477 lines
19 KiB
Java
477 lines
19 KiB
Java
import java.io.*;
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import java.util.*;
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import java.util.concurrent.CountDownLatch;
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import java.util.concurrent.atomic.AtomicInteger;
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import java.util.stream.IntStream;
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//////////////////////////////// Solve Sudoku Puzzles ////////////////////////////////
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//////////////////////////////// @author Peter Norvig ////////////////////////////////
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//////////////////////////////// 2007, 2021 ////////////////////////////////
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/** Solve Sudoku Puzzles
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** @author Peter Norvig
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** Mostly 2007, som2 2021, 2026
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**
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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 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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"Options and filenames are processed left-to-right. Use '-no' to turn an option off\n",
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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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" -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 the naked pairs strategy (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(ummary) Print per-file summary stats (default on)",
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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 25)",
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" -R<number> Repeat the solving of 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 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 printFileStats = true; // -s
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boolean printThreadStats = false; // -t
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boolean verifySolution = true; // -v
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int nThreads = 25; // -T
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int repeat = 1; // -R
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private final AtomicInteger backtracks = new AtomicInteger(0);
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private volatile boolean headerPrinted = false;
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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 'g' -> s.printGrid = value;
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case 'h' -> System.out.println(USAGE);
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case 'n' -> s.runNakedPairs = value;
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case 'p' -> s.printPuzzleStats = value;
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case 'r' -> s.reversePuzzle = value;
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case 's' -> s.printFileStats = value;
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case 't' -> s.printThreadStats = value;
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case 'u' -> s.runUnitTests();
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case 'v' -> s.verifySolution = value;
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case 'T' -> s.nThreads = Integer.parseInt(arg.substring(2));
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case 'R' -> s.repeat = Integer.parseInt(arg.substring(2));
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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 = readPuzzlesFromFile(filename);
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long startFileTime = System.nanoTime();
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if (nThreads == 1) {
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solveList(grids);
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} else {
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solveListThreaded(grids, nThreads);
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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];
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int[][] gridpool = new int[N * N][N * N];
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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);
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solution = search(solution, gridpool, 0);
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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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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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}).start();
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}
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latch.await();
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} catch (InterruptedException e) {
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Thread.currentThread().interrupt();
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System.err.println("Solver thread was interrupted.");
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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) {
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for (int c : cols) {
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result[i++] = N * r + c;
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}
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}
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return result;
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}
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/** Return true iff item is an element of array. **/
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boolean member(int item, int[] array) { return member(item, array, array.length); }
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/** Return true iff item appears within array[0..end). **/
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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;
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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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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) {
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for (int[] cb : BLOCKS) { ALL_UNITS[i++] = cross(rb, cb); }
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}
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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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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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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) return null;
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int s = select_square(grid);
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if (s == -1) return grid; // All squares filled — puzzle is solved.
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for (int d : DIGITS) {
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if ((d & grid[s]) > 0) {
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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) return result;
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backtracks.incrementAndGet(); // thread-safe
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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 valid solution to puzzle. **/
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boolean verify(int[] grid, int[] puzzle) {
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if (grid == null) return false;
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for (int s : SQUARES) {
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if (NUM_DIGITS[grid[s]] != 1
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|| (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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for (int[] u : ALL_UNITS) {
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int unitDigits = 0;
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for (int s : u) { unitDigits |= grid[s]; }
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if (unitDigits != ALL_DIGITS) return false;
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}
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return true;
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}
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/** Choose the unfilled square with the fewest possible values.
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** Return -1 if all squares are filled (puzzle 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) return s; // Can't do better than 2
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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. Return null if this creates a contradiction. **/
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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;
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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)) return null;
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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 all three constraint-propagation routines.
