Add hex grid eternal domination UI
Implement Eternal Domination on a fixed 12x10 hexagonal grid, render hex adjacency, and initialize guards per Figure 10. Update defense logic,domination checks, and UI to reflect hex grid, including guards, attacks, and legend. X-Lovable-Edit-ID: edt-35bb8b52-5d18-4fcb-9079-5c2f56316cc4
This commit is contained in:
gpt-engineer-app[bot]
commit
ad9ee173f5
2 changed files with 210 additions and 152 deletions
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src/assets/fig10-reference.jpg
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@ -4,15 +4,18 @@ 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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// Hexagonal grid F₃(12, 10) - 12 columns × 10 rows
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// Following the "brick wall" offset pattern for hexagonal grids
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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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// Position utilities
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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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// Check if position is valid
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@ -20,35 +23,55 @@ 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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// Hexagonal grid adjacency (brick pattern)
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// Even rows: neighbors at (-1,0), (1,0), (-1,-1), (0,-1), (-1,1), (0,1)
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// Odd rows: neighbors at (-1,0), (1,0), (0,-1), (1,-1), (0,1), (1,1)
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const getHexNeighbors = (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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// Horizontal neighbors (same for all rows)
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if (isValidPos(x - 1, y)) neighbors.push({ x: x - 1, y });
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if (isValidPos(x + 1, y)) neighbors.push({ x: x + 1, y });
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// Diagonal neighbors depend on row parity (brick pattern)
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const isEvenRow = y % 2 === 0;
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if (isEvenRow) {
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// Even row: upper-left, upper-right at x-1 and x
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if (isValidPos(x - 1, y - 1)) neighbors.push({ x: x - 1, y: y - 1 });
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if (isValidPos(x, y - 1)) neighbors.push({ x: x, y: y - 1 });
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// Lower neighbors
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if (isValidPos(x - 1, y + 1)) neighbors.push({ x: x - 1, y: y + 1 });
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if (isValidPos(x, y + 1)) neighbors.push({ x: x, y: y + 1 });
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} else {
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// Odd row: upper-left, upper-right at x and x+1
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if (isValidPos(x, y - 1)) neighbors.push({ x: x, y: y - 1 });
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if (isValidPos(x + 1, y - 1)) neighbors.push({ x: x + 1, y: y - 1 });
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// Lower neighbors
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if (isValidPos(x, y + 1)) neighbors.push({ x: x, y: y + 1 });
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if (isValidPos(x + 1, y + 1)) neighbors.push({ x: x + 1, y: y + 1 });
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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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// Check if a position is on the border of the "interested rectangle"
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// Following Figure 10: border forms cycle C around 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 === ROWS - 1;
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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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// Interior positions (not on border)
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const isInterior = (x: number, y: number): boolean => {
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return x > 0 && x < COLS - 1 && y > 0 && y < ROWS - 1;
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};
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// Generate initial guard placement following the paper's U₃ configuration
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// Interior guards follow a specific pattern, all border vertices are guarded
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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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// All border vertices are guarded (forming cycle C)
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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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@ -57,14 +80,15 @@ const generateInitialGuards = (): Set<string> => {
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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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// Interior guards following the eternal dominating set pattern
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// Based on the paper: we need interior guards at density 7/15 nm
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// Pattern: guards at positions creating a dominating set
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// Using pattern similar to Figure 10's interior placement
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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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for (let y = 1; y < ROWS - 1; y++) {
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// Place guards following a hexagonal domination pattern
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// Every vertex in interior needs to be within distance 1 of a guard
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// Pattern: (2x + y) mod 5 === 0 creates suitable coverage
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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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@ -74,11 +98,11 @@ const generateInitialGuards = (): Set<string> => {
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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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// Check if a vertex is dominated
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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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const neighbors = getHexNeighbors(x, y);
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return neighbors.some(p => guards.has(posKey(p)));
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};
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// Check if all vertices are dominated
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@ -91,34 +115,31 @@ const isFullyDominated = (guards: Set<string>): boolean => {
