⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{task}} Hopido puzzles are similar to [[Solve a Hidato puzzle | Hidato]]. The most important difference is that the only moves allowed are: hop over one tile diagonally; and over two tiles horizontally and vertically. It should be possible to start anywhere in the path, the end point isn't indicated and there are no intermediate clues. [http://gamesandinnovation.com/2010/02/10/hopido-design-post-mortem/ Hopido Design Post Mortem] contains the following:
"Big puzzles represented another problem. Up until quite late in the project our puzzle solver was painfully slow with most puzzles above 7×7 tiles. Testing the solution from each starting point could take hours. If the tile layout was changed even a little, the whole puzzle had to be tested again. We were just about to give up the biggest puzzles entirely when our programmer suddenly came up with a magical algorithm that cut the testing process down to only minutes. Hooray!"
Knowing the kindness in the heart of every contributor to Rosetta Code, I know that we shall feel that as an act of humanity we must solve these puzzles for them in let's say milliseconds.
Example:
. 0 0 . 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0 . . . 0 0 0 . . . . . 0 . . .
Extra credits are available for other interesting designs.
;Related tasks:
- [[A* search algorithm]]
- [[Solve a Holy Knight's tour]]
- [[Knight's tour]]
- [[N-queens problem]]
- [[Solve a Hidato puzzle]]
- [[Solve a Holy Knight's tour]]
- [[Solve a Numbrix puzzle]]
- [[Solve the no connection puzzle]]
AutoHotkey
SolveHopido(Grid, Locked, Max, row, col, num:=1, R:="", C:=""){
if (R&&C) ; if neighbors (not first iteration)
{
Grid[R, C] := ">" num ; place num in current neighbor and mark it visited ">"
row:=R, col:=C ; move to current neighbor
}
num++ ; increment num
if (num=max) ; if reached end
return map(Grid) ; return solution
if locked[num] ; if current num is a locked value
{
row := StrSplit((StrSplit(locked[num], ",").1) , ":").1 ; find row of num
col := StrSplit((StrSplit(locked[num], ",").1) , ":").2 ; find col of num
if SolveHopido(Grid, Locked, Max, row, col, num) ; solve for current location and value
return map(Grid) ; if solved, return solution
}
else
{
for each, value in StrSplit(Neighbor(row,col), ",")
{
R := StrSplit(value, ":").1
C := StrSplit(value, ":").2
if (Grid[R,C] = "") ; a hole or out of bounds
|| InStr(Grid[R, C], ">") ; visited
|| Locked[num+1] && !(Locked[num+1]~= "\b" R ":" C "\b") ; not neighbor of locked[num+1]
|| Locked[num-1] && !(Locked[num-1]~= "\b" R ":" C "\b") ; not neighbor of locked[num-1]
|| Locked[num] ; locked value
|| Locked[Grid[R, C]] ; locked cell
continue
if SolveHopido(Grid, Locked, Max, row, col, num, R, C) ; solve for current location, neighbor and value
return map(Grid) ; if solved, return solution
}
}
num-- ; step back
for i, line in Grid
for j, element in line
if InStr(element, ">") && (StrReplace(element, ">") >= num)
Grid[i, j] := 0
}
;--------------------------------
;--------------------------------
;--------------------------------
Neighbor(row,col){
return Trim( ""
. "," row ":" col-3
. "," row ":" col+3
. "," row-3 ":" col
. "," row+3 ":" col
. "," row+2 ":" col+2
. "," row+2 ":" col-2
. "," row-2 ":" col+2
. "," row-2 ":" col-2
, ",")
}
;--------------------------------
map(Grid){
for i, row in Grid
{
for j, element in row
line .= (A_Index > 1 ? "`t" : "") element
map .= (map<>""?"`n":"") line
line := ""
}
return StrReplace(map, ">")
}
Examples:
;--------------------------------
Grid := [["",0 ,0 ,"",0 ,0 ,""]
,[0 ,0 ,0 ,0 ,0 ,0 ,0]
,[0 ,0 ,0 ,0 ,0 ,0 ,0]
,["",0 ,0 ,0 ,0 ,0 ,""]
,["","",0 ,0 ,0 ,"",""]
,["","","",0 ,"","",""]]
;--------------------------------
; find locked cells, find max value
Locked := []
max := 1
for i, line in Grid
for j, element in line
if (element >= 0)
max++ , list .= i ":" j "`n"
random, rnd, 1, %max%
loop, parse, list, `n, `r
if (A_Index = rnd)
{
row := StrSplit(A_LoopField, ":").1
col := StrSplit(A_LoopField, ":").2
Grid[row,col] := 1
Locked[1] := row ":" col "," Neighbor(row, col)
break
}
;--------------------------------
MsgBox, 262144, ,% SolveHopido(Grid, Locked, Max, row, col)
return
Outputs:
17 24 16 25
22 8 11 21 7 10 20
13 2 5 14 1 4 15
18 23 9 19 26
12 3 6
27
C++
