChildren[kLeft_Child];
+    bool hasRight = NULL != x->fChildren[kRight_Child];
+    Child c = hasLeft ? kLeft_Child : kRight_Child;
+
+    if (hasLeft && hasRight) {
+        // first and last can't have two children.
+        GrAssert(fFirst != x);
+        GrAssert(fLast != x);
+        // if x is an interior node then we find it's successor
+        // and swap them.
+        Node* s = x->fChildren[kRight_Child];
+        while (NULL != s->fChildren[kLeft_Child]) {
+            s = s->fChildren[kLeft_Child];
+        }
+        GrAssert(NULL != s);
+        // this might be expensive relative to swapping node ptrs around.
+        // depends on T.
+        x->fItem = s->fItem;
+        x = s;
+        c = kRight_Child;
+    } else if (NULL == x->fParent) {
+        // if x was the root we just replace it with its child and make
+        // the new root (if the tree is not empty) black.
+        GrAssert(fRoot == x);
+        fRoot = x->fChildren[c];
+        if (NULL != fRoot) {
+            fRoot->fParent = NULL;
+            fRoot->fColor = kBlack_Color;
+            if (x == fLast) {
+                GrAssert(c == kLeft_Child);
+                fLast = fRoot;
+            } else if (x == fFirst) {
+                GrAssert(c == kRight_Child);
+                fFirst = fRoot;
+            }
+        } else {
+            GrAssert(fFirst == fLast && x == fFirst);
+            fFirst = NULL;
+            fLast = NULL;
+            GrAssert(0 == fCount);
+        }
+        delete x;
+        validate();
+        return;
+    }
+
+    Child pc;
+    Node* p = x->fParent;
+    pc = p->fChildren[kLeft_Child] == x ? kLeft_Child : kRight_Child;
+
+    if (NULL == x->fChildren[c]) {
+        if (fLast == x) {
+            fLast = p;
+            GrAssert(p == PredecessorNode(x));
+        } else if (fFirst == x) {
+            fFirst = p;
+            GrAssert(p == SuccessorNode(x));
+        }
+        // x has two implicit black children.
+        Color xcolor = x->fColor;
+        p->fChildren[pc] = NULL;
+        delete x;
+        // when x is red it can be with an implicit black leaf without
+        // violating any of the red-black tree properties.
+        if (kRed_Color == xcolor) {
+            validate();
+            return;
+        }
+        // s is p's other child (x's sibling)
+        Node* s = p->fChildren[1-pc];
+
+        //s cannot be an implicit black node because the original
+        // black-height at x was >= 2 and s's black-height must equal the
+        // initial black height of x.
+        GrAssert(NULL != s);
+        GrAssert(p == s->fParent);
+
+        // assigned in loop
+        Node* sl;
+        Node* sr;
+        bool slRed;
+        bool srRed;
+
+        do {
+            // When we start this loop x may already be deleted it is/was
+            // p's child on its pc side. x's children are/were black. The
+            // first time through the loop they are implict children.
+            // On later passes we will be walking up the tree and they will
+            // be real nodes.
+            // The x side of p has a black-height that is one less than the
+            // s side. It must be rebalanced.
+            GrAssert(NULL != s);
+            GrAssert(p == s->fParent);
+            GrAssert(NULL == x || x->fParent == p);
+
+            //sl and sr are s's children, which may be implicit.
+            sl = s->fChildren[kLeft_Child];
+            sr = s->fChildren[kRight_Child];
+
+            // if the s is red we will rotate s and p, swap their colors so
+            // that x's new sibling is black
+            if (kRed_Color == s->fColor) {
+                // if s is red then it's parent must be black.
+                GrAssert(kBlack_Color == p->fColor);
+                // s's children must also be black since s is red. They can't
+                // be implicit since s is red and it's black-height is >= 2.