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** Return false if a contradiction is detected. **/
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boolean eliminate(int[] grid, int s, int d) {
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if ((grid[s] & d) == 0) return true; // Already eliminated
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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 arc consistency: either s has multiple possibilities, or its single
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** remaining value can be filled without contradiction. **/
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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 eliminating d from grid[s], ensure d still has at least one valid
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** position in each of s's units. If exactly one remains, fill it. **/
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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;
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int dPlace = -1;
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for (int s2 : u) {
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if ((grid[s2] & d) > 0) {
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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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/** If two squares in a unit share exactly the same two possible values, eliminate
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** those values from every other square in that unit (naked pairs strategy). **/
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boolean naked_pairs(int[] grid, int s) {
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if (!runNakedPairs || NUM_DIGITS[grid[s]] != 2) return true;
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int val = grid[s];
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for (int s2 : PEERS[s]) {
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if (grid[s2] == val) {
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for (int[] u : UNITS[s]) {
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if (member(s2, u)) {
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int d = HIGHEST_DIGIT[val];
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int d2 = val - d;
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for (int s3 : u) {
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if (s3 != s && s3 != s2) {
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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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/** Read one puzzle per line from filename and return a list of puzzle grids. **/
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List<int[]> readPuzzlesFromFile(String filename) throws IOException {
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try (BufferedReader in = new BufferedReader(new FileReader(filename))) {
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List<int[]> grids = new ArrayList<>(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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}
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/** Parse a gridstring into a puzzle grid. **/
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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'];
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} else if (c == '0' || c == '.') {
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grid[s++] = ALL_DIGITS;
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}
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}
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if (s != N * N) {
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throw new IllegalArgumentException(
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"Grid string yielded " + s + " squares; expected " + (N * N) + ": \"" + gridstring + "\"");
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}
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return grid;
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}
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/** Initialize a fresh grid from puzzle, then fill known squares to trigger constraint propagation. **/
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int[] initialize(int[] puzzle) {
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int[] grid = new int[N * N];
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Arrays.fill(grid, ALL_DIGITS);
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for (int s : SQUARES) {
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if (puzzle[s] != ALL_DIGITS) fill(grid, s, puzzle[s]);
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}
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return grid;
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}
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//////////////////////////////// Output and Tests ////////////////////////////////
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/** Print stats: puzzles solved, average µs, KHz, threads, backtracks, and name. **/
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void printStats(int nGrids, long startTime, String name) {
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double usecs = (System.nanoTime() - startTime) / 1_000.0;
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int bt = backtracks.getAndSet(0); // thread-safe
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String line = String.format("%7d %6.1f %7.3f %7d %10.1f %s",
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nGrids, usecs / nGrids, 1_000 * nGrids / usecs, nThreads, bt * 1.0 / nGrids, name);
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synchronized (this) {
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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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}
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}
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/** Print the original puzzle grid alongside the solution grid. **/
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void printGrids(String name, int[] puzzle, int[] solution) {
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final String BAR = "------+-------+------";
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final String GAP = " ";
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if (solution == null) solution = new int[N * N];
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synchronized (this) {
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System.out.format("\n%-22s%s%s\n", name + ":", GAP,
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verify(solution, puzzle) ? "Solution:" : "FAILED:");
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for (int r = 0; r < N; ++r) {
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System.out.println(rowString(puzzle, r) + GAP + rowString(solution, r));
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if (r == 2 || r == 5) System.out.println(BAR + GAP + " " + BAR);
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}
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}
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}
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/** Return a String representing one row of the grid. **/
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String rowString(int[] grid, int r) {
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StringBuilder row = new StringBuilder(30);
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for (int s = r * 9; s < (r + 1) * 9; ++s) {
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int nd = NUM_DIGITS[grid[s]];
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char cell = nd == 9 ? '.' : nd != 1 ? '?' : (char)('1' + Integer.numberOfTrailingZeros(grid[s]));
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row.append(cell);
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row.append(s % 9 == 2 || s % 9 == 5 ? " | " : " ");
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}
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return row.toString();
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}
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/** Unit Tests. **/
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void runUnitTests() {
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assert N == 9;
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assert SQUARES.length == 81;
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for (int s : SQUARES) {
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assert UNITS[s].length == 3;
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assert PEERS[s].length == 20;
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}
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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});
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|
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]]");
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|
System.out.println("Unit tests pass.");
|
|
}
|
|
}
|