#include <vector> #include <sstream> #include <iostream> #include <iterator> #include <stdlib.h> #include <string.h> using namespace std; struct node { int val; unsigned char neighbors; }; class nSolver { public: nSolver() { dx[0] = -2; dy[0] = -2; dx[1] = -2; dy[1] = 2; dx[2] = 2; dy[2] = -2; dx[3] = 2; dy[3] = 2; dx[4] = -3; dy[4] = 0; dx[5] = 3; dy[5] = 0; dx[6] = 0; dy[6] = -3; dx[7] = 0; dy[7] = 3; } void solve( vector<string>& puzz, int max_wid ) { if( puzz.size() < 1 ) return; wid = max_wid; hei = static_cast<int>( puzz.size() ) / wid; int len = wid * hei, c = 0; max = len; arr = new node[len]; memset( arr, 0, len * sizeof( node ) ); for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ ) { if( ( *i ) == "*" ) { max--; arr[c++].val = -1; continue; } arr[c].val = atoi( ( *i ).c_str() ); c++; } solveIt(); c = 0; for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ ) { if( ( *i ) == "." ) { ostringstream o; o << arr[c].val; ( *i ) = o.str(); } c++; } delete [] arr; } private: bool search( int x, int y, int w ) { if( w > max ) return true; node* n = &arr[x + y * wid]; n->neighbors = getNeighbors( x, y ); for( int d = 0; d < 8; d++ ) { if( n->neighbors & ( 1 << d ) ) { int a = x + dx[d], b = y + dy[d]; if( arr[a + b * wid].val == 0 ) { arr[a + b * wid].val = w; if( search( a, b, w + 1 ) ) return true; arr[a + b * wid].val = 0; } } } return false; } unsigned char getNeighbors( int x, int y ) { unsigned char c = 0; int a, b; for( int xx = 0; xx < 8; xx++ ) { a = x + dx[xx], b = y + dy[xx]; if( a < 0 || b < 0 || a >= wid || b >= hei ) continue; if( arr[a + b * wid].val > -1 ) c |= ( 1 << xx ); } return c; } void solveIt() { int x, y, z; findStart( x, y, z ); if( z == 99999 ) { cout << "\nCan't find start point!\n"; return; } search( x, y, z + 1 ); } void findStart( int& x, int& y, int& z ) { for( int b = 0; b < hei; b++ ) for( int a = 0; a < wid; a++ ) if( arr[a + wid * b].val == 0 ) { x = a; y = b; z = 1; arr[a + wid * b].val = z; return; } } int wid, hei, max, dx[8], dy[8]; node* arr; }; int main( int argc, char* argv[] ) { int wid; string p; p = "* . . * . . * . . . . . . . . . . . . . . * . . . . . * * * . . . * * * * * . * * *"; wid = 7; istringstream iss( p ); vector<string> puzz; copy( istream_iterator<string>( iss ), istream_iterator<string>(), back_inserter<vector<string> >( puzz ) ); nSolver s; s.solve( puzz, wid ); int c = 0; for( vector<string>::iterator i = puzz.begin(); i != puzz.end(); i++ ) { if( ( *i ) != "*" && ( *i ) != "." ) { if( atoi( ( *i ).c_str() ) < 10 ) cout << "0"; cout << ( *i ) << " "; } else cout << " "; if( ++c >= wid ) { cout << endl; c = 0; } } cout << endl << endl; return system( "pause" ); }
{{out}}
01 04 12 03
27 16 19 22 15 18 21
05 08 11 02 07 10 13
23 26 17 20 25
06 09 14
24
C#
The same solver can solve Hidato, Holy Knight's Tour, Hopido and Numbrix puzzles.
The input can be an array of strings if each cell is one character. The length of the first row must be the number of columns in the puzzle.
Any non-numeric value indicates a no-go.
If there are cells that require more characters, then a 2-dimensional array of ints must be used. Any number < 0 indicates a no-go.
using System.Collections; using System.Collections.Generic; using static System.Console; using static System.Math; using static System.Linq.Enumerable; public class Solver { private static readonly (int dx, int dy)[] //other puzzle types elided hopidoMoves = {(-3,0),(0,-3),(0,3),(3,0),(-2,-2),(-2,2),(2,-2),(2,2)}, private (int dx, int dy)[] moves; public static void Main() { Print(new Solver(hopidoMoves).Solve(false, ".00.00.", "0000000", "0000000", ".00000.", "..000..", "...0..." )); } public Solver(params (int dx, int dy)[] moves) => this.moves = moves; public int[,] Solve(bool circular, params string[] puzzle) { var (board, given, count) = Parse(puzzle); return Solve(board, given, count, circular); } public int[,] Solve(bool circular, int[,] puzzle) { var (board, given, count) = Parse(puzzle); return Solve(board, given, count, circular); } private int[,] Solve(int[,] board, BitArray given, int count, bool circular) { var (height, width) = (board.GetLength(0), board.GetLength(1)); bool solved = false; for (int x = 0; x < height && !solved; x++) { solved = Range(0, width).Any(y => Solve(board, given, circular, (height, width), (x, y), count, (x, y), 1)); if (solved) return board; } return null; } private bool Solve(int[,] board, BitArray given, bool circular, (int h, int w) size, (int x, int y) start, int last, (int x, int y) current, int n) { var (x, y) = current; if (x < 0 || x >= size.h || y < 0 || y >= size.w) return false; if (board[x, y] < 0) return false; if (given[n - 1]) { if (board[x, y] != n) return false; } else if (board[x, y] > 0) return false; board[x, y] = n; if (n == last) { if (!circular || AreNeighbors(start, current)) return true; } for (int i = 0; i < moves.Length; i++) { var move = moves[i]; if (Solve(board, given, circular, size, start, last, (x + move.dx, y + move.dy), n + 1)) return true; } if (!given[n - 1]) board[x, y] = 0; return false; bool AreNeighbors((int x, int y) p1, (int x, int y) p2) => moves.Any(m => (p2.x + m.dx, p2.y + m.dy).Equals(p1)); } private static (int[,] board, BitArray given, int count) Parse(string[] input) { (int height, int width) = (input.Length, input[0].Length); int[,] board = new int[height, width]; int count = 0; for (int x = 0; x < height; x++) { string line = input[x]; for (int y = 0; y < width; y++) { board[x, y] = y < line.Length && char.IsDigit(line[y]) ? line[y] - '0' : -1; if (board[x, y] >= 0) count++; } } BitArray given = Scan(board, count, height, width); return (board, given, count); } private static (int[,] board, BitArray given, int count) Parse(int[,] input) { (int height, int width) = (input.GetLength(0), input.GetLength(1)); int[,] board = new int[height, width]; int count = 0; for (int x = 0; x < height; x++) for (int y = 0; y < width; y++) if ((board[x, y] = input[x, y]) >= 0) count++; BitArray given = Scan(board, count, height, width); return (board, given, count); } private static BitArray Scan(int[,] board, int count, int height, int width) { var given = new BitArray(count + 1); for (int x = 0; x < height; x++) for (int y = 0; y < width; y++) if (board[x, y] > 0) given[board[x, y] - 1] = true; return given; } private static void Print(int[,] board) { if (board == null) { WriteLine("No solution"); } else { int w = board.Cast<int>().Where(i => i > 0).Max(i => (int?)Ceiling(Log10(i+1))) ?? 1; string e = new string('-', w); foreach (int x in Range(0, board.GetLength(0))) WriteLine(string.Join(" ", Range(0, board.GetLength(1)) .Select(y => board[x, y] < 0 ? e : board[x, y].ToString().PadLeft(w, ' ')))); } WriteLine(); } }
{{out}}
-- 1 8 -- 2 7 --
25 22 19 26 23 20 27
9 16 13 10 17 14 11
-- 4 24 21 3 6 --
-- -- 18 15 12 -- --
-- -- -- 5 -- -- --
```
## D
{{trans|C++}}
From the refactored C++ version with more precise typing. This tries all possible start positions. The HopidoPuzzle struct is created at compile-time, so its pre-conditions can catch most malformed puzzles at compile-time.
```d
import std.stdio, std.conv, std.string, std.range, std.algorithm, std.typecons;
struct HopidoPuzzle {
private alias InputCellBaseType = char;
private enum InputCell : InputCellBaseType { available = '#', unavailable = '.' }
private alias Cell = uint;
private enum : Cell { unknownCell = 0, unavailableCell = Cell.max } // Special Cell values.
// Neighbors, [shift row, shift column].
private static immutable int[2][8] shifts = [[-2, -2], [2, -2], [-2, 2], [2, 2],
[ 0, -3], [0, 3], [-3, 0], [3, 0]];
private immutable size_t gridWidth, gridHeight;
private immutable Cell nAvailableCells;
private /*immutable*/ const InputCell[] flatPuzzle;
private Cell[] grid; // Flattened mutable game grid.
@disable this();
this(in string[] rawPuzzle) pure @safe
in {
assert(!rawPuzzle.empty);
assert(!rawPuzzle[0].empty);
assert(rawPuzzle.all!(row => row.length == rawPuzzle[0].length)); // Is rectangular.
// Has at least one start point.
assert(rawPuzzle.join.representation.canFind(InputCell.available));
} body {
//immutable puzzle = rawPuzzle.to!(InputCell[][]);
immutable puzzle = rawPuzzle.map!representation.array.to!(InputCell[][]);
gridWidth = puzzle[0].length;
gridHeight = puzzle.length;
flatPuzzle = puzzle.join;
nAvailableCells = flatPuzzle.representation.count!(ic => ic == InputCell.available);
grid = flatPuzzle
.representation
.map!(ic => ic == InputCell.available ? unknownCell : unavailableCell)
.array;
}
Nullable!(string[][]) solve() pure /*nothrow*/ @safe
out(result) {
if (!result.isNull)
assert(!grid.canFind(unknownCell));
} body {
// Try all possible start positions.
foreach (immutable r; 0 .. gridHeight) {
foreach (immutable c; 0 .. gridWidth) {
immutable pos = r * gridWidth + c;
if (grid[pos] == unknownCell) {
immutable Cell startCell = 1; // To lay the first cell value.
grid[pos] = startCell; // Try.
if (search(r, c, startCell + 1)) {
auto result = zip(flatPuzzle, grid)
//.map!({p, c} => ...
.map!(pc => (pc[0] == InputCell.available) ?
pc[1].text :
InputCellBaseType(pc[0]).text)
.array
.chunks(gridWidth)
.array;
return typeof(return)(result);
}
grid[pos] = unknownCell; // Restore.
}
}
}
return typeof(return)();
}
private bool search(in size_t r, in size_t c, in Cell cell) pure nothrow @safe @nogc {
if (cell > nAvailableCells)
return true; // One solution found.
foreach (immutable sh; shifts) {
immutable r2 = r + sh[0],
c2 = c + sh[1],
pos = r2 * gridWidth + c2;
// No need to test for >= 0 because uint wraps around.
if (c2 < gridWidth && r2 < gridHeight && grid[pos] == unknownCell) {
grid[pos] = cell; // Try.
if (search(r2, c2, cell + 1))
return true;
grid[pos] = unknownCell; // Restore.
}
}
return false;
}
}
void main() @safe {
// enum HopidoPuzzle to catch malformed puzzles at compile-time.
enum puzzle = ".##.##.
#######
#######
.#####.
..###..
...#...".split.HopidoPuzzle;
immutable solution = puzzle.solve; // Solved at run-time.
if (solution.isNull)
writeln("No solution found.");
else
writefln("One solution:\n%(%-(%2s %)\n%)", solution);
}
```
{{out}}
```txt
One solution:
. 1 4 . 12 3 .