+                GrAssert(NULL != sl && kBlack_Color == sl->fColor);
+                GrAssert(NULL != sr && kBlack_Color == sr->fColor);
+                p->fColor = kRed_Color;
+                s->fColor = kBlack_Color;
+                if (kLeft_Child == pc) {
+                    rotateLeft(p);
+                    s = sl;
+                } else {
+                    rotateRight(p);
+                    s = sr;
+                }
+                sl = s->fChildren[kLeft_Child];
+                sr = s->fChildren[kRight_Child];
+            }
+            // x and s are now both black.
+            GrAssert(kBlack_Color == s->fColor);
+            GrAssert(kBlack_Color == x->fColor);
+            GrAssert(p == s->fParent);
+            GrAssert(p == x->fParent);
+
+            // when x is deleted its subtree will have reduced black-height.
+            slRed = (NULL != sl && kRed_Color == sl->fColor);
+            srRed = (NULL != sr && kRed_Color == sr->fColor);
+            if (!slRed && !srRed) {
+                // if s can be made red that will balance out x's removal
+                // to make both subtrees of p have the same black-height.
+                if (kBlack_Color == p->fColor) {
+                    s->fColor = kRed_Color;
+                    // now subtree at p has black-height of one less than
+                    // p's parent's other child's subtree. We move x up to
+                    // p and go through the loop again. At the top of loop
+                    // we assumed x and x's children are black, which holds
+                    // by above ifs.
+                    // if p is the root there is no other subtree to balance
+                    // against.
+                    x = p;
+                    p = x->fParent;
+                    if (NULL == p) {
+                        GrAssert(fRoot == x);
+                        validate();
+                        return;
+                    } else {
+                        pc = p->fChildren[kLeft_Child] == x ? kLeft_Child :
+                                                              kRight_Child;
+
+                    }
+                    s = p->fChildren[1-pc];
+                    GrAssert(NULL != s);
+                    GrAssert(p == s->fParent);
+                    continue;
+                } else if (kRed_Color == p->fColor) {
+                    // we can make p black and s red. This balance out p's
+                    // two subtrees and keep the same black-height as it was
+                    // before the delete.
+                    s->fColor = kRed_Color;
+                    p->fColor = kBlack_Color;
+                    validate();
+                    return;
+                }
+            }
+            break;
+        } while (true);
+        // if we made it here one or both of sl and sr is red.
+        // s and x are black. We make sure that a red child is on
+        // the same side of s as s is of p.
+        GrAssert(slRed || srRed);
+        if (kLeft_Child == pc && !srRed) {
+            s->fColor = kRed_Color;
+            sl->fColor = kBlack_Color;
+            rotateRight(s);
+            sr = s;
+            s = sl;
+            //sl = s->fChildren[kLeft_Child]; don't need this
+        } else if (kRight_Child == pc && !slRed) {
+            s->fColor = kRed_Color;
+            sr->fColor = kBlack_Color;
+            rotateLeft(s);
+            sl = s;
+            s = sr;
+            //sr = s->fChildren[kRight_Child]; don't need this
+        }
+        // now p is either red or black, x and s are red and s's 1-pc
+        // child is red.
+        // We rotate p towards x, pulling s up to replace p. We make
+        // p be black and s takes p's old color.
+        // Whether p was red or black, we've increased its pc subtree
+        // rooted at x by 1 (balancing the imbalance at the start) and
+        // we've also its subtree rooted at s's black-height by 1. This
+        // can be balanced by making s's red child be black.
+        s->fColor = p->fColor;
+        p->fColor = kBlack_Color;
+        if (kLeft_Child == pc) {
+            GrAssert(NULL != sr && kRed_Color == sr->fColor);
+            sr->fColor = kBlack_Color;
+            rotateLeft(p);
+        } else {
+            GrAssert(NULL != sl && kRed_Color == sl->fColor);
+            sl->fColor = kBlack_Color;
+            rotateRight(p);
+        }
+    }
+    else {
+        // x has exactly one implicit black child. x cannot be red.
+        // Proof by contradiction: Assume X is red. Let c0 be x's implicit
+        // child and c1 be its non-implicit child. c1 must be black because
+        // red nodes always have two black children. Then the two subtrees
+        // of x rooted at c0 and c1 will have different black-heights.
