gpu/src/GrRedBlackTree.h

/*
    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 = kLeft_Child; // suppress uninit warning
    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