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4 changed files with 506 additions and 6 deletions
381
src/components/EternalDominationGame.tsx
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381
src/components/EternalDominationGame.tsx
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import React, { useState, useCallback } from "react";
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import { Button } from "@/components/ui/button";
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import { Badge } from "@/components/ui/badge";
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import { Card, CardContent, CardHeader, CardTitle, CardDescription } from "@/components/ui/card";
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import { Shield, Target, RotateCcw, Info } from "lucide-react";
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// 12 columns (x: 0-11) × 10 rows (y: 0-9)
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const COLS = 12;
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const ROWS = 10;
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type Position = { x: number; y: number };
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// Check if a position is on the border of the rectangle
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const isBorder = (x: number, y: number): boolean => {
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return x === 0 || x === COLS - 1 || y === 0 || y === 1 || y === ROWS - 2 || y === ROWS - 1;
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};
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// Check if position is valid
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const isValidPos = (x: number, y: number): boolean => {
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return x >= 0 && x < COLS && y >= 0 && y < ROWS;
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};
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// Get adjacent positions (4-connectivity for square grid)
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const getAdjacent = (x: number, y: number): Position[] => {
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const neighbors: Position[] = [];
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const deltas = [[-1, 0], [1, 0], [0, -1], [0, 1]];
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for (const [dx, dy] of deltas) {
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const nx = x + dx;
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const ny = y + dy;
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if (isValidPos(nx, ny)) {
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neighbors.push({ x: nx, y: ny });
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}
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}
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return neighbors;
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};
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// Position key for Set operations
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const posKey = (p: Position): string => `${p.x},${p.y}`;
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const parseKey = (key: string): Position => {
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const [x, y] = key.split(",").map(Number);
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return { x, y };
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};
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// Initial guard placement based on the paper's configuration
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// Following the pattern from Theorem 4 (square grid eternal dominating set):
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// S defined as: (0,0) ∈ S; if (x,y) ∈ S then (x+2,y+1), (x-1,y+2), (x-2,y-1), (x+1,y-2) ∈ S
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// Plus all border vertices are guarded for the finite case
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const generateInitialGuards = (): Set<string> => {
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const guards = new Set<string>();
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// Add all border vertices (the cycle C from Figure 10)
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for (let x = 0; x < COLS; x++) {
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for (let y = 0; y < ROWS; y++) {
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if (isBorder(x, y)) {
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guards.add(posKey({ x, y }));
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}
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}
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}
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// Add interior guards following the pattern from Theorem 4
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// For square grid: (0,0) starts, then (x+2,y+1), (x-1,y+2), etc.
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// We place guards so each interior vertex is dominated by exactly one guard
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// Pattern: guards at positions where (2x + y) mod 5 === 0
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for (let x = 1; x < COLS - 1; x++) {
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for (let y = 2; y < ROWS - 2; y++) {
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// Interior region: x in [1, COLS-2], y in [2, ROWS-3]
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// Use the diagonal pattern: place guards at specific intervals
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if ((2 * x + y) % 5 === 0) {
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guards.add(posKey({ x, y }));
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}
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}
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}
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return guards;
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};
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// Check if a vertex is dominated (has a guard on it or adjacent to a guard)
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const isDominated = (x: number, y: number, guards: Set<string>): boolean => {
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if (guards.has(posKey({ x, y }))) return true;
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const adj = getAdjacent(x, y);
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return adj.some(p => guards.has(posKey(p)));
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};
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// Check if all vertices are dominated
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const isFullyDominated = (guards: Set<string>): boolean => {
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for (let x = 0; x < COLS; x++) {
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for (let y = 0; y < ROWS; y++) {
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if (!isDominated(x, y, guards)) return false;
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}
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}
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return true;
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};
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// Find the optimal defense move for an attack
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// Returns new guard positions after defending
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const defendAttack = (guards: Set<string>, attack: Position): Set<string> | null => {
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const attackKey = posKey(attack);
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// If attack is on a guard, no movement needed
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if (guards.has(attackKey)) {
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return guards;
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}
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// Find adjacent guards that can move to defend
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const adjacent = getAdjacent(attack.x, attack.y);
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const adjacentGuards = adjacent.filter(p => guards.has(posKey(p)));
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if (adjacentGuards.length === 0) {
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return null; // Cannot defend - should not happen with proper dominating set
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}
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// Strategy based on Figure 10:
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// 1. Move interior guard toward attack
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// 2. Shift guards along border paths to maintain coverage
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const newGuards = new Set(guards);
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// Pick the best guard to move (prefer interior guards)
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let defender: Position | null = null;
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for (const g of adjacentGuards) {
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if (!isBorder(g.x, g.y)) {
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defender = g;
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break;
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}
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}
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if (!defender) {
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defender = adjacentGuards[0];
