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#include <vector>
#include <queue>
#include <iostream>
#include <unordered_map>
struct GraphNode
{
// Adjacency list
std::vector<GraphNode*> mAdjacent;
};
struct Graph
{
// A graph contains nodes
std::vector<GraphNode*> mNodes;
};
struct WeightedEdge
{
// Which nodes are connected by this edge?
struct WeightedGraphNode* mFrom;
struct WeightedGraphNode* mTo;
// Weight of this edge
float mWeight;
};
struct WeightedGraphNode
{
std::vector<WeightedEdge*> mEdges;
};
struct WeightedGraph
{
std::vector<WeightedGraphNode*> mNodes;
};
struct GBFSScratch
{
const WeightedEdge* mParentEdge = nullptr;
float mHeuristic = 0.0f;
bool mInOpenSet = false;
bool mInClosedSet = false;
};
using GBFSMap =
std::unordered_map<const WeightedGraphNode*, GBFSScratch>;
struct AStarScratch
{
const WeightedEdge* mParentEdge = nullptr;
float mHeuristic = 0.0f;
float mActualFromStart = 0.0f;
bool mInOpenSet = false;
bool mInClosedSet = false;
};
using AStarMap =
std::unordered_map<const WeightedGraphNode*, AStarScratch>;
float ComputeHeuristic(const WeightedGraphNode* a, const WeightedGraphNode* b)
{
return 0.0f;
}
bool AStar(const WeightedGraph& g, const WeightedGraphNode* start,
const WeightedGraphNode* goal, AStarMap& outMap)
{
std::vector<const WeightedGraphNode*> openSet;
// Set current node to start, and mark in closed set
const WeightedGraphNode* current = start;
outMap[current].mInClosedSet = true;
do
{
// Add adjacent nodes to open set
for (const WeightedEdge* edge : current->mEdges)
{
const WeightedGraphNode* neighbor = edge->mTo;
// Get scratch data for this node
AStarScratch& data = outMap[neighbor];
// Only check nodes that aren't in the closed set
if (!data.mInClosedSet)
{
if (!data.mInOpenSet)
{
// Not in the open set, so parent must be current
data.mParentEdge = edge;
data.mHeuristic = ComputeHeuristic(neighbor, goal);
// Actual cost is the parent's plus cost of traversing edge
data.mActualFromStart = outMap[current].mActualFromStart +
edge->mWeight;
data.mInOpenSet = true;
openSet.emplace_back(neighbor);
}
else
{
// Compute what new actual cost is if current becomes parent
float newG = outMap[current].mActualFromStart + edge->mWeight;
if (newG < data.mActualFromStart)
{
// Current should adopt this node
data.mParentEdge = edge;
data.mActualFromStart = newG;
}
}
}
}
// If open set is empty, all possible paths are exhausted
if (openSet.empty())
{
break;
}
// Find lowest cost node in open set
auto iter = std::min_element(openSet.begin(), openSet.end(),
[&outMap](const WeightedGraphNode* a, const WeightedGraphNode* b) {
// Calculate f(x) for nodes a/b
float fOfA = outMap[a].mHeuristic + outMap[a].mActualFromStart;
float fOfB = outMap[b].mHeuristic + outMap[b].mActualFromStart;
return fOfA < fOfB;
});
// Set to current and move from open to closed
current = *iter;
openSet.erase(iter);
outMap[current].mInOpenSet = true;
outMap[current].mInClosedSet = true;
} while (current != goal);
// Did we find a path?
return (current == goal) ? true : false;
}
bool GBFS(const WeightedGraph& g, const WeightedGraphNode* start,
const WeightedGraphNode* goal, GBFSMap& outMap)
{
std::vector<const WeightedGraphNode*> openSet;
// Set current node to start, and mark in closed set
const WeightedGraphNode* current = start;
outMap[current].mInClosedSet = true;
do
{
// Add adjacent nodes to open set
for (const WeightedEdge* edge : current->mEdges)
{
// Get scratch data for this node
GBFSScratch& data = outMap[edge->mTo];
// Add it only if it's not in the closed set
if (!data.mInClosedSet)
{
// Set the adjacent node's parent edge
data.mParentEdge = edge;
if (!data.mInOpenSet)
{
// Compute the heuristic for this node, and add to open set
data.mHeuristic = ComputeHeuristic(edge->mTo, goal);
data.mInOpenSet = true;
openSet.emplace_back(edge->mTo);
}
}
}
// If open set is empty, all possible paths are exhausted
if (openSet.empty())
{
break;
}
// Find lowest cost node in open set
auto iter = std::min_element(openSet.begin(), openSet.end(),
[&outMap](const WeightedGraphNode* a, const WeightedGraphNode* b) {
return outMap[a].mHeuristic < outMap[b].mHeuristic;
});
// Set to current and move from open to closed
current = *iter;
openSet.erase(iter);
outMap[current].mInOpenSet = false;
outMap[current].mInClosedSet = true;
} while (current != goal);
// Did we find a path?
