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/*
* Copyright 2018 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "include/core/SkRefCnt.h"
#include "src/core/SkTSort.h"
#include "tests/Test.h"
#include "tools/ToolUtils.h"
// A node in the graph. This corresponds to an opsTask in the MDB world.
class Node : public SkRefCnt {
public:
char id() const { return fID; }
int indexInSort() const { SkASSERT(fIndexInSort >= 0); return fIndexInSort; }
bool visited() const { return fVisited; }
#ifdef SK_DEBUG
void print() const {
SkDebugf("%d: id %c", fIndexInSort, fID);
if (fNodesIDependOn.count()) {
SkDebugf(" I depend on (%d): ", fNodesIDependOn.count());
for (Node* tmp : fNodesIDependOn) {
SkDebugf("%c, ", tmp->id());
}
}
if (fNodesThatDependOnMe.count()) {
SkDebugf(" (%d) depend on me: ", fNodesThatDependOnMe.count());
for (Node* tmp : fNodesThatDependOnMe) {
SkDebugf("%c, ", tmp->id());
}
}
SkDebugf("\n");
}
#endif
void validate(skiatest::Reporter* reporter) const {
for (Node* dependedOn : fNodesIDependOn) {
REPORTER_ASSERT(reporter, dependedOn->indexInSort() < this->indexInSort());
}
for (Node* dependent : fNodesThatDependOnMe) {
REPORTER_ASSERT(reporter, this->indexInSort() < dependent->indexInSort());
}
REPORTER_ASSERT(reporter, !fVisited); // this flag should only be true w/in depEdges()
}
static bool CompareIndicesGT(Node* const& a, Node* const& b) {
return a->indexInSort() > b->indexInSort();
}
int numDependents() const { return fNodesThatDependOnMe.count(); }
Node* dependent(int index) const {
SkASSERT(0 <= index && index < fNodesThatDependOnMe.count());
return fNodesThatDependOnMe[index];
}
private:
friend class Graph;
explicit Node(char id) : fID(id), fIndexInSort(-1), fVisited(false) {}
void setIndexInSort(int indexInSort) { fIndexInSort = indexInSort; }
void setVisited(bool visited) { fVisited = visited; }
void addDependency(Node* dependedOn) {
fNodesIDependOn.push_back(dependedOn);
dependedOn->addDependent(this);
}
void addDependent(Node* dependent) {
fNodesThatDependOnMe.push_back(dependent);
}
char fID;
SkTDArray<Node*> fNodesIDependOn; // These nodes must appear before this one in the sort
SkTDArray<Node*> fNodesThatDependOnMe; // These ones must appear after this one
int fIndexInSort;
bool fVisited; // only used in addEdges()
};
// The DAG driving the incremental topological sort. This corresponds to the opsTask DAG in
// the MDB world.
class Graph {
public:
Graph(int numNodesToReserve, skiatest::Reporter* reporter)
: fNodes(numNodesToReserve)
, fReporter(reporter) {
}
Node* addNode(uint32_t id) {
this->validate();
sk_sp<Node> tmp(new Node(id));
fNodes.push_back(tmp); // The graph gets the creation ref
tmp->setIndexInSort(fNodes.count()-1);
this->validate();
return tmp.get();
}
// 'dependedOn' must appear before 'dependent' in the sort
void addEdge(Node* dependedOn, Node* dependent) {
// TODO: this would be faster if all the SkTDArray code was stripped out of
// addEdges but, when used in MDB sorting, this entry point will never be used.
SkTDArray<Node*> tmp(&dependedOn, 1);
this->addEdges(&tmp, dependent);
}
// All the nodes in 'dependedOn' must appear before 'dependent' in the sort.