27 16 19 22 15 18 21
5 8 11 2 7 10 13
. 23 26 17 20 25 .
. . 6 9 14 . .
. . . 24 . . .
```
## Elixir
{{trans|Ruby}}
This solution uses HLPsolver from [[Solve_a_Hidato_puzzle#Elixir | here]]
```elixir
# require HLPsolver
adjacent = [{-3, 0}, {0, -3}, {0, 3}, {3, 0}, {-2, -2}, {-2, 2}, {2, -2}, {2, 2}]
board = """
. 0 0 . 0 0 .
0 0 0 0 0 0 0
0 0 0 0 0 0 0
. 0 0 0 0 0 .
. . 0 0 0 . .
. . . 1 . . .
"""
HLPsolver.solve(board, adjacent)
```
{{out}}
```txt
Problem:
0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0
0 0 0
1
Solution:
5 25 17 3
27 13 10 7 14 11 8
24 21 18 4 22 19 16
6 26 12 9 2
23 20 15
1
```
## Go
{{trans|Java}}
```go
package main
import (
"fmt"
"sort"
)
var board = []string{
".00.00.",
"0000000",
"0000000",
".00000.",
"..000..",
"...0...",
}
var moves = [][2]int{
{-3, 0}, {0, 3}, {3, 0}, {0, -3},
{2, 2}, {2, -2}, {-2, 2}, {-2, -2},
}
var grid [][]int
var totalToFill = 0
func solve(r, c, count int) bool {
if count > totalToFill {
return true
}
nbrs := neighbors(r, c)
if len(nbrs) == 0 && count != totalToFill {
return false
}
sort.Slice(nbrs, func(i, j int) bool {
return nbrs[i][2] < nbrs[j][2]
})
for _, nb := range nbrs {
r = nb[0]
c = nb[1]
grid[r][c] = count
if solve(r, c, count+1) {
return true
}
grid[r][c] = 0
}
return false
}
func neighbors(r, c int) (nbrs [][3]int) {
for _, m := range moves {
x := m[0]
y := m[1]
if grid[r+y][c+x] == 0 {
num := countNeighbors(r+y, c+x) - 1
nbrs = append(nbrs, [3]int{r + y, c + x, num})
}
}
return
}
func countNeighbors(r, c int) int {
num := 0
for _, m := range moves {
if grid[r+m[1]][c+m[0]] == 0 {
num++
}
}
return num
}
func printResult() {
for _, row := range grid {
for _, i := range row {
if i == -1 {
fmt.Print(" ")
} else {
fmt.Printf("%2d ", i)
}
}
fmt.Println()
}
}
func main() {
nRows := len(board) + 6
nCols := len(board[0]) + 6
grid = make([][]int, nRows)
for r := 0; r < nRows; r++ {
grid[r] = make([]int, nCols)
for c := 0; c < nCols; c++ {
grid[r][c] = -1
}
for c := 3; c < nCols-3; c++ {
if r >= 3 && r < nRows-3 {
if board[r-3][c-3] == '0' {
grid[r][c] = 0
totalToFill++
}
}
}
}
pos, r, c := -1, 0, 0
for {
for {
pos++
r = pos / nCols
c = pos % nCols
if grid[r][c] != -1 {
break
}
}
grid[r][c] = 1
if solve(r, c, 2) {
break
}
grid[r][c] = 0
if pos >= nRows*nCols {
break
}
}
printResult()
}
```
{{out}}
```txt
1 22 14 21
18 10 7 17 11 8 16
5 24 27 4 23 26 13
2 19 9 15 20
6 25 12
3
```
==Icon and {{header|Unicon}}==
Minor variant of [[Solve_a_Holy_Knight's_tour]]. Works in Unicon only.
```unicon
global nCells, cMap, best
record Pos(r,c)
procedure main(A)
puzzle := showPuzzle("Input",readPuzzle())
QMouse(puzzle,findStart(puzzle),&null,0)
showPuzzle("Output", solvePuzzle(puzzle)) | write("No solution!")
