Files
nonograms/src/utils/solver.js

452 lines
16 KiB
JavaScript

/**
* Represents the state of a cell in the solver.
* -1: Unknown
* 0: Empty
* 1: Filled
*/
// Memoized helper for checking if hints fit
const memo = new Map();
/**
* Solves a single line (row or column) based on hints and current knowledge.
* Uses the "Left-Right Overlap" algorithm to find common filled cells.
* Also identifies definitely empty cells (reachable by no block).
*
* @param {number[]} currentLine - Array of -1, 0, 1
* @param {number[]} hints - Array of block lengths
* @returns {number[]} - Updated line (or null if contradiction/impossible - though shouldn't happen for valid puzzles)
*/
export function solveLine(currentLine, hints) {
const length = currentLine.length;
// If no hints, all must be empty
// Clear memo for this line solve
memo.clear();
if (hints.length === 0 || (hints.length === 1 && hints[0] === 0)) {
return Array(length).fill(0);
}
// Helper to check if a block can be placed at start index
const canPlace = (line, start, blockSize) => {
if (start + blockSize > line.length) return false;
// Check if any cell in block is 0 (Empty) -> Invalid
for (let i = start; i < start + blockSize; i++) {
if (line[i] === 0) return false;
}
// Check boundaries (must be separated by empty or edge)
if (start > 0 && line[start - 1] === 1) return false;
if (start + blockSize < line.length && line[start + blockSize] === 1) return false;
return true;
};
// 1. Calculate Left-Most Positions
const leftPositions = [];
let currentIdx = 0;
for (let hIndex = 0; hIndex < hints.length; hIndex++) {
const block = hints[hIndex];
// Find first valid position
while (currentIdx <= length - block) {
if (canPlace(currentLine, currentIdx, block)) {
// Verify we can fit remaining blocks
if (canFitRest(currentLine, currentIdx + block + 1, hints, hIndex + 1)) {
leftPositions.push(currentIdx);
currentIdx += block + 1; // Move past this block + 1 space
break;
}
}
// Cannot skip a filled cell - if we pass a '1', it becomes uncovered
if (currentLine[currentIdx] === 1) return null;
currentIdx++;
}
if (leftPositions.length <= hIndex) return null; // Impossible
}
// Clear memo for right-side calculation (different line/hints)
memo.clear();
// 2. Calculate Right-Most Positions (by reversing line and hints)
const reversedLine = [...currentLine].reverse();
const reversedHints = [...hints].reverse();
const rightPositionsReversed = [];
currentIdx = 0;
for (let hIndex = 0; hIndex < reversedHints.length; hIndex++) {
const block = reversedHints[hIndex];
while (currentIdx <= length - block) {
if (canPlace(reversedLine, currentIdx, block)) {
if (canFitRest(reversedLine, currentIdx + block + 1, reversedHints, hIndex + 1)) {
rightPositionsReversed.push(currentIdx);
currentIdx += block + 1;
break;
}
}
// Cannot skip a filled cell
if (reversedLine[currentIdx] === 1) return null;
currentIdx++;
}
if (rightPositionsReversed.length <= hIndex) return null;
}
// Convert reversed positions to actual indices
const rightPositions = rightPositionsReversed.map((rStart, i) => {
const block = reversedHints[i];
return length - rStart - block;
}).reverse();
// 3. Intersect
const newLine = [...currentLine];
// Fill intersection
for (let i = 0; i < hints.length; i++) {
const l = leftPositions[i];
const r = rightPositions[i];
const block = hints[i];
// If overlap exists: [r, l + block - 1]
if (r < l + block) {
for (let k = r; k < l + block; k++) {
newLine[k] = 1;
}
}
}
// Determine Empty cells?
// Mask of possible filled cells
const possibleFilled = Array(length).fill(false);
for (let i = 0; i < hints.length; i++) {
for (let k = leftPositions[i]; k < rightPositions[i] + hints[i]; k++) {
possibleFilled[k] = true;
}
}
for (let k = 0; k < length; k++) {
if (!possibleFilled[k]) {
newLine[k] = 0;
}
}
return newLine;
}
// Memoized helper for checking if hints fit
export function canFitRest(line, startIndex, hints, hintIndex) {
// Optimization: If hints are empty, we just need to check if remaining line has no '1's
if (hintIndex >= hints.length) {
for (let i = startIndex; i < line.length; i++) {
if (line[i] === 1) return false;
}
return true;
}
// Memoization key
const key = `${startIndex}-${hintIndex}`;
if (memo.has(key)) return memo.get(key);
const remainingLen = line.length - startIndex;
// Min space needed: sum of hints + (hints.length - 1) spaces
let minSpace = 0;
for(let i=hintIndex; i<hints.length; i++) minSpace += hints[i] + (i < hints.length - 1 ? 1 : 0);
if (remainingLen < minSpace) {
memo.set(key, false);
return false;
}
const block = hints[hintIndex];
// Try to find *any* valid placement for this block
for (let i = startIndex; i <= line.length - minSpace; i++) {
// If we skipped a '1', we went too far. All 1s must be covered by blocks.