// This is O(v + e + cost_of_sorting(b)) where:
// v: number of nodes
// e: number of edges
// b: number of new edges in 'dependedOn'
//
// The algorithm works by first finding the "affected region" that contains all the
// nodes whose position in the topological sort is invalidated by the addition of the new
// edges. It then traverses the affected region from left to right, temporarily removing
// invalid nodes from 'fNodes' and shifting valid nodes left to fill in the gaps. In this
// left to right traversal, when a node is shifted to the left the current set of invalid
// nodes is examined to see if any needed to be moved to the right of that node. If so,
// they are reintroduced to the 'fNodes' array but now in the appropriate position. The
// separation of the algorithm into search (the dfs method) and readjustment (the shift
// method) means that each node affected by the new edges is only ever moved once.
void addEdges(SkTDArray<Node*>* dependedOn, Node* dependent) {
this->validate();
// remove any of the new dependencies that are already satisfied
for (int i = 0; i < dependedOn->count(); ++i) {
if ((*dependedOn)[i]->indexInSort() < dependent->indexInSort()) {
dependent->addDependency((*dependedOn)[i]);
dependedOn->removeShuffle(i);
i--;
} else {
dependent->addDependency((*dependedOn)[i]);
}
}
if (dependedOn->isEmpty()) {
return;
}
// Sort the remaining dependencies into descending order based on their indices in the
// sort. This means that we will be proceeding from right to left in the sort when
// correcting the order.
// TODO: QSort is waaay overkill here!
SkTQSort<Node*>(dependedOn->begin(), dependedOn->end() - 1, Node::CompareIndicesGT);
// TODO: although this is the general algorithm, I think this can be simplified for our
// use case (i.e., the same dependent for all the new edges).
int lowerBound = fNodes.count(); // 'lowerBound' tracks the left of the affected region
for (int i = 0; i < dependedOn->count(); ++i) {
if ((*dependedOn)[i]->indexInSort() < lowerBound) {
this->shift(lowerBound);
}
if (!dependent->visited()) {
this->dfs(dependent, (*dependedOn)[i]->indexInSort());
}
lowerBound = std::min(dependent->indexInSort(), lowerBound);
}
this->shift(lowerBound);
this->validate();
}
// Get the list of node ids in the current sorted order
void getActual(SkString* actual) const {
this->validate();
for (int i = 0; i < fNodes.count(); ++i) {
(*actual) += fNodes[i]->id();
if (i < fNodes.count()-1) {
(*actual) += ',';
}
}
}
#ifdef SK_DEBUG
void print() const {
SkDebugf("-------------------\n");
for (int i = 0; i < fNodes.count(); ++i) {
if (fNodes[i]) {
SkDebugf("%c ", fNodes[i]->id());
} else {
SkDebugf("0 ");
}
}
SkDebugf("\n");
for (int i = 0; i < fNodes.count(); ++i) {
if (fNodes[i]) {
fNodes[i]->print();
}
}
SkDebugf("Stack: ");
for (int i = 0; i < fStack.count(); ++i) {
SkDebugf("%c/%c ", fStack[i].fNode->id(), fStack[i].fDest->id());
}
SkDebugf("\n");
}
#endif
private:
void validate() const {
REPORTER_ASSERT(fReporter, fStack.empty());
for (int i = 0; i < fNodes.count(); ++i) {
REPORTER_ASSERT(fReporter, fNodes[i]->indexInSort() == i);
fNodes[i]->validate(fReporter);
}
// All the nodes in the Queue had better have been marked as visited
for (int i = 0; i < fStack.count(); ++i) {
SkASSERT(fStack[i].fNode->visited());
}
}
// Collect the nodes that need to be moved within the affected region. All the nodes found
// to be in violation of the topological constraints are placed in 'fStack'.
void dfs(Node* node, int upperBound) {
node->setVisited(true);
for (int i = 0; i < node->numDependents(); ++i) {
Node* dependent = node->dependent(i);
SkASSERT(dependent->indexInSort() != upperBound); // this would be a cycle
if (!dependent->visited() && dependent->indexInSort() < upperBound) {
this->dfs(dependent, upperBound);
}
}
fStack.push_back({ sk_ref_sp(node), fNodes[upperBound].get() });
}
// Move 'node' to the index-th slot of the sort. The index-th slot should not have a current
// occupant.