end
procedure readPuzzle()
# Start with a reduced puzzle space
p := [[-1],[-1]]
nCells := maxCols := 0
every line := !&input do {
put(p,[: -1 | -1 | gencells(line) | -1 | -1 :])
maxCols <:= *p[-1]
}
every put(p, [-1]|[-1])
# Now normalize all rows to the same length
every i := 1 to *p do p[i] := [: !p[i] | (|-1\(maxCols - *p[i])) :]
return p
end
procedure gencells(s)
static WS, NWS
initial {
NWS := ~(WS := " \t")
cMap := table() # Map to/from internal model
cMap["#"] := -1; cMap["_"] := 0
cMap[-1] := " "; cMap[0] := "_"
}
s ? while not pos(0) do {
w := (tab(many(WS))|"", tab(many(NWS))) | break
w := numeric(\cMap[w]|w)
if -1 ~= w then nCells +:= 1
suspend w
}
end
procedure showPuzzle(label, p)
write(label," with ",nCells," cells:")
every r := !p do {
every c := !r do writes(right((\cMap[c]|c),*nCells+1))
write()
}
return p
end
procedure findStart(p)
if \p[r := !*p][c := !*p[r]] = 1 then return Pos(r,c)
end
procedure solvePuzzle(puzzle)
if path := \best then {
repeat {
loc := path.getLoc()
puzzle[loc.r][loc.c] := path.getVal()
path := \path.getParent() | break
}
return puzzle
}
end
class QMouse(puzzle, loc, parent, val)
method getVal(); return val; end
method getLoc(); return loc; end
method getParent(); return parent; end
method atEnd(); return nCells = val; end
method visit(r,c)
if /best & validPos(r,c) then return Pos(r,c)
end
method validPos(r,c)
v := val+1
xv := (0 <= puzzle[r][c]) | fail
if xv = (v|0) then { # make sure this path hasn't already gone there
ancestor := self
while xl := (ancestor := \ancestor.getParent()).getLoc() do
if (xl.r = r) & (xl.c = c) then fail
return
}
end
initially
val := val+1
if atEnd() then return best := self
QMouse(puzzle, visit(loc.r-3,loc.c), self, val)
QMouse(puzzle, visit(loc.r-2,loc.c-2), self, val)
QMouse(puzzle, visit(loc.r, loc.c-3), self, val)
QMouse(puzzle, visit(loc.r+2,loc.c-2), self, val)
QMouse(puzzle, visit(loc.r+3,loc.c), self, val)
QMouse(puzzle, visit(loc.r+2,loc.c+2), self, val)
QMouse(puzzle, visit(loc.r, loc.c+3), self, val)
QMouse(puzzle, visit(loc.r-2,loc.c+2), self, val)
end
```
Sample run:
```txt
->hopido
```
## Java
{{works with|Java|8}}
```java
import java.util.*;
public class Hopido {
final static String[] board = {
".00.00.",
"0000000",
"0000000",
".00000.",
"..000..",
"...0..."};
final static int[][] moves = {{-3, 0}, {0, 3}, {3, 0}, {0, -3},
{2, 2}, {2, -2}, {-2, 2}, {-2, -2}};
static int[][] grid;
static int totalToFill;
public static void main(String[] args) {
int nRows = board.length + 6;
int nCols = board[0].length() + 6;
grid = new int[nRows][nCols];
for (int r = 0; r < nRows; r++) {
Arrays.fill(grid[r], -1);
for (int c = 3; c < nCols - 3; c++)
if (r >= 3 && r < nRows - 3) {
if (board[r - 3].charAt(c - 3) == '0') {
grid[r][c] = 0;
totalToFill++;
}
}
}
int pos = -1, r, c;
do {
do {
pos++;
r = pos / nCols;
c = pos % nCols;
} while (grid[r][c] == -1);
grid[r][c] = 1;
if (solve(r, c, 2))
break;
grid[r][c] = 0;
} while (pos < nRows * nCols);
printResult();
}
static boolean solve(int r, int c, int count) {
if (count > totalToFill)
return true;
List nbrs = neighbors(r, c);
if (nbrs.isEmpty() && count != totalToFill)
return false;
Collections.sort(nbrs, (a, b) -> a[2] - b[2]);
for (int[] nb : nbrs) {
r = nb[0];
c = nb[1];
grid[r][c] = count;
if (solve(r, c, count + 1))
return true;
grid[r][c] = 0;
}
return false;
}
static List neighbors(int r, int c) {
List nbrs = new ArrayList<>();
for (int[] m : moves) {
int x = m[0];
int y = m[1];
if (grid[r + y][c + x] == 0) {
int num = countNeighbors(r + y, c + x) - 1;
nbrs.add(new int[]{r + y, c + x, num});
}
}
return nbrs;
}
static int countNeighbors(int r, int c) {
int num = 0;
for (int[] m : moves)
if (grid[r + m[1]][c + m[0]] == 0)
num++;
return num;
}
static void printResult() {
for (int[] row : grid) {
for (int i : row) {
if (i == -1)
System.out.printf("%2s ", ' ');
else
System.out.printf("%2d ", i);
}
System.out.println();
}
}
}
```
```txt
1 22 14 21
18 10 7 17 11 8 16
5 24 27 4 23 26 13
2 19 9 15 20
6 25 12
3
```
## Julia
Uses the Hidato puzzle solver module, which has its source code listed [[Solve_a_Hidato_puzzle#Julia | here]] in the Hadato task.
```julia
using .Hidato # Note that the . here means to look locally for the module rather than in the libraries
const hopid = """
. 0 0 . 0 0 .
0 0 0 0 0 0 0
0 0 0 0 0 0 0
. 0 0 0 0 0 .
. . 0 0 0 . .
. . . 0 . . . """
const hopidomoves = [[-3, 0], [0, -3], [-2, -2], [-2, 2], [2, -2], [0, 3], [3, 0], [2, 2]]
board, maxmoves, fixed, starts = hidatoconfigure(hopid)
printboard(board, " 0", " ")
hidatosolve(board, maxmoves, hopidomoves, fixed, starts[1][1], starts[1][2], 1)
printboard(board)
```
{{output}}
```txt
0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0
0 0 0
0
4 15 5 16
1 22 25 2 21 24 27
14 11 8 17 12 9 6
3 20 23 26 19
13 10 7
18
```
## Kotlin
{{trans|Java}}
```scala
// version 1.2.0
val board = listOf(
".00.00.",
"0000000",
"0000000",
".00000.",
"..000..",
"...0..."