return (current == goal) ? true : false;
}
using NodeToParentMap =
std::unordered_map<const GraphNode*, const GraphNode*>;
bool BFS(const Graph& graph, const GraphNode* start, const GraphNode* goal, NodeToParentMap& outMap)
{
// Whether we found a path
bool pathFound = false;
// Nodes to consider
std::queue<const GraphNode*> q;
// Enqueue the first node
q.emplace(start);
while (!q.empty())
{
// Dequeue a node
const GraphNode* current = q.front();
q.pop();
if (current == goal)
{
pathFound = true;
break;
}
// Enqueue adjacent nodes that aren't already in the queue
for (const GraphNode* node : current->mAdjacent)
{
// If the parent is null, it hasn't been enqueued
// (except for the start node)
const GraphNode* parent = outMap[node];
if (parent == nullptr && node != start)
{
// Enqueue this node, setting its parent
outMap[node] = current;
q.emplace(node);
}
}
}
return pathFound;
}
void testBFS()
{
Graph g;
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
GraphNode* node = new GraphNode;
g.mNodes.emplace_back(node);
}
}
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
GraphNode* node = g.mNodes[i * 5 + j];
if (i > 0)
{
node->mAdjacent.emplace_back(g.mNodes[(i - 1) * 5 + j]);
}
if (i < 4)
{
node->mAdjacent.emplace_back(g.mNodes[(i + 1) * 5 + j]);
}
if (j > 0)
{
node->mAdjacent.emplace_back(g.mNodes[i * 5 + j - 1]);
}
if (j < 4)
{
node->mAdjacent.emplace_back(g.mNodes[i * 5 + j + 1]);
}
}
}
NodeToParentMap map;
bool found = BFS(g, g.mNodes[0], g.mNodes[9], map);
std::cout << found << '\n';
}
void testHeuristic(bool useAStar)
{
WeightedGraph g;
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
WeightedGraphNode* node = new WeightedGraphNode;
g.mNodes.emplace_back(node);
}
}
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
WeightedGraphNode* node = g.mNodes[i * 5 + j];
if (i > 0)
{
WeightedEdge* e = new WeightedEdge;
e->mFrom = node;
e->mTo = g.mNodes[(i - 1) * 5 + j];
e->mWeight = 1.0f;
node->mEdges.emplace_back(e);
}
if (i < 4)
{
WeightedEdge* e = new WeightedEdge;
e->mFrom = node;
e->mTo = g.mNodes[(i + 1) * 5 + j];
e->mWeight = 1.0f;
node->mEdges.emplace_back(e);
}
if (j > 0)
{
WeightedEdge* e = new WeightedEdge;
e->mFrom = node;
e->mTo = g.mNodes[i * 5 + j - 1];
e->mWeight = 1.0f;
node->mEdges.emplace_back(e);
}
if (j < 4)
{
WeightedEdge* e = new WeightedEdge;
e->mFrom = node;
e->mTo = g.mNodes[i * 5 + j + 1];
e->mWeight = 1.0f;
node->mEdges.emplace_back(e);
}
}
}
bool found = false;
if (useAStar)
{
AStarMap map;
found = AStar(g, g.mNodes[0], g.mNodes[9], map);
}
else
{
GBFSMap map;
found = GBFS(g, g.mNodes[0], g.mNodes[9], map);
}
std::cout << found << '\n';
}
struct GameState
{
// (For tic-tac-toe, array of board)
enum SquareState { Empty, X, O };
SquareState mBoard[3][3];
};
struct GTNode
{
// Children nodes
std::vector<GTNode*> mChildren;
// State of game
GameState mState;
};
void GenStates(GTNode* root, bool xPlayer)
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
if (root->mState.mBoard[i][j] == GameState::Empty)
{
GTNode* node = new GTNode;
root->mChildren.emplace_back(node);
node->mState = root->mState;
node->mState.mBoard[i][j] = xPlayer ? GameState::X : GameState::O;
GenStates(node, !xPlayer);
}
}
}
}
float GetScore(const GameState& state)
{
// Are any of the rows the same?