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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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// Defense strategy from Figure 10 and page 23:
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// 1. Interior guards shift toward attack
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// 2. If a guard moves from interior to border, border guards shift along complementary paths
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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 attack is on a guard, already defended
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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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const neighbors = getHexNeighbors(attack.x, attack.y);
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const adjacentGuards = neighbors.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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return null; // 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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// Strategy: prefer interior guards to move (as per Figure 10)
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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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if (isInterior(g.x, g.y)) {
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defender = g;
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break;
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}
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@ -131,57 +152,71 @@ const defendAttack = (guards: Set<string>, attack: Position): Set<string> | null
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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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// If defender was interior and attack is on border, apply border shift strategy
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// Following the complementary paths P₁,₃ and P₂,₄ from Figure 10
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if (isInterior(defender.x, defender.y)) {
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// Interior to border movement: shift guards along border cycle
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// to maintain the dominating set property
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applyBorderShift(newGuards, defender, attack);
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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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// Ensure domination is maintained
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ensureDomination(newGuards);
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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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// Border shift strategy: when interior guard moves out, shift border guards
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// along complementary paths to fill gaps
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const applyBorderShift = (guards: Set<string>, from: Position, to: Position): void => {
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// Check if any interior vertices became undominated
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for (let x = 1; x < COLS - 1; x++) {
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for (let y = 1; y < ROWS - 1; y++) {
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if (!isDominated(x, y, guards)) {
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// Find a neighboring guard to shift in
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const neighbors = getHexNeighbors(x, y);
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for (const n of neighbors) {
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if (guards.has(posKey(n))) {
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// Check if we can shift this guard
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const nNeighbors = getHexNeighbors(n.x, n.y);
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const canShift = nNeighbors.some(nn =>
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guards.has(posKey(nn)) &&
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posKey(nn) !== posKey(n) &&
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posKey(nn) !== posKey(to)
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);
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if (canShift || isBorder(n.x, n.y)) {
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// Shift a border guard toward the gap
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const borderNeighbors = neighbors.filter(nb =>
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isBorder(nb.x, nb.y) && guards.has(posKey(nb))
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);
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if (borderNeighbors.length > 0) {
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const shifter = borderNeighbors[0];
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guards.delete(posKey(shifter));
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guards.add(posKey({ x, y }));
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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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};
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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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// Ensure all vertices remain dominated after movement
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const ensureDomination = (guards: Set<string>): void => {
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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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// Emergency: place a guard at nearest available position
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const neighbors = getHexNeighbors(x, y);
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for (const n of neighbors) {
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const nNeighbors = getHexNeighbors(n.x, n.y);
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for (const nn of nNeighbors) {
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if (guards.has(posKey(nn))) {
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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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guards.delete(posKey(nn));
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guards.add(posKey(n));
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return;
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}
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}
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@ -194,20 +229,18 @@ const ensureDominatingSet = (guards: Set<string>, attackPos: Position): void =>
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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 [message, setMessage] = useState<string>("Click any cell to attack. Guards will shift 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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@ -228,65 +261,41 @@ const EternalDominationGame: React.FC = () => {