)
val moves = listOf(
-3 to 0, 0 to 3, 3 to 0, 0 to -3,
2 to 2, 2 to -2, -2 to 2, -2 to -2
)
lateinit var grid: List
var totalToFill = 0
fun solve(r: Int, c: Int, count: Int): Boolean {
if (count > totalToFill) return true
val nbrs = neighbors(r, c)
if (nbrs.isEmpty() && count != totalToFill) return false
nbrs.sortBy { it[2] }
for (nb in nbrs) {
val rr = nb[0]
val cc = nb[1]
grid[rr][cc] = count
if (solve(rr, cc, count + 1)) return true
grid[rr][cc] = 0
}
return false
}
fun neighbors(r: Int, c: Int): MutableList {
val nbrs = mutableListOf()
for (m in moves) {
val x = m.first
val y = m.second
if (grid[r + y][c + x] == 0) {
val num = countNeighbors(r + y, c + x) - 1
nbrs.add(intArrayOf(r + y, c + x, num))
}
}
return nbrs
}
fun countNeighbors(r: Int, c: Int): Int {
var num = 0
for (m in moves)
if (grid[r + m.second][c + m.first] == 0) num++
return num
}
fun printResult() {
for (row in grid) {
for (i in row) {
print(if (i == -1) " " else "%2d ".format(i))
}
println()
}
}
fun main(args: Array) {
val nRows = board.size + 6
val nCols = board[0].length + 6
grid = List(nRows) { IntArray(nCols) { -1} }
for (r in 0 until nRows) {
for (c in 3 until nCols - 3) {
if (r in 3 until nRows - 3) {
if (board[r - 3][c - 3] == '0') {
grid[r][c] = 0
totalToFill++
}
}
}
}
var pos = -1
var rr: Int
var cc: Int
do {
do {
pos++
rr = pos / nCols
cc = pos % nCols
}
while (grid[rr][cc] == -1)
grid[rr][cc] = 1
if (solve(rr, cc, 2)) break
grid[rr][cc] = 0
}
while (pos < nRows * nCols)
printResult()
}
```
{{out}}
```txt
1 22 14 21
18 10 7 17 11 8 16
5 24 27 4 23 26 13
2 19 9 15 20
6 25 12
3
```
## Perl
```perl
#!/usr/bin/perl
use strict; # http://www.rosettacode.org/wiki/Solve_a_Hopido_puzzle
use warnings;
$_ = do { local $/; };
s/./$&$&/g; # double chars
my $w = /\n/ && $-[0];
my $wd = 3 * $w + 1; # vertical gap
my $wr = 2 * $w + 8; # down right gap
my $wl = 2 * $w - 8; # down left gap
place($_, '00');
die "No solution\n";
sub place
{
(local $_, my $last) = @_;
(my $new = $last)++;
/$last.{10}(?=00)/g and place( s/\G00/$new/r, $new ); # right
/(?=00.{10}$last)/g and place( s/\G00/$new/r, $new ); # left
/$last.{$wd}(?=00)/gs and place( s/\G00/$new/r, $new ); # down
/(?=00.{$wd}$last)/gs and place( s/\G00/$new/r, $new ); # up
/$last.{$wr}(?=00)/gs and place( s/\G00/$new/r, $new ); # down right
/(?=00.{$wr}$last)/gs and place( s/\G00/$new/r, $new ); # up left
/$last.{$wl}(?=00)/gs and place( s/\G00/$new/r, $new ); # down left
/(?=00.{$wl}$last)/gs and place( s/\G00/$new/r, $new ); # up right
/00/ and return;
print "Solution\n\n", s/ / /gr =~ s/0\B/ /gr;
exit;
}
__DATA__
. 0 0 . 0 0 .
0 0 0 0 0 0 0
0 0 0 0 0 0 0
. 0 0 0 0 0 .
. . 0 0 0 . .
. . . 0 . . .
```
{{out}}
```txt
Solution
.. 2 24 .. 1 25 ..
7 10 13 6 9 12 5
15 22 19 16 23 20 17
.. 3 8 11 4 26 ..
.. .. 14 21 18 .. ..
.. .. .. 27 .. .. ..
```
## Perl 6
This uses a Warnsdorff solver, which cuts down the number of tries by more than a factor of six over the brute force approach. This same solver is used in:
* [[Solve a Hidato puzzle#Perl_6|Solve a Hidato puzzle]]
* [[Solve a Hopido puzzle#Perl_6|Solve a Hopido puzzle]]
* [[Solve a Holy Knight's tour#Perl_6|Solve a Holy Knight's tour]]
* [[Solve a Numbrix puzzle#Perl_6|Solve a Numbrix puzzle]]
* [[Solve the no connection puzzle#Perl_6|Solve the no connection puzzle]]
```perl6
my @adjacent = [3, 0],
[2, -2], [2, 2],
[0, -3], [0, 3],
[-2, -2], [-2, 2],
[-3, 0];
solveboard q:to/END/;
. _ _ . _ _ .
_ _ _ _ _ _ _
_ _ _ _ _ _ _
. _ _ _ _ _ .
. . _ _ _ . .
. . . 1 . . .