for (int i = 0; i < 3; i++)
{
bool same = true;
GameState::SquareState v = state.mBoard[i][0];
for (int j = 1; j < 3; j++)
{
if (state.mBoard[i][j] != v)
{
same = false;
}
}
if (same)
{
if (v == GameState::X)
{
return 1.0f;
}
else
{
return -1.0f;
}
}
}
// Are any of the columns the same?
for (int j = 0; j < 3; j++)
{
bool same = true;
GameState::SquareState v = state.mBoard[0][j];
for (int i = 1; i < 3; i++)
{
if (state.mBoard[i][j] != v)
{
same = false;
}
}
if (same)
{
if (v == GameState::X)
{
return 1.0f;
}
else
{
return -1.0f;
}
}
}
// What about diagonals?
if (((state.mBoard[0][0] == state.mBoard[1][1]) &&
(state.mBoard[1][1] == state.mBoard[2][2])) ||
((state.mBoard[2][0] == state.mBoard[1][1]) &&
(state.mBoard[1][1] == state.mBoard[0][2])))
{
if (state.mBoard[1][1] == GameState::X)
{
return 1.0f;
}
else
{
return -1.0f;
}
}
// We tied
return 0.0f;
}
float MinPlayer(const GTNode* node);
float MaxPlayer(const GTNode* node)
{
// If this is a leaf, return score
if (node->mChildren.empty())
{
return GetScore(node->mState);
}
float maxValue = -std::numeric_limits<float>::infinity();
// Find the subtree with the maximum value
for (const GTNode* child : node->mChildren)
{
maxValue = std::max(maxValue, MinPlayer(child));
}
return maxValue;
}
float MinPlayer(const GTNode* node)
{
// If this is a leaf, return score
if (node->mChildren.empty())
{
return GetScore(node->mState);
}
float minValue = std::numeric_limits<float>::infinity();
// Find the subtree with the minimum value
for (const GTNode* child : node->mChildren)
{
minValue = std::min(minValue, MaxPlayer(child));
}
return minValue;
}
const GTNode* MinimaxDecide(const GTNode* root)
{
// Find the subtree with the maximum value, and save the choice
const GTNode* choice = nullptr;
float maxValue = -std::numeric_limits<float>::infinity();
for (const GTNode* child : root->mChildren)
{
float v = MinPlayer(child);
if (v > maxValue)
{
maxValue = v;
choice = child;
}
}
return choice;
}
float AlphaBetaMin(const GTNode* node, float alpha, float beta);
float AlphaBetaMax(const GTNode* node, float alpha, float beta)
{
// If this is a leaf, return score
if (node->mChildren.empty())
{
return GetScore(node->mState);
}
float maxValue = -std::numeric_limits<float>::infinity();
// Find the subtree with the maximum value
for (const GTNode* child : node->mChildren)
{
maxValue = std::max(maxValue, AlphaBetaMin(child, alpha, beta));
if (maxValue >= beta)
{
return maxValue; // Beta prune
}
alpha = std::max(maxValue, alpha);
}
return maxValue;
}
float AlphaBetaMin(const GTNode* node, float alpha, float beta)
{
// If this is a leaf, return score
if (node->mChildren.empty())
{
return GetScore(node->mState);
}
float minValue = std::numeric_limits<float>::infinity();
// Find the subtree with the minimum value
for (const GTNode* child : node->mChildren)
{
minValue = std::min(minValue, AlphaBetaMax(child, alpha, beta));
if (minValue <= alpha)
{
return minValue; // Alpha prune
}
beta = std::min(minValue, beta);
}
return minValue;
}
const GTNode* AlphaBetaDecide(const GTNode* root)
{
// Find the subtree with the maximum value, and save the choice
const GTNode* choice = nullptr;
float maxValue = -std::numeric_limits<float>::infinity();
float beta = std::numeric_limits<float>::infinity();
for (const GTNode* child : root->mChildren)
{
float v = AlphaBetaMin(child, maxValue, beta);
if (v > maxValue)
{
maxValue = v;
choice = child;
}
}
return choice;
}
void testTicTac()
{
GTNode* root = new GTNode;
root->mState.mBoard[0][0] = GameState::O;
root->mState.mBoard[0][1] = GameState::Empty;
root->mState.mBoard[0][2] = GameState::X;
root->mState.mBoard[1][0] = GameState::X;
root->mState.mBoard[1][1] = GameState::O;
root->mState.mBoard[1][2] = GameState::O;
root->mState.mBoard[2][0] = GameState::X;
root->mState.mBoard[2][1] = GameState::Empty;
root->mState.mBoard[2][2] = GameState::Empty;
GenStates(root, true);
const GTNode* choice = AlphaBetaDecide(root);
std::cout << choice->mChildren.size();
}