+        GrAssert(kBlack_Color == x->fColor);
+        // So we know x is black and has one implicit black child, c0. c1
+        // must be red, otherwise the subtree at c1 will have a different
+        // black-height than the subtree rooted at c0.
+        GrAssert(kRed_Color == x->fChildren[c]->fColor);
+        // replace x with c1, making c1 black, preserves all red-black tree
+        // props.
+        Node* c1 = x->fChildren[c];
+        if (x == fFirst) {
+            GrAssert(c == kRight_Child);
+            fFirst = c1;
+            while (NULL != fFirst->fChildren[kLeft_Child]) {
+                fFirst = fFirst->fChildren[kLeft_Child];
+            }
+            GrAssert(fFirst == SuccessorNode(x));
+        } else if (x == fLast) {
+            GrAssert(c == kLeft_Child);
+            fLast = c1;
+            while (NULL != fLast->fChildren[kRight_Child]) {
+                fLast = fLast->fChildren[kRight_Child];
+            }
+            GrAssert(fLast == PredecessorNode(x));
+        }
+        c1->fParent = p;
+        p->fChildren[pc] = c1;
+        c1->fColor = kBlack_Color;
+        delete x;
+        validate();
+    }
+    validate();
+}
+
+template <typename T, typename C>
+void GrRedBlackTree<T,C>::RecursiveDelete(Node* x) {
+    if (NULL != x) {
+        RecursiveDelete(x->fChildren[kLeft_Child]);
+        RecursiveDelete(x->fChildren[kRight_Child]);
+        delete x;
+    }
+}
+
+#if GR_DEBUG
+template <typename T, typename C>
+void GrRedBlackTree<T,C>::validate() const {
+    if (fCount) {
+        GrAssert(NULL == fRoot->fParent);
+        GrAssert(NULL != fFirst);
+        GrAssert(NULL != fLast);
+
+        GrAssert(kBlack_Color == fRoot->fColor);
+        if (1 == fCount) {
+            GrAssert(fFirst == fRoot);
+            GrAssert(fLast == fRoot);
+            GrAssert(0 == fRoot->fChildren[kLeft_Child]);
+            GrAssert(0 == fRoot->fChildren[kRight_Child]);
+        }
+    } else {
+        GrAssert(NULL == fRoot);
+        GrAssert(NULL == fFirst);
+        GrAssert(NULL == fLast);
+    }
+#if DEEP_VALIDATE
+    int bh;
+    int count = checkNode(fRoot, &bh);
+    GrAssert(count == fCount);
+#endif
+}
+
+template <typename T, typename C>
+int GrRedBlackTree<T,C>::checkNode(Node* n, int* bh) const {
+    if (NULL != n) {
+        GrAssert(validateChildRelations(n, false));
+        if (kBlack_Color == n->fColor) {
+            *bh += 1;
+        }
+        GrAssert(!fComp(n->fItem, fFirst->fItem));
+        GrAssert(!fComp(fLast->fItem, n->fItem));
+        int leftBh = *bh;
+        int rightBh = *bh;
+        int cl = checkNode(n->fChildren[kLeft_Child], &leftBh);
+        int cr = checkNode(n->fChildren[kRight_Child], &rightBh);
+        GrAssert(leftBh == rightBh);
+        *bh = leftBh;
+        return 1 + cl + cr;
+    }
+    return 0;
+}
+
+template <typename T, typename C>
+bool GrRedBlackTree<T,C>::validateChildRelations(const Node* n,
+                                                 bool allowRedRed) const {
+    if (NULL != n) {
+        if (NULL != n->fChildren[kLeft_Child] ||
+            NULL != n->fChildren[kRight_Child]) {
+            if (n->fChildren[kLeft_Child] == n->fChildren[kRight_Child]) {
+                return validateChildRelationsFailed();
+            }
+            if (n->fChildren[kLeft_Child] == n->fParent &&
+                NULL != n->fParent) {
+                return validateChildRelationsFailed();
+            }
+            if (n->fChildren[kRight_Child] == n->fParent &&
+                NULL != n->fParent) {
+                return validateChildRelationsFailed();
+            }