// Since we are placing the *next* block, any 1s between startIndex and i are uncovered.
// Thus, if we find a 1 in [startIndex, i-1], we must stop.
let skippedOne = false;
for (let x = startIndex; x < i; x++) {
if (line[x] === 1) { skippedOne = true; break; }
}
if (skippedOne) break;
// Check placement
let valid = true;
// Block
for (let k = 0; k < block; k++) {
if (line[i+k] === 0) { valid = false; break; }
}
if (!valid) continue;
// Boundary before
if (i > 0 && line[i-1] === 1) valid = false;
// Boundary after (check implicit in next block placement or end of line, but we need to check i+block cell)
if (i + block < line.length && line[i+block] === 1) valid = false;
if (valid) {
// Recurse
if (canFitRest(line, i + block + 1, hints, hintIndex + 1)) {
memo.set(key, true);
return true;
}
}
}
memo.set(key, false);
return false;
}
/**
* Main solver function that attempts to solve the puzzle using logic and backtracking (DFS).
* Uses an efficient propagation queue and undo stack to avoid deep copying the grid.
*
* @param {number[][]} rowHints
* @param {number[][]} colHints
* @param {function} onProgress - Optional callback for progress reporting (percent)
* @param {number[][]} initialGrid - Optional initial grid state
* @param {boolean} logicOnly - If true, stops after logical propagation (no guessing)
* @returns {object} result
*/
export function solvePuzzle(rowHints, colHints, onProgress, initialGrid = null, logicOnly = false) {
const rows = rowHints.length;
const cols = colHints.length;
const totalCells = rows * cols;
// Grid initialization: -1 (Unknown), 0 (Empty), 1 (Filled)
// Use initialGrid if provided (deep copy to be safe)
const grid = initialGrid
? initialGrid.map(row => [...row])
: Array(rows).fill().map(() => Array(cols).fill(-1));
// Stats
let iterations = 0; // Total calls to solve()
let maxDepth = 0; // Max recursion depth
let backtracks = 0; // Failed guesses
let logicSteps = 0; // Cells filled by propagation
let lastProgressTime = 0;
function reportProgress() {
if (!onProgress) return;
const now = Date.now();
if (now - lastProgressTime >= 50) {
let filled = 0;
for(let r=0; r<rows; r++) {
for(let c=0; c<cols; c++) {
if(grid[r][c] !== -1) filled++;
}
}
onProgress(Math.floor((filled/totalCells) * 100));
lastProgressTime = now;
}
}
// Queue for propagation (Set of strings "r{i}" or "c{i}")
const queue = new Set();
for(let r=0; r<rows; r++) queue.add(`r${r}`);
for(let c=0; c<cols; c++) queue.add(`c${c}`);
// Helper: Undo changes from a propagation step
function undo(changes) {
for(let i=changes.length-1; i>=0; i--) {
const {r, c, old} = changes[i];
grid[r][c] = old;
}
}
// Helper: Propagate logic constraints until fixed point or contradiction
// Returns list of changes made, or null if contradiction found
function propagate() {
const changes = [];
try {
while(queue.size > 0) {
reportProgress();
const item = queue.values().next().value;
queue.delete(item);
const type = item[0];
const idx = parseInt(item.slice(1));
let currentLine, hints;
if (type === 'r') {
currentLine = grid[idx]; // Reference for row (fast)
hints = rowHints[idx];
} else {
currentLine = grid.map(row => row[idx]); // Copy for col (slower)
hints = colHints[idx];
}
const newLine = solveLine(currentLine, hints);
if (!newLine) throw 'contradiction';
// Apply changes
for(let i=0; i<newLine.length; i++) {
if (currentLine[i] !== newLine[i]) {
// If we try to change a known value to something else -> Contradiction
if (currentLine[i] !== -1 && currentLine[i] !== newLine[i]) throw 'contradiction';
if (currentLine[i] === -1) {
const r = type === 'r' ? idx : i;
const c = type === 'r' ? i : idx;
// Double check if already set by orthogonal update in same loop?