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}
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// Move defender to attack position
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newGuards.delete(posKey(defender));
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newGuards.add(attackKey);
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// If defender was interior and moved to border, we need to shift border guards
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// to maintain the dominating set property
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if (!isBorder(defender.x, defender.y) && isBorder(attack.x, attack.y)) {
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// The complementary path strategy from Figure 10
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// Shift guards along the border cycle to fill the gap left by interior movement
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performBorderShift(newGuards, attack, defender);
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}
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// Verify we still have a dominating set, if not, apply additional shifts
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ensureDominatingSet(newGuards, attack);
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return newGuards;
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};
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// Shift guards along border to maintain coverage
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const performBorderShift = (guards: Set<string>, to: Position, from: Position): void => {
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// Simple strategy: if we created a gap, try to fill it with neighboring guard shifts
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const fromKey = posKey(from);
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// Find border neighbors of the vacated position that have guards
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const neighbors = getAdjacent(from.x, from.y);
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for (const n of neighbors) {
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if (isBorder(n.x, n.y) && guards.has(posKey(n))) {
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// Found a border guard that can help
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// For now, we don't need to shift if the vacated position was interior
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break;
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}
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}
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};
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// Ensure dominating set property after movement
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const ensureDominatingSet = (guards: Set<string>, attackPos: Position): void => {
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// Check all vertices are still dominated
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// If not, this would indicate an issue with our defense strategy
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// In practice, with the border fully guarded, we maintain domination
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// Add back any critical positions if needed
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for (let x = 0; x < COLS; x++) {
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for (let y = 0; y < ROWS; y++) {
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if (!isDominated(x, y, guards)) {
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// Find nearest guard and shift toward this position
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const adj = getAdjacent(x, y);
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for (const a of adj) {
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const adjKey = posKey(a);
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// Try to find a guard that can shift
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const adjAdj = getAdjacent(a.x, a.y);
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for (const aa of adjAdj) {
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if (guards.has(posKey(aa)) && !posKey(aa).includes(posKey(attackPos))) {
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// Shift this guard
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guards.delete(posKey(aa));
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guards.add(adjKey);
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return;
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}
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}
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}
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}
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}
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}
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};
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const EternalDominationGame: React.FC = () => {
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const [guards, setGuards] = useState<Set<string>>(generateInitialGuards);
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const [attackHistory, setAttackHistory] = useState<Position[]>([]);
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const [message, setMessage] = useState<string>("Click any cell to attack. Guards will move to defend.");
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const [moveCount, setMoveCount] = useState(0);
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const [showInfo, setShowInfo] = useState(false);
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const handleCellClick = useCallback((x: number, y: number) => {
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const attack: Position = { x, y };
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// Check if attack is valid (not on a guard)
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if (guards.has(posKey(attack))) {
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setMessage("Cannot attack a guarded position. Choose an unguarded cell.");
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return;
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}
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// Defend the attack
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const newGuards = defendAttack(guards, attack);
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if (newGuards) {
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setGuards(newGuards);
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setAttackHistory(prev => [...prev, attack]);
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setMoveCount(prev => prev + 1);
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if (isFullyDominated(newGuards)) {
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setMessage(`Attack defended! All vertices remain dominated. (Move ${moveCount + 1})`);
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} else {
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setMessage("Defense failed! Some vertices are not dominated.");
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}
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} else {
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setMessage("Cannot defend this attack - no adjacent guards!");
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}
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}, [guards, moveCount]);
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const handleReset = useCallback(() => {
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setGuards(generateInitialGuards());
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setAttackHistory([]);
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setMessage("Click any cell to attack. Guards will move to defend.");
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setMoveCount(0);
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}, []);
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const getCellStyle = (x: number, y: number): string => {
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const key = posKey({ x, y });
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const hasGuard = guards.has(key);
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const isOnBorder = isBorder(x, y);
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const dominated = isDominated(x, y, guards);
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let base = "w-8 h-8 border border-border flex items-center justify-center text-lg cursor-pointer transition-all hover:scale-105 ";
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if (hasGuard) {
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base += isOnBorder
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? "bg-primary/30 border-primary"
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: "bg-accent/50 border-accent-foreground";
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} else if (dominated) {
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base += "bg-muted hover:bg-muted/80";
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} else {
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base += "bg-destructive/20 hover:bg-destructive/30"; // Should not happen
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}
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return base;
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};
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const guardCount = guards.size;
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const interiorGuards = Array.from(guards).filter(k => {