void moveNodeInSort(sk_sp<Node> node, int index) {
SkASSERT(!fNodes[index]);
fNodes[index] = node;
node->setIndexInSort(index);
}
#ifdef SK_DEBUG
// Does 'fStack' have 'node'? That is, was 'node' discovered to be in violation of the
// topological constraints?
bool stackContains(Node* node) {
for (int i = 0; i < fStack.count(); ++i) {
if (node == fStack[i].fNode.get()) {
return true;
}
}
return false;
}
#endif
// The 'shift' method iterates through the affected area from left to right moving Nodes that
// were found to be in violation of the topological order (i.e., in 'fStack') to their correct
// locations and shifting the non-violating nodes left, into the holes the violating nodes left
// behind.
void shift(int index) {
int numRemoved = 0;
while (!fStack.empty()) {
sk_sp<Node> node = fNodes[index];
if (node->visited()) {
// This node is in 'fStack' and was found to be in violation of the topological
// constraints. Remove it from 'fNodes' so non-violating nodes can be shifted
// left.
SkASSERT(this->stackContains(node.get()));
node->setVisited(false); // reset for future use
fNodes[index] = nullptr;
numRemoved++;
} else {
// This node was found to not be in violation of any topological constraints but
// must be moved left to fill in for those that were.
SkASSERT(!this->stackContains(node.get()));
SkASSERT(numRemoved); // should be moving left
this->moveNodeInSort(node, index - numRemoved);
fNodes[index] = nullptr;
}
while (!fStack.empty() && node.get() == fStack.back().fDest) {
// The left to right loop has finally encountered the destination for one or more
// of the nodes in 'fStack'. Place them to the right of 'node' in the sort. Note
// that because the violating nodes were already removed from 'fNodes' there
// should be enough empty space for them to be placed now.
numRemoved--;
this->moveNodeInSort(fStack.back().fNode, index - numRemoved);
fStack.pop_back();
}
index++;
}
}
SkTArray<sk_sp<Node>> fNodes;
struct StackInfo {
sk_sp<Node> fNode; // This gets a ref bc, in 'shift' it will be pulled out of 'fNodes'
Node* fDest;
};
SkTArray<StackInfo> fStack; // only used in addEdges()
skiatest::Reporter* fReporter;
};
// This test adds a single invalidating edge.
static void test_1(skiatest::Reporter* reporter) {
Graph g(10, reporter);
Node* nodeQ = g.addNode('q');
Node* nodeY = g.addNode('y');
Node* nodeA = g.addNode('a');
Node* nodeZ = g.addNode('z');
Node* nodeB = g.addNode('b');
/*Node* nodeC =*/ g.addNode('c');
Node* nodeW = g.addNode('w');
Node* nodeD = g.addNode('d');
Node* nodeX = g.addNode('x');
Node* nodeR = g.addNode('r');
// All these edge are non-invalidating
g.addEdge(nodeD, nodeR);
g.addEdge(nodeZ, nodeW);
g.addEdge(nodeA, nodeB);
g.addEdge(nodeY, nodeZ);
g.addEdge(nodeQ, nodeA);
{
const SkString kExpectedInitialState("q,y,a,z,b,c,w,d,x,r");
SkString actualInitialState;
g.getActual(&actualInitialState);
REPORTER_ASSERT(reporter, kExpectedInitialState == actualInitialState);
}
// Add the invalidating edge
g.addEdge(nodeX, nodeY);
{
const SkString kExpectedFinalState("q,a,b,c,d,x,y,z,w,r");
SkString actualFinalState;