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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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setMessage("Click any cell to attack. Guards will shift 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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return isInterior(p.x, p.y);
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}).length;
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const borderGuards = guardCount - interiorGuards;
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// Hexagonal cell dimensions
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const cellWidth = 36;
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const cellHeight = 32;
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const rowOffset = cellWidth / 2;
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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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Eternal Domination on a Hexagonal 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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12×10 hexagonal grid F₃(12, 10) with m-eternal dominating set defense
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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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<Badge variant="outline">Guards: {guardCount}</Badge>
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<Badge variant="secondary">Border: {borderGuards}</Badge>
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<Badge variant="secondary">Interior: {interiorGuards}</Badge>
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<Badge variant="outline">Attacks: {moveCount}</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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@ -302,9 +311,9 @@ const EternalDominationGame: React.FC = () => {
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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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<p><strong>m-Eternal Domination on Hexagonal Grid:</strong> Guards form a dominating set on F₃(n,m). Each attack must be defended by moving guards while maintaining domination.</p>
|
||||
<p><strong>Strategy (Figure 10):</strong> Border vertices form cycle C (always guarded). Interior guards shift toward attacks. Complementary paths along the border shift guards to fill gaps.</p>
|
||||
<p><strong>Goal:</strong> Try to find an attack sequence that leaves some vertex undominated!</p>
|
||||
</div>
|
||||
)}
|
||||
|
||||
|
|
@ -313,53 +322,102 @@ const EternalDominationGame: React.FC = () => {
|
|||
{message}
|
||||
</div>
|
||||
|
||||
{/* Grid */}
|
||||
{/* Hexagonal Grid */}
|
||||
<div className="flex justify-center overflow-x-auto pb-4">
|
||||
<div className="inline-block">
|
||||
<div className="text-xs text-muted-foreground mb-1 pl-4">
|
||||
<div className="flex">
|
||||
{Array.from({ length: COLS }, (_, i) => (
|
||||
<div key={i} className="w-8 text-center">{i}</div>
|
||||
))}
|
||||
</div>
|
||||
</div>
|
||||
{Array.from({ length: ROWS }, (_, y) => (
|
||||
<div key={y} className="flex items-center">
|
||||
<div className="w-4 text-xs text-muted-foreground text-right pr-1">
|
||||
{y}
|
||||
</div>
|
||||
{Array.from({ length: COLS }, (_, x) => (
|
||||
<div
|
||||
className="relative"
|
||||
style={{
|
||||
width: COLS * cellWidth + rowOffset + 20,
|
||||
height: ROWS * cellHeight + 20
|
||||
}}
|
||||
>
|
||||
{/* Draw edges first */}
|
||||
<svg
|
||||
className="absolute inset-0 pointer-events-none"
|
||||
width={COLS * cellWidth + rowOffset + 20}
|
||||
height={ROWS * cellHeight + 20}
|
||||
>
|
||||
{Array.from({ length: ROWS }, (_, y) =>
|
||||
Array.from({ length: COLS }, (_, x) => {
|
||||
const offset = y % 2 === 1 ? rowOffset : 0;
|
||||
const cx = x * cellWidth + cellWidth / 2 + offset + 10;
|
||||
const cy = y * cellHeight + cellHeight / 2 + 10;
|
||||
|
||||
return getHexNeighbors(x, y)
|
||||
.filter(n => n.x > x || (n.x === x && n.y > y))
|
||||
.map((neighbor, i) => {
|
||||
const nOffset = neighbor.y % 2 === 1 ? rowOffset : 0;
|
||||
const ncx = neighbor.x * cellWidth + cellWidth / 2 + nOffset + 10;
|
||||
const ncy = neighbor.y * cellHeight + cellHeight / 2 + 10;
|
||||
return (
|
||||
<line
|
||||
key={`${x}-${y}-${i}`}
|
||||
x1={cx}
|
||||
y1={cy}
|
||||
x2={ncx}
|
||||
y2={ncy}
|
||||
stroke="currentColor"
|
||||
strokeOpacity={0.2}
|
||||
strokeWidth={1}
|
||||
/>
|
||||
);
|
||||
});
|
||||
})
|
||||
)}
|
||||
</svg>
|
||||
|
||||
{/* Cells */}
|
||||
{Array.from({ length: ROWS }, (_, y) =>
|
||||
Array.from({ length: COLS }, (_, x) => {
|
||||
const offset = y % 2 === 1 ? rowOffset : 0;
|
||||
const hasGuard = guards.has(posKey({ x, y }));
|
||||
const onBorder = isBorder(x, y);
|
||||
const dominated = isDominated(x, y, guards);
|
||||
|
||||
let bgClass = "bg-muted hover:bg-muted/80";
|
||||
if (hasGuard) {
|
||||
bgClass = onBorder
|
||||
? "bg-primary/40 border-primary"
|
||||
: "bg-accent border-accent-foreground";
|
||||
} else if (!dominated) {
|
||||
bgClass = "bg-destructive/30";
|
||||
}
|
||||
|
||||
return (
|
||||
<div
|
||||
key={x}
|
||||
className={getCellStyle(x, y)}
|
||||
key={`${x}-${y}`}
|
||||
className={`absolute w-7 h-7 rounded-full border flex items-center justify-center text-sm cursor-pointer transition-all hover:scale-110 ${bgClass}`}
|
||||
style={{
|
||||
left: x * cellWidth + offset + 10 + (cellWidth - 28) / 2,
|
||||
top: y * cellHeight + 10 + (cellHeight - 28) / 2,
|
||||
}}
|
||||
onClick={() => handleCellClick(x, y)}
|
||||
title={`(${x}, ${y}) - ${guards.has(posKey({ x, y })) ? "Guard" : "Empty"}`}
|
||||
title={`(${x}, ${y}) - ${hasGuard ? "Guard" : dominated ? "Dominated" : "Undominated!"}`}
|
||||
>
|
||||
{guards.has(posKey({ x, y })) ? "🛡️" : ""}
|
||||
{hasGuard ? "🛡️" : ""}
|
||||
</div>
|
||||
))}
|
||||
</div>
|
||||
))}
|
||||
);
|
||||
})
|
||||
)}
|
||||
</div>
|
||||
</div>
|
||||
|
||||
{/* Legend */}
|
||||
<div className="flex flex-wrap gap-4 text-sm">
|
||||
<div className="flex items-center gap-2">
|
||||
<div className="w-6 h-6 bg-primary/30 border border-primary rounded flex items-center justify-center text-xs">🛡️</div>
|
||||
<div className="w-6 h-6 bg-primary/40 border border-primary rounded-full flex items-center justify-center text-xs">🛡️</div>
|
||||
<span>Border Guard</span>
|
||||
</div>
|
||||
<div className="flex items-center gap-2">
|
||||
<div className="w-6 h-6 bg-accent/50 border border-accent-foreground rounded flex items-center justify-center text-xs">🛡️</div>
|
||||
<div className="w-6 h-6 bg-accent border border-accent-foreground rounded-full flex items-center justify-center text-xs">🛡️</div>
|
||||
<span>Interior Guard</span>
|
||||
</div>
|
||||
<div className="flex items-center gap-2">
|
||||
<div className="w-6 h-6 bg-muted border border-border rounded"></div>
|
||||
<span>Dominated (unguarded)</span>
|
||||
<div className="w-6 h-6 bg-muted border border-border rounded-full"></div>
|
||||
<span>Dominated</span>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
{/* Attack History */}
|
||||
{attackHistory.length > 0 && (
|
||||
<div className="text-sm">
|
||||
<p className="text-muted-foreground mb-1">Recent attacks:</p>
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue