488 lines
21 KiB
Java
488 lines
21 KiB
Java
import java.io.*;
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import java.lang.Integer.*;
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import java.util.*;
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import java.util.stream.*;
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import java.lang.StringBuilder;
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import java.util.concurrent.CountDownLatch;
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//////////////////////////////// Solve Sudoku Puzzles ////////////////////////////////
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//////////////////////////////// @author Peter Norvig ////////////////////////////////
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/** There are two representations of puzzles that we will use:
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** 1. A gridstring is 81 chars, with characters '0' or '.' for blank and '1' to '9' for digits.
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** 2. A puzzle grid is an int[81] with a digit d (1-9) represented by the integer (1 << (d - 1));
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** that is, a bit pattern that has a single 1 bit representing the digit.
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** A blank is represented by the OR of all the digits 1-9, meaning that any digit is possible.
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** While solving the puzzle, some of these digits are eliminated, leaving fewer possibilities.
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** The puzzle is solved when every square has only a single possibility.
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**
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** Search for a solution with `search`:
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** - Fill an empty square with a guessed digit and do constraint propagation.
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** - If the guess is consistent, search deeper; if not, try a different guess for the square.
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** - If all guesses fail, back up to the previous level.
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** - In selecting an empty square, we pick one that has the minimum number of possible digits.
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** - To be able to back up, we need to keep the grid from the previous recursive level.
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** But we only need to keep one grid for each level, so to save garbage collection,
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** we pre-allocate one grid per level (there are 81 levels) in a `gridpool`.
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** Do constraint propagation with `arcConsistent`, `dualConsistent`, and `nakedPairs`.
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**/
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public class Sudoku {
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//////////////////////////////// main; command line options //////////////////////////////
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static final String usage = String.join("\n",
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"usage: java Sudoku -(no)[fghnprstuv] | -[RT]<number> | <filename> ...",
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"E.g., -v turns verify flag on, -nov turns it off. -R and -T require a number. The options:\n",
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" -f(ile) Print summary stats for each file (default on)",
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" -g(rid) Print each puzzle grid and solution grid (default off)",
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" -h(elp) Print this usage message",
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" -n(aked) Run naked pairs (default on)",
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" -p(uzzle) Print summary stats for each puzzle (default off)",
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" -r(everse) Solve the reverse of each puzzle as well as each puzzle itself (default off)",
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" -s(earch) Run search (default on, but some puzzles can be solved with CSP methods alone)",
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" -t(hread) Print summary stats for each thread (default off)",
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" -u(nitTest)Run a suite of unit tests (default off)",
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" -v(erify) Verify each solution is valid (default on)",
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" -T<number> Concurrently run <number> threads (default 26)",
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" -R<number> Repeat each puzzle <number> times (default 1)",
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" <filename> Solve all puzzles in filename, which has one puzzle per line");
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boolean printFileStats = true; // -f
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boolean printGrid = false; // -g
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boolean runNakedPairs = true; // -n
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boolean printPuzzleStats = false; // -p
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boolean reversePuzzle = false; // -r
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boolean runSearch = true; // -s
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boolean printThreadStats = false; // -t
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boolean verifySolution = true; // -v
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int nThreads = 26; // -T
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int repeat = 1; // -R
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int backtracks = 0; // count total backtracks
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/** Parse command line args and solve puzzles in files. **/
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public static void main(String[] args) throws IOException {
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Sudoku s = new Sudoku();
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for (String arg: args) {
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if (!arg.startsWith("-")) {
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s.solveFile(arg);
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} else {
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boolean value = !arg.startsWith("-no");
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switch(arg.charAt(value ? 1 : 3)) {
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case 'f': s.printFileStats = value; break;
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case 'g': s.printGrid = value; break;
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case 'h': System.out.println(usage); break;
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case 'n': s.runNakedPairs = value; break;
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case 'p': s.printPuzzleStats = value; break;
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case 'r': s.reversePuzzle = value; break;
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case 's': s.runSearch = value; break;
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case 't': s.printThreadStats = value; break;
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case 'u': s.runUnitTests(); break;
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case 'v': s.verifySolution = value; break;
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case 'T': s.nThreads = Integer.parseInt(arg.substring(2)); break;
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case 'R': s.repeat = Integer.parseInt(arg.substring(2)); break;
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default: System.out.println("Unrecognized option: " + arg + "\n" + usage);
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}
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}
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}
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}
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//////////////////////////////// Handling Lists of Puzzles ////////////////////////////////
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/** Solve all the puzzles in a file. Report timing statistics. **/
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void solveFile(String filename) throws IOException {
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List<int[]> grids = readFile(filename);
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long startFileTime = System.nanoTime();
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switch(nThreads) {
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case 1: solveList(grids); break;
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default: solveListThreaded(grids, nThreads); break;
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}
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if (printFileStats) printStats(grids.size() * repeat, startFileTime, filename);
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}
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/** Solve a list of puzzles in a single thread.