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const p = parseKey(k);
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return !isBorder(p.x, p.y);
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}).length;
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const borderGuards = guardCount - interiorGuards;
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return (
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<div className="space-y-6">
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<Card>
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<CardHeader>
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<CardTitle className="flex items-center gap-2">
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<Shield className="w-5 h-5" />
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Eternal Domination on a Grid
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</CardTitle>
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<CardDescription>
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12×10 grid with m-eternal dominating set defense strategy
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</CardDescription>
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</CardHeader>
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<CardContent className="space-y-4">
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<div className="flex flex-wrap gap-2 items-center justify-between">
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<div className="flex gap-2">
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<Badge variant="outline">
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Total Guards: {guardCount}
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</Badge>
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<Badge variant="secondary">
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Border: {borderGuards}
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</Badge>
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<Badge variant="secondary">
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Interior: {interiorGuards}
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</Badge>
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<Badge variant="outline">
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Attacks: {moveCount}
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</Badge>
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</div>
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<div className="flex gap-2">
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<Button variant="outline" size="sm" onClick={() => setShowInfo(!showInfo)}>
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<Info className="w-4 h-4 mr-1" />
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{showInfo ? "Hide" : "Show"} Info
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</Button>
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<Button variant="outline" size="sm" onClick={handleReset}>
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<RotateCcw className="w-4 h-4 mr-1" />
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Reset
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</Button>
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</div>
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</div>
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{showInfo && (
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<div className="p-4 bg-muted rounded-lg text-sm space-y-2">
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<p><strong>m-Eternal Domination:</strong> Guards occupy vertices forming a dominating set. When you attack an unguarded vertex, guards move to defend while maintaining domination of all vertices.</p>
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<p><strong>Strategy:</strong> Border vertices are always guarded (cycle C). Interior guards shift toward attacks, while border guards shift along complementary paths to maintain coverage.</p>
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<p><strong>Goal:</strong> The attacker wins if they can find an attack sequence that leaves some vertex undominated. Try to break the defense!</p>
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</div>
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)}
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<div className="p-3 rounded-md bg-muted/50 text-sm flex items-center gap-2">
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<Target className="w-4 h-4 text-primary flex-shrink-0" />
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{message}
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</div>
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{/* Grid */}
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<div className="flex justify-center overflow-x-auto pb-4">
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<div className="inline-block">
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<div className="text-xs text-muted-foreground mb-1 pl-4">
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<div className="flex">
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{Array.from({ length: COLS }, (_, i) => (
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<div key={i} className="w-8 text-center">{i}</div>
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))}
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</div>
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</div>
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{Array.from({ length: ROWS }, (_, y) => (
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<div key={y} className="flex items-center">
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<div className="w-4 text-xs text-muted-foreground text-right pr-1">
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{y}
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</div>
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{Array.from({ length: COLS }, (_, x) => (
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<div
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key={x}
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className={getCellStyle(x, y)}
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onClick={() => handleCellClick(x, y)}
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title={`(${x}, ${y}) - ${guards.has(posKey({ x, y })) ? "Guard" : "Empty"}`}
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>
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{guards.has(posKey({ x, y })) ? "🛡️" : ""}
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</div>
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))}
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</div>
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))}
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</div>
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</div>
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{/* Legend */}
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<div className="flex flex-wrap gap-4 text-sm">
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<div className="flex items-center gap-2">
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<div className="w-6 h-6 bg-primary/30 border border-primary rounded flex items-center justify-center text-xs">🛡️</div>
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<span>Border Guard</span>
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</div>
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<div className="flex items-center gap-2">
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<div className="w-6 h-6 bg-accent/50 border border-accent-foreground rounded flex items-center justify-center text-xs">🛡️</div>
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<span>Interior Guard</span>
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</div>
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<div className="flex items-center gap-2">
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<div className="w-6 h-6 bg-muted border border-border rounded"></div>
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<span>Dominated (unguarded)</span>
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</div>
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</div>
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{/* Attack History */}
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{attackHistory.length > 0 && (
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<div className="text-sm">
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<p className="text-muted-foreground mb-1">Recent attacks:</p>
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<div className="flex flex-wrap gap-1">
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{attackHistory.slice(-10).map((pos, i) => (
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<Badge key={i} variant="outline" className="text-xs">
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({pos.x}, {pos.y})
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</Badge>
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))}
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</div>
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</div>
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)}
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</CardContent>
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</Card>
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</div>
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);
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};
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export default EternalDominationGame;
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