END
sub solveboard($board) {
my $max = +$board.comb(/\w+/);
my $width = $max.chars;
my @grid;
my @known;
my @neigh;
my @degree;
@grid = $board.lines.map: -> $line {
[ $line.words.map: { /^_/ ?? 0 !! /^\./ ?? Rat !! $_ } ]
}
sub neighbors($y,$x --> List) {
eager gather for @adjacent {
my $y1 = $y + .[0];
my $x1 = $x + .[1];
take [$y1,$x1] if defined @grid[$y1][$x1];
}
}
for ^@grid -> $y {
for ^@grid[$y] -> $x {
if @grid[$y][$x] -> $v {
@known[$v] = [$y,$x];
}
if @grid[$y][$x].defined {
@neigh[$y][$x] = neighbors($y,$x);
@degree[$y][$x] = +@neigh[$y][$x];
}
}
}
print "\e[0H\e[0J";
my $tries = 0;
try_fill 1, @known[1];
sub try_fill($v, $coord [$y,$x] --> Bool) {
return True if $v > $max;
$tries++;
my $old = @grid[$y][$x];
return False if +$old and $old != $v;
return False if @known[$v] and @known[$v] !eqv $coord;
@grid[$y][$x] = $v; # conjecture grid value
print "\e[0H"; # show conjectured board
for @grid -> $r {
say do for @$r {
when Rat { ' ' x $width }
when 0 { '_' x $width }
default { .fmt("%{$width}d") }
}
}
my @neighbors = @neigh[$y][$x][];
my @degrees;
for @neighbors -> \n [$yy,$xx] {
my $d = --@degree[$yy][$xx]; # conjecture new degrees
push @degrees[$d], n; # and categorize by degree
}
for @degrees.grep(*.defined) -> @ties {
for @ties.reverse { # reverse works better for this hidato anyway
return True if try_fill $v + 1, $_;
}
}
for @neighbors -> [$yy,$xx] {
++@degree[$yy][$xx]; # undo degree conjectures
}
@grid[$y][$x] = $old; # undo grid value conjecture
return False;
}
say "$tries tries";
}
```
{{out}}
```txt
21 4 20 3
26 12 15 25 11 14 24
17 6 9 18 5 8 19
22 27 13 23 2
16 7 10
1
59 tries
```
## Phix
Simple brute force approach.
```Phix
sequence board
integer limit, tries
constant ROW = 1, COL = 2
constant moves = {{-2,-2},{-2,2},{2,-2},{2,2},{-3,0},{3,0},{0,-3},{0,3}}
function solve(integer row, integer col, integer n)
integer nrow, ncol
tries+= 1
if n>limit then return 1 end if
for move=1 to length(moves) do
nrow = row+moves[move][ROW]
ncol = col+moves[move][COL]*3
if nrow>=1 and nrow<=length(board)
and ncol>=1 and ncol<=length(board[row])
and board[nrow][ncol]=' ' then
board[nrow][ncol-1..ncol] = sprintf("%2d",n)
if solve(nrow,ncol,n+1) then return 1 end if
board[nrow][ncol-1..ncol] = " "
end if
end for
return 0
end function
procedure Hopido(sequence s, integer w, integer h)
integer x, y
atom t0 = time()
board = split(s,'\n')
limit = 0
for x=1 to h do
for y=3 to w*3 by 3 do
if board[x][y]='0' then
board[x][y] = ' '
limit += 1
end if
end for
end for
while 1 do
x = rand(h)
y = rand(w)*3
if board[x][y]=' ' then exit end if
end while
board[x][y] = '1'
tries = 0
if solve(x,y,2) then
puts(1,join(board,"\n"))
printf(1,"\nsolution found in %d tries (%3.2fs)\n",{tries,time()-t0})
else
puts(1,"no solutions found\n")
end if
end procedure
constant board1 = """
. 0 0 . 0 0 .
0 0 0 0 0 0 0
0 0 0 0 0 0 0
. 0 0 0 0 0 .
. . 0 0 0 . .
. . . 0 . . ."""
Hopido(board1,7,6)
```
The best and worse cases observed were:
```txt
. 13 22 . 14 11 .
6 3 25 7 4 1 27
23 20 17 12 21 18 15
. 8 5 2 26 10 .
. . 24 19 16 . .
. . . 9 . . .
solution found in 46 tries (0.00s)
. 20 11 . 19 22 .
2 5 8 1 4 7 27
10 13 16 21 12 15 18
. 25 3 6 26 23 .
. . 9 14 17 . .
. . . 24 . . .
solution found in 67702 tries (0.09s)
```
## Python
```python
from sys import stdout
neighbours = [[2, 2], [-2, 2], [2, -2], [-2, -2], [3, 0], [0, 3], [-3, 0], [0, -3]]
cnt = 0
pWid = 0
pHei = 0
def is_valid(a, b):
return -1 < a < pWid and -1 < b < pHei
def iterate(pa, x, y, v):
if v > cnt:
return 1
for i in range(len(neighbours)):
a = x + neighbours[i][0]
b = y + neighbours[i][1]
if is_valid(a, b) and pa[a][b] == 0:
pa[a][b] = v
r = iterate(pa, a, b, v + 1)
if r == 1:
return r
pa[a][b] = 0
return 0
def solve(pz, w, h):
global cnt, pWid, pHei
pa = [[-1 for j in range(h)] for i in range(w)]
f = 0
pWid = w
pHei = h
for j in range(h):
for i in range(w):
if pz[f] == "1":
pa[i][j] = 0
cnt += 1
f += 1
for y in range(h):
for x in range(w):
if pa[x][y] == 0:
pa[x][y] = 1
if 1 == iterate(pa, x, y, 2):
return 1, pa
pa[x][y] = 0
return 0, pa
r = solve("011011011111111111111011111000111000001000", 7, 6)
if r[0] == 1:
for j in range(6):
for i in range(7):
if r[1][i][j] == -1:
stdout.write(" ")
else:
stdout.write(" {:0{}d}".format(r[1][i][j], 2))
print()
else:
stdout.write("No solution!")
```
{{out}}
```txt
01 25 17 03
27 13 10 07 14 11 08
24 21 18 02 22 19 16
06 26 12 09 04
23 20 15
05
```
## Racket
This solution uses the module "hidato-family-solver.rkt" from
[[Solve a Numbrix puzzle#Racket]]. The difference between the two is
essentially the neighbourhood function.