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** repeat -R<number> times; print each puzzle's stats if -p; print grid if -g; verify if -v. **/
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void solveList(List<int[]> grids) {
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int[] puzzle = new int[N * N]; // Used to save a copy of the original grid
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int[][] gridpool = new int[N * N][N * N]; // Reuse grids during the search
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for (int g=0; g<grids.size(); ++g) {
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int grid[] = grids.get(g);
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System.arraycopy(grid, 0, puzzle, 0, grid.length);
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for (int i = 0; i < repeat; ++i) {
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long startTime = printPuzzleStats ? System.nanoTime() : 0;
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int[] solution = initialize(grid); // All the real work is
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if (runSearch) solution = search(solution, gridpool, 0); // on these 2 lines.
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if (printPuzzleStats) {
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printStats(1, startTime, "Puzzle " + (g + 1));
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}
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if (i == 0 && (printGrid || (verifySolution && !verify(solution, puzzle)))) {
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printGrids("Puzzle " + (g + 1), grid, solution);
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}
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}
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}
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}
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/** Break a list of puzzles into nThreads sublists and solve each sublist in a separate thread. **/
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void solveListThreaded(List<int[]> grids, int nThreads) {
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try {
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final long startTime = System.nanoTime();
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int nGrids = grids.size();
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final CountDownLatch latch = new CountDownLatch(nThreads);
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int size = nGrids / nThreads;
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for (int c = 0; c < nThreads; ++c) {
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int end = c == nThreads - 1 ? nGrids : (c + 1) * size;
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final List<int[]> sublist = grids.subList(c * size, end);
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new Thread() {
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public void run() {
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solveList(sublist);
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latch.countDown();
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if (printThreadStats) {
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printStats(repeat * sublist.size(), startTime, "Thread");
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}
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}
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}.start();
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}
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latch.await(); // Wait for all threads to finish
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} catch (InterruptedException e) {
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System.err.println("And you may ask yourself, 'Well, how did I get here?'");
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}
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}
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//////////////////////////////// Utility functions ////////////////////////////////
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/** Return an array of all squares in the intersection of these rows and cols **/
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int[] cross(int[] rows, int[] cols) {
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int[] result = new int[rows.length * cols.length];
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int i = 0;
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for (int r: rows) { for (int c: cols) { result[i++] = N * r + c; } }
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return result;
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}
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/** Return true iff item is an element of array, or of array[0:end]. **/
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boolean member(int item, int[] array) { return member(item, array, array.length); }
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boolean member(int item, int[] array, int end) {
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for (int i = 0; i<end; ++i) {
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if (array[i] == item) { return true; }
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}
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return false;
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}
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//////////////////////////////// Constants ////////////////////////////////
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final int N = 9; // Number of cells on a side of grid.