// (Should be handled by -1 check above, as grid is shared)
if (grid[r][c] === -1) {
grid[r][c] = newLine[i];
changes.push({r, c, old: -1});
logicSteps++;
// Add orthogonal line to queue
if (type === 'r') queue.add(`c${c}`);
else queue.add(`r${r}`);
} else if (grid[r][c] !== newLine[i]) {
console.log('Contradiction: Orthogonal Conflict at', r, c, 'Grid:', grid[r][c], 'New:', newLine[i]);
throw 'contradiction';
}
}
}
}
}
} catch (e) {
// Revert changes from this failed propagation
undo(changes);
return null;
}
return changes;
}
// DFS Solver
function solve(depth) {
maxDepth = Math.max(maxDepth, depth);
iterations++;
reportProgress();
// 1. Propagate Logic
const changes = propagate();
if (!changes) return false; // Contradiction
// 2. Find Best Branch Candidate
let bestR = -1, bestC = -1;
let minUnknowns = Infinity;
let isComplete = true;
// Scan for unknowns and pick heuristic
// Heuristic: Line with fewest unknowns (most constrained)
for(let r=0; r<rows; r++) {
let unknowns = 0;
let firstUnknownC = -1;
for(let c=0; c<cols; c++) {
if(grid[r][c] === -1) {
unknowns++;
if (firstUnknownC === -1) firstUnknownC = c;
}
}
if (unknowns > 0) {
isComplete = false;
if (unknowns < minUnknowns) {
minUnknowns = unknowns;
bestR = r;
bestC = firstUnknownC;
}
if (minUnknowns === 1) break; // Optimal
}
}
if (isComplete) return true; // Solved!
// 3. Branching (Guessing)
// Try 1
grid[bestR][bestC] = 1;
queue.add(`r${bestR}`);
queue.add(`c${bestC}`);
if (solve(depth + 1)) return true;
// Backtrack from 1
grid[bestR][bestC] = -1; // Undo guess
// (Recursive call already undid its propagation changes)
// Try 0
grid[bestR][bestC] = 0;
queue.add(`r${bestR}`);
queue.add(`c${bestC}`);
if (solve(depth + 1)) return true;
// Backtrack from 0
grid[bestR][bestC] = -1; // Undo guess
backtracks++;
// Undo propagation from this level
undo(changes);
return false;
}
// Start Solving
if (logicOnly) {
// Just logical propagation without guessing
if (initialGrid) {
// If resuming, ensure queue has all lines to check consistency
queue.clear();
for(let r=0; r<rows; r++) queue.add(`r${r}`);
for(let c=0; c<cols; c++) queue.add(`c${c}`);
}
// Propagate logic constraints
propagate();
// No DFS, so iterations/backtracks remain 0
} else if (!initialGrid) {
// Normal start (full solver)
solve(0);
} else {
// Resume from provided state (full solver)
// We need to populate the queue with all rows/cols since we don't know what changed
queue.clear();
for(let r=0; r<rows; r++) queue.add(`r${r}`);
for(let c=0; c<cols; c++) queue.add(`c${c}`);
solve(0);
}
// Calculate Percent Solved
let solvedCount = 0;
grid.forEach(r => r.forEach(c => { if(c !== -1) solvedCount++; }));
let percentSolved = (solvedCount / totalCells) * 100;
if (onProgress) onProgress(Math.floor(percentSolved));
// Difficulty Calculation
// Logic:
// - Base: 0-20% based on size/density
// - Logic: 0-30% based on iterations needed (depth 0)
// - Guessing: 0-50% based on backtracks/depth
let difficultyScore = 0;
const effectiveSize = Math.sqrt(totalCells);
if (percentSolved < 100) {
difficultyScore = 100; // Unsolvable (or timed out/too hard)
} else {
if (maxDepth === 0) {
// Pure logic
difficultyScore = Math.min(30, effectiveSize);
} else {
// Required guessing
// Simple heuristic: 30 + backtracks * 5 + depth * 2
difficultyScore = 30 + (backtracks * 2) + (maxDepth * 5);
difficultyScore = Math.min(100, difficultyScore);
}
}
return {
percentSolved,
difficultyScore: Math.round(difficultyScore),
lookaheadUsed: maxDepth > 0,
iterations,
maxDepth,
backtracks
};
}