g.getActual(&actualFinalState);
REPORTER_ASSERT(reporter, kExpectedFinalState == actualFinalState);
}
}
// This test adds two invalidating edge sequentially
static void test_2(skiatest::Reporter* reporter) {
Graph g(10, reporter);
Node* nodeY = g.addNode('y');
/*Node* nodeA =*/ g.addNode('a');
Node* nodeW = g.addNode('w');
/*Node* nodeB =*/ g.addNode('b');
Node* nodeZ = g.addNode('z');
Node* nodeU = g.addNode('u');
/*Node* nodeC =*/ g.addNode('c');
Node* nodeX = g.addNode('x');
/*Node* nodeD =*/ g.addNode('d');
Node* nodeV = g.addNode('v');
// All these edge are non-invalidating
g.addEdge(nodeU, nodeX);
g.addEdge(nodeW, nodeU);
g.addEdge(nodeW, nodeZ);
g.addEdge(nodeY, nodeZ);
{
const SkString kExpectedInitialState("y,a,w,b,z,u,c,x,d,v");
SkString actualInitialState;
g.getActual(&actualInitialState);
REPORTER_ASSERT(reporter, kExpectedInitialState == actualInitialState);
}
// Add the first invalidating edge
g.addEdge(nodeX, nodeY);
{
const SkString kExpectedFirstState("a,w,b,u,c,x,y,z,d,v");
SkString actualFirstState;
g.getActual(&actualFirstState);
REPORTER_ASSERT(reporter, kExpectedFirstState == actualFirstState);
}
// Add the second invalidating edge
g.addEdge(nodeV, nodeW);
{
const SkString kExpectedSecondState("a,b,c,d,v,w,u,x,y,z");
SkString actualSecondState;
g.getActual(&actualSecondState);
REPORTER_ASSERT(reporter, kExpectedSecondState == actualSecondState);
}
}
static void test_diamond(skiatest::Reporter* reporter) {
Graph g(4, reporter);
/* Create the graph (the '.' is the pointy side of the arrow):
* b
* . \
* / .
* a d
* \ .
* . /
* c
* Possible topological orders are [a,c,b,d] and [a,b,c,d].
*/
Node* nodeD = g.addNode('d');
Node* nodeC = g.addNode('c');
Node* nodeB = g.addNode('b');
{
SkTDArray<Node*> dependedOn;
dependedOn.push_back(nodeB);
dependedOn.push_back(nodeC);
g.addEdges(&dependedOn, nodeD); // nodes B and C must come before node D
}
Node* nodeA = g.addNode('a');
g.addEdge(nodeA, nodeB); // node A must come before node B
g.addEdge(nodeA, nodeC); // node A must come before node C
const SkString kExpected0("a,c,b,d");
const SkString kExpected1("a,b,c,d");
SkString actual;
g.getActual(&actual);
REPORTER_ASSERT(reporter, kExpected0 == actual || kExpected1 == actual);
}
static void test_lopsided_binary_tree(skiatest::Reporter* reporter) {
Graph g(7, reporter);
/* Create the graph (the '.' is the pointy side of the arrow):
* a
* / \
* . .
* b c
* / \
* . .
* d e
* / \
* . .
* f g
*
* Possible topological order is: [a,b,c,d,e,f,g].
*/
Node* nodeG = g.addNode('g');
Node* nodeF = g.addNode('f');
Node* nodeE = g.addNode('e');
Node* nodeD = g.addNode('d');
Node* nodeC = g.addNode('c');
Node* nodeB = g.addNode('b');
Node* nodeA = g.addNode('a');
g.addEdge(nodeE, nodeG);
g.addEdge(nodeE, nodeF);
g.addEdge(nodeC, nodeE);
g.addEdge(nodeC, nodeD);
g.addEdge(nodeA, nodeC);
g.addEdge(nodeA, nodeB);
const SkString kExpected("a,b,c,d,e,f,g");
SkString actual;
g.getActual(&actual);
REPORTER_ASSERT(reporter, kExpected == actual);
}
DEF_TEST(IncrTopoSort, reporter) {
test_1(reporter);
test_2(reporter);
test_diamond(reporter);
test_lopsided_binary_tree(reporter);
}