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final int[] DIGITS = {1<<0, 1<<1, 1<<2, 1<<3, 1<<4, 1<<5, 1<<6, 1<<7, 1<<8};
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final int ALL_DIGITS = Integer.parseInt("111111111", 2);
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final int[] ROWS = IntStream.range(0, N).toArray();
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final int[] COLS = ROWS;
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final int[] SQUARES = IntStream.range(0, N * N).toArray();
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final int[][] BLOCKS = {{0, 1, 2}, {3, 4, 5}, {6, 7, 8}};
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final int[][] ALL_UNITS = new int[3 * N][];
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final int[][][] UNITS = new int[N * N][3][N];
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final int[][] PEERS = new int[N * N][20];
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final int[] NUM_DIGITS = new int[ALL_DIGITS + 1];
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final int[] HIGHEST_DIGIT = new int[ALL_DIGITS + 1];
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{
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// Initialize ALL_UNITS to be an array of the 27 units: rows, columns, and blocks
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int i = 0;
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for (int r: ROWS) {ALL_UNITS[i++] = cross(new int[] {r}, COLS); }
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for (int c: COLS) {ALL_UNITS[i++] = cross(ROWS, new int[] {c}); }
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for (int[] rb: BLOCKS) {for (int[] cb: BLOCKS) {ALL_UNITS[i++] = cross(rb, cb); } }
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// Initialize each UNITS[s] to be an array of the 3 units for square s.
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for (int s: SQUARES) {
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i = 0;
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for (int[] u: ALL_UNITS) {
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if (member(s, u)) UNITS[s][i++] = u;
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}
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}
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// Initialize each PEERS[s] to be an array of the 20 squares that are peers of square s.
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for (int s: SQUARES) {
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i = 0;
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for (int[] u: UNITS[s]) {
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for (int s2: u) {
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if (s2 != s && !member(s2, PEERS[s], i)) {
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PEERS[s][i++] = s2;
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}
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}
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}
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}
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// Initialize NUM_DIGITS[val] to be the number of 1 bits in the bitset val
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// and HIGHEST_DIGIT[val] to the highest bit set in the bitset val
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for (int val = 0; val <= ALL_DIGITS; val++) {
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NUM_DIGITS[val] = Integer.bitCount(val);
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HIGHEST_DIGIT[val] = Integer.highestOneBit(val);
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}
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}
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//////////////////////////////// Search algorithm ////////////////////////////////
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/** Search for a solution to grid. If there is an unfilled square, select one
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** and try--that is, search recursively--every possible digit for the square. **/
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int[] search(int[] grid, int[][] gridpool, int level) {
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if (grid == null) {
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return null;
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}
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int s = select_square(grid);
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if (s == -1) {
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return grid; // No squares to select means we are done!
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}
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for (int d: DIGITS) {
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// For each possible digit d that could fill square s, try it
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if ((d & grid[s]) > 0) {
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// Copy grid's contents into gridpool[level], and use that at the next level
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System.arraycopy(grid, 0, gridpool[level], 0, grid.length);
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int[] result = search(fill(gridpool[level], s, d), gridpool, level + 1);
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if (result != null) {
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return result;
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}
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backtracks += 1;
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}
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}
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return null;
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}
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/** Verify that grid is a solution to the puzzle. **/
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boolean verify(int[] grid, int[] puzzle) {
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if (grid == null) { return false; }
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// Check that all squares have a single digit, and
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// no filled square in the puzzle was changed in the solution.
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for (int s: SQUARES) {
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if ((NUM_DIGITS[grid[s]] != 1) || (NUM_DIGITS[puzzle[s]] == 1 && grid[s] != puzzle[s])) {
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return false;
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}
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}
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// Check that each unit is a permutation of digits
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for (int[] u: ALL_UNITS) {
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int unit_digits = 0; // All the digits in a unit.
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for (int s : u) {unit_digits |= grid[s]; }
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if (unit_digits != ALL_DIGITS) {
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return false;
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}
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}
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return true;
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}
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/** Choose an unfilled square with the minimum number of possible values.