+            if (NULL != n->fChildren[kLeft_Child]) {
+                if (!allowRedRed &&
+                    kRed_Color == n->fChildren[kLeft_Child]->fColor &&
+                    kRed_Color == n->fColor) {
+                    return validateChildRelationsFailed();
+                }
+                if (n->fChildren[kLeft_Child]->fParent != n) {
+                    return validateChildRelationsFailed();
+                }
+                if (!(fComp(n->fChildren[kLeft_Child]->fItem, n->fItem) ||
+                      (!fComp(n->fChildren[kLeft_Child]->fItem, n->fItem) &&
+                       !fComp(n->fItem, n->fChildren[kLeft_Child]->fItem)))) {
+                    return validateChildRelationsFailed();
+                }
+            }
+            if (NULL != n->fChildren[kRight_Child]) {
+                if (!allowRedRed &&
+                    kRed_Color == n->fChildren[kRight_Child]->fColor &&
+                    kRed_Color == n->fColor) {
+                    return validateChildRelationsFailed();
+                }
+                if (n->fChildren[kRight_Child]->fParent != n) {
+                    return validateChildRelationsFailed();
+                }
+                if (!(fComp(n->fItem, n->fChildren[kRight_Child]->fItem) ||
+                      (!fComp(n->fChildren[kRight_Child]->fItem, n->fItem) &&
+                       !fComp(n->fItem, n->fChildren[kRight_Child]->fItem)))) {
+                    return validateChildRelationsFailed();
+                }
+            }
+        }
+    }
+    return true;
+}
+#endif
+
+#include "GrRandom.h"
+
+template <typename T, typename C>
+void GrRedBlackTree<T,C>::UnitTest() {
+    GrRedBlackTree<int> tree;
+    typedef GrRedBlackTree<int>::Iter iter;
+
+    GrRandom r;
+
+    int count[100] = {0};
+    // add 10K ints
+    for (int i = 0; i < 10000; ++i) {
+        int x = r.nextU()%100;
+        Iter xi = tree.insert(x);
+        GrAssert(*xi == x);
+        ++count[x];
+    }
+
+    tree.insert(0);
+    ++count[0];
+    tree.insert(99);
+    ++count[99];
+    GrAssert(*tree.begin() == 0);
+    GrAssert(*tree.last() == 99);
+    GrAssert(--(++tree.begin()) == tree.begin());
+    GrAssert(--tree.end() == tree.last());
+    GrAssert(tree.count() == 10002);
+
+    int c = 0;
+    // check that we iterate through the correct number of
+    // elements and they are properly sorted.
+    for (Iter a = tree.begin(); tree.end() != a; ++a) {
+        Iter b = a;
+        ++b;
+        ++c;
+        GrAssert(b == tree.end() || *a <= *b);
+    }
+    GrAssert(c == tree.count());
+
+    // check that the tree reports the correct number of each int
+    // and that we can iterate through them correctly both forward
+    // and backward.
+    for (int i = 0; i < 100; ++i) {
+        int c;
+        c = tree.countOf(i);
+        GrAssert(c == count[i]);
+        c = 0;
+        Iter iter = tree.findFirst(i);
+        while (iter != tree.end() && *iter == i) {
+            ++c;
+            ++iter;
+        }
+        GrAssert(count[i] == c);
+        c = 0;
+        iter = tree.findLast(i);
+        if (iter != tree.end()) {
+            do {
+                if (*iter == i) {
+                    ++c;
+                } else {
+                    break;
+                }
+                if (iter != tree.begin()) {
+                    --iter;
+                } else {
+                    break;
+                }
+            } while (true);
+        }
+        GrAssert(c == count[i]);
+    }
+    // remove all the ints between 25 and 74. Randomly chose to remove
+    // the first, last, or any entry for each.