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** If all squares are filled, return -1 (which means the puzzle is complete). **/
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int select_square(int[] grid) {
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int square = -1;
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int min = N + 1;
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for (int s: SQUARES) {
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int c = NUM_DIGITS[grid[s]];
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if (c == 2) {
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return s; // Can't get fewer than 2 possible digits
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} else if (c > 1 && c < min) {
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square = s;
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min = c;
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}
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}
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return square;
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}
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/** fill grid[s] = d. If this leads to contradiction, return null. **/
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int[] fill(int[] grid, int s, int d) {
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if ((grid == null) || ((grid[s] & d) == 0)) { return null; } // d not possible for grid[s]
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grid[s] = d;
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for (int p: PEERS[s]) {
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if (!eliminate(grid, p, d)) { // If we can't eliminate d from all peers of s, then fail
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return null;
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}
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}
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return grid;
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}
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/** Eliminate digit d as a possibility for grid[s].
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** Run the 3 constraint propagation routines.
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** If constraint propagation detects a contradiction, return false. **/
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boolean eliminate(int[] grid, int s, int d) {
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if ((grid[s] & d) == 0) { return true; } // d already eliminated from grid[s]
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grid[s] -= d;
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return arc_consistent(grid, s) && dual_consistent(grid, s, d) && naked_pairs(grid, s);
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}
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//////////////////////////////// Constraint Propagation ////////////////////////////////
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/** Check if square s is consistent: that is, it has multiple possible values, or it has
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** one possible value which we can consistently fill. **/
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boolean arc_consistent(int[] grid, int s) {
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int count = NUM_DIGITS[grid[s]];
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return count >= 2 || (count == 1 && (fill(grid, s, grid[s]) != null));
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}
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/** After we eliminate d from possibilities for grid[s], check each unit of s
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** and make sure there is some position in the unit where d can go.
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** If there is only one possible place for d, fill it with d. **/
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boolean dual_consistent(int[] grid, int s, int d) {
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for (int[] u: UNITS[s]) {
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int dPlaces = 0; // The number of possible places for d within unit u
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int dplace = -1; // Try to find a place in the unit where d can go
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for (int s2: u) {
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if ((grid[s2] & d) > 0) { // s2 is a possible place for d
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dPlaces++;
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if (dPlaces > 1) break;
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dplace = s2;
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}
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}
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if (dPlaces == 0 || (dPlaces == 1 && (fill(grid, dplace, d) == null))) {
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return false;
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}
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}
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return true;
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}
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/** Look for two squares in a unit with the same two possible values, and no other values.
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** For example, if s and s2 both have the possible values 8|9, then we know that 8 and 9
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** must go in those two squares. We don't know which is which, but we can eliminate
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** 8 and 9 from any other square s3 that is in the unit. **/
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boolean naked_pairs(int[] grid, int s) {
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if (!runNakedPairs) { return true; }
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int val = grid[s];
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if (NUM_DIGITS[val] != 2) { return true; } // Doesn't apply
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for (int s2: PEERS[s]) {
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if (grid[s2] == val) {
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// s and s2 are a naked pair; find what unit(s) they share
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for (int[] u: UNITS[s]) {
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if (member(s2, u)) {
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for (int s3: u) { // s3 can't have either of the values in val (e.g. 8|9)
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if (s3 != s && s3 != s2) {
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int d = HIGHEST_DIGIT[val];
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int d2 = val - d;
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if (!eliminate(grid, s3, d) || !eliminate(grid, s3, d2)) {
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return false;
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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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return true;
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}
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//////////////////////////////// Input ////////////////////////////////
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/** The method `readFile` reads one puzzle per file line and returns a List of puzzle grids. **/
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List<int[]> readFile(String filename) throws IOException {
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BufferedReader in = new BufferedReader(new FileReader(filename));
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List<int[]> grids = new ArrayList<int[]>(1000);
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String gridstring;
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while ((gridstring = in.readLine()) != null) {
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grids.add(parseGrid(gridstring));
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if (reversePuzzle) {
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grids.add(parseGrid(new StringBuilder(gridstring).reverse().toString()));
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}
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}
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return grids;
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}
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/** Parse a gridstring into a puzzle grid: an int[] with values DIGITS[0-9] or ALL_DIGITS. **/
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int[] parseGrid(String gridstring) {
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int[] grid = new int[N * N];
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int s = 0;
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for (int i = 0; i<gridstring.length(); ++i) {
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char c = gridstring.charAt(i);
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if ('1' <= c && c <= '9') {
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grid[s++] = DIGITS[c - '1']; // A single-bit set to represent a digit
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} else if (c == '0' || c == '.') {
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grid[s++] = ALL_DIGITS; // Any digit is possible
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}
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}
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assert s == N * N;
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return grid;
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}
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/** Initialize a grid from a puzzle.
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** First initialize every square in the new grid to ALL_DIGITS, meaning any value is possible.
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** Then, call `fill` on the puzzle's filled squares to initiate constraint propagation. **/
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int[] initialize(int[] puzzle) {
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int[] grid = new int[N * N]; Arrays.fill(grid, ALL_DIGITS);
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for (int s: SQUARES) { if (puzzle[s] != ALL_DIGITS) { fill(grid, s, puzzle[s]); } }
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return grid;
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}
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//////////////////////////////// Output and Tests ////////////////////////////////
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boolean headerPrinted = false;
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/** Print stats on puzzles solved, average time, frequency, threads used, and name. **/
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void printStats(int nGrids, long startTime, String name) {
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double usecs = (System.nanoTime() - startTime) / 1000.;
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String line = String.format("%7d %6.1f %7.3f %7d %10.1f %s",
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nGrids, usecs / nGrids, 1000 * nGrids / usecs, nThreads, backtracks * 1. / nGrids, name);
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synchronized (this) { // So that printing from different threads doesn't get garbled
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if (!headerPrinted) {
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System.out.println("Puzzles μsec KHz Threads Backtracks Name\n"
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+ "======= ====== ======= ======= ========== ====");
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headerPrinted = true;
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}
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System.out.println(line);
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backtracks = 0;
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}
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}
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/** Print the original puzzle grid and the solution grid. **/
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void printGrids(String name, int[] puzzle, int[] solution) {
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String bar = "------+-------+------";
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String gap = " "; // Space between the puzzle grid and solution grid
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if (solution == null) solution = new int[N * N];
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synchronized (this) { // So that printing from different threads doesn't get garbled
|
|
System.out.format("\n%-22s%s%s\n", name + ":", gap,
|
|
(verify(solution, puzzle) ? "Solution:" : "FAILED:"));
|
|
for (int r = 0; r < N; ++r) {
|
|
System.out.println(rowString(puzzle, r) + gap + rowString(solution, r));
|
|
if (r == 2 || r == 5) System.out.println(bar + gap + " " + bar);
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/** Return a String representing a row of this puzzle. **/
|
|
String rowString(int[] grid, int r) {
|
|
String row = "";
|
|
for (int s = r * 9; s < (r + 1) * 9; ++s) {
|
|
row += (char) ((NUM_DIGITS[grid[s]] == 9) ? '.' : (NUM_DIGITS[grid[s]] != 1) ? '?' :
|
|
('1' + Integer.numberOfTrailingZeros(grid[s])));
|
|
row += (s % 9 == 2 || s % 9 == 5 ? " | " : " ");
|
|
}
|
|
return row;
|
|
}
|
|
|
|
|
|
/** Unit Tests. Just getting started with these. **/
|
|
void runUnitTests() {
|
|
assert N == 9;
|
|
assert SQUARES.length == 81;
|
|
for (int s: SQUARES) {
|
|
assert UNITS[s].length == 3;
|
|
assert PEERS[s].length == 20;
|
|
}
|
|
assert Arrays.equals(PEERS[19],
|
|
new int[] {18, 20, 21, 22, 23, 24, 25, 26, 1, 10, 28, 37, 46, 55, 64, 73, 0, 2, 9, 11});
|
|
assert Arrays.deepToString(UNITS[19]).equals(
|
|
"[[18, 19, 20, 21, 22, 23, 24, 25, 26], [1, 10, 19, 28, 37, 46, 55, 64, 73], [0, 1, 2, 9, 10, 11, 18, 19, 20]]");
|
|
System.out.println("Unit tests pass.");
|
|
}
|
|
} |