+    for (int i = 25; i < 75; ++i) {
+        while (0 != tree.countOf(i)) {
+            --count[i];
+            int x = r.nextU() % 3;
+            Iter iter;
+            switch (x) {
+            case 0:
+                iter = tree.findFirst(i);
+                break;
+            case 1:
+                iter = tree.findLast(i);
+                break;
+            case 2:
+            default:
+                iter = tree.find(i);
+                break;
+            }
+            tree.remove(iter);
+        }
+        GrAssert(0 == count[i]);
+        GrAssert(tree.findFirst(i) == tree.end());
+        GrAssert(tree.findLast(i) == tree.end());
+        GrAssert(tree.find(i) == tree.end());
+    }
+    // remove all of the 0 entries. (tests removing begin())
+    GrAssert(*tree.begin() == 0);
+    GrAssert(*(--tree.end()) == 99);
+    while (0 != tree.countOf(0)) {
+        --count[0];
+        tree.remove(tree.find(0));
+    }
+    GrAssert(0 == count[0]);
+    GrAssert(tree.findFirst(0) == tree.end());
+    GrAssert(tree.findLast(0) == tree.end());
+    GrAssert(tree.find(0) == tree.end());
+    GrAssert(0 < *tree.begin());
+
+    // remove all the 99 entries (tests removing last()).
+    while (0 != tree.countOf(99)) {
+        --count[99];
+        tree.remove(tree.find(99));
+    }
+    GrAssert(0 == count[99]);
+    GrAssert(tree.findFirst(99) == tree.end());
+    GrAssert(tree.findLast(99) == tree.end());
+    GrAssert(tree.find(99) == tree.end());
+    GrAssert(99 > *(--tree.end()));
+    GrAssert(tree.last() == --tree.end());
+
+    // Make sure iteration still goes through correct number of entries
+    // and is still sorted correctly.
+    c = 0;
+    for (Iter a = tree.begin(); tree.end() != a; ++a) {
+        Iter b = a;
+        ++b;
+        ++c;
+        GrAssert(b == tree.end() || *a <= *b);
+    }
+    GrAssert(c == tree.count());
+
+    // repeat check that correct number of each entry is in the tree
+    // and iterates correctly both forward and backward.
+    for (int i = 0; i < 100; ++i) {
+        GrAssert(tree.countOf(i) == count[i]);
+        int c = 0;
+        Iter iter = tree.findFirst(i);
+        while (iter != tree.end() && *iter == i) {
+            ++c;
+            ++iter;
+        }
+        GrAssert(count[i] == c);
+        c = 0;
+        iter = tree.findLast(i);
+        if (iter != tree.end()) {
+            do {
+                if (*iter == i) {
+                    ++c;
+                } else {
+                    break;
+                }
+                if (iter != tree.begin()) {
+                    --iter;
+                } else {
+                    break;
+                }
+            } while (true);
+        }
+        GrAssert(count[i] == c);
+    }
+
+    // remove all entries
+    while (!tree.empty()) {
+        tree.remove(tree.begin());
+    }
+
+    // test reset on empty tree.
+    tree.reset();
+}
+
+#endif
diff --git a/gpu/src/gr_unittests.cpp b/gpu/src/gr_unittests.cpp
index a9fd40d124..8ef61b1605 100644
--- a/gpu/src/gr_unittests.cpp
+++ b/gpu/src/gr_unittests.cpp
@@ -19,6 +19,7 @@
 #include "GrTDArray.h"
 #include "GrTBSearch.h"
 #include "GrMatrix.h"
+#include "GrRedBlackTree.h"
 
 static void dump(const GrTDArray<int>& array) {
 #if 0
@@ -31,7 +32,7 @@ static void dump(const GrTDArray<int>& array) {
 
 static void test_tdarray() {
     GrTDArray<int> array;
-    
+
     *array.append() = 0; dump(array);
     *array.append() = 2; dump(array);
     *array.append() = 4; dump(array);
@@ -138,6 +139,7 @@ void gr_run_unittests() {
     test_bsearch();
     test_clip();
     GrMatrix::UnitTest();
+    GrRedBlackTree<int>::UnitTest();
 }