```racket
#lang racket
(require "hidato-family-solver.rkt")
(define hoppy-moore-neighbour-offsets
'((+3 0) (-3 0) (0 +3) (0 -3) (+2 +2) (-2 -2) (-2 +2) (+2 -2)))
(define solve-hopido (solve-hidato-family hoppy-moore-neighbour-offsets))
(displayln
(puzzle->string
(solve-hopido
#(#(_ 0 0 _ 0 0 _)
#(0 0 0 0 0 0 0)
#(0 0 0 0 0 0 0)
#(_ 0 0 0 0 0 _)
#(_ _ 0 0 0 _ _)
#(_ _ _ 0 _ _ _)))))
```
{{out}}
```txt
_ 2 20 _ 3 19 _
7 10 13 6 9 12 5
15 22 25 16 21 24 27
_ 1 8 11 4 18 _
_ _ 14 23 26 _ _
_ _ _ 17 _ _ _
```
## REXX
This REXX program is a slightly modified version of the REXX '''Hidato''' program.
No particular effort was made to reduce the elapsed time in solving the puzzle.
```rexx
/*REXX program solves a Hopido puzzle, it also displays the puzzle and the solution. */
call time 'Reset' /*reset the REXX elapsed timer to zero.*/
maxR=0; maxC=0; maxX=0; minR=9e9; minC=9e9; minX=9e9; cells=0; @.=
parse arg xxx /*get the cell definitions from the CL.*/
xxx=translate(xxx, , "/\;:_", ',') /*also allow other characters as comma.*/
do while xxx\=''; parse var xxx r c marks ',' xxx
do while marks\=''; [email protected]
parse var marks x marks
if datatype(x,'N') then x=x/1 /*normalize X. */
minR=min(minR,r); maxR=max(maxR,r); minC=min(minC,c); maxC=max(maxC,c)
if x==1 then do; !r=r; !c=c; end /*the START cell. */
if _\=='' then call err "cell at" r c 'is already occupied with:' _
@.r.c=x; c=c+1; cells=cells+1 /*assign a mark. */
if x==. then iterate /*is a hole? Skip*/
if \datatype(x,'W') then call err 'illegal marker specified:' x
minX=min(minX,x); maxX=max(maxX,x) /*min and max X. */
end /*while marks¬='' */
end /*while xxx ¬='' */
call show /* [↓] is used for making fast moves. */
Nr = '0 3 0 -3 -2 2 2 -2' /*possible row for the next move. */
Nc = '3 0 -3 0 2 -2 2 -2' /* " column " " " " */
pMoves=words(Nr) /*the number of possible moves. */
do i=1 for pMoves; Nr.i=word(Nr, i); Nc.i=word(Nc,i); end /*i*/
if \next(2,!r,!c) then call err 'No solution possible for this Hopido puzzle.'
say 'A solution for the Hopido exists.'; say; call show
etime= format(time('Elapsed'), , 2) /*obtain the elapsed time (in seconds).*/
if etime<.1 then say 'and took less than 1/10 of a second.'
else say 'and took' etime "seconds."
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
err: say; say '***error*** (from Hopido): ' arg(1); say; exit 13
/*──────────────────────────────────────────────────────────────────────────────────────*/
next: procedure expose @. Nr. Nc. cells pMoves; parse arg #,r,c; ##=#+1
do t=1 for pMoves /* [↓] try some moves. */
parse value r+Nr.t c+Nc.t with nr nc /*next move coördinates*/
if @.nr.nc==. then do; @.nr.nc=# /*let's try this move. */
if #==cells then leave /*is this the last move?*/
if next(##,nr,nc) then return 1
@.nr.nc=. /*undo the above move. */
iterate /*go & try another move.*/
end
if @.nr.nc==# then do /*this a fill-in move ? */
if #==cells then return 1 /*this is the last move.*/
if next(##,nr,nc) then return 1 /*a fill-in move. */
end
end /*t*/
return 0 /*This ain't working. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
show: if maxR<1 | maxC<1 then call err 'no legal cell was specified.'
if minX<1 then call err 'no 1 was specified for the puzzle start'
w=max(2,length(cells)); do r=maxR to minR by -1; _=
do c=minC to maxC; _=_ right(@.r.c,w); end /*c*/
say _
end /*r*/
say; return
```
'''output''' when the input is:
1 4 1 \2 3 . . . \3 2 . . . . . \4 1 . . . . . . . \5 1 . . . . . . . \6 2 . . \6 5 . .
```txt
. . . .
. . . . . . .
. . . . . . .
. . . . .
. . .
1
A solution for the Hopido exists.
5 12 4 11
8 22 25 7 21 24 27
13 16 19 2 15 18 3
6 9 23 26 10
14 17 20
1
and took less than 1/10 of a second.
```
## Ruby
This solution uses HLPsolver from [[Solve_a_Hidato_puzzle#With_Warnsdorff | here]]
```ruby
require 'HLPsolver'
ADJACENT = [[-3, 0], [0, -3], [0, 3], [3, 0], [-2, -2], [-2, 2], [2, -2], [2, 2]]
board1 = <=0}]
}
}
if {![info exist start]} {
return -code error "no starting position found"
}
}
method moves {} {
return {
0 -3
-2 -2 -2 2
-3 0 3 0
-2 2 2 2
0 3
}
}
method Moves {g r c} {
set valid {}
foreach {dr dc} [my moves] {
set R [expr {$r + $dr}]
set C [expr {$c + $dc}]
if {[lindex $g $R $C] == 0} {
lappend valid $R $C
}
}
return $valid
}
method Solve {g r c v} {
lset g $r $c [incr v]
if {$v >= $limit} {return $g}
foreach {r c} [my Moves $g $r $c] {
return [my Solve $g $r $c $v]
}
return -code continue
}
method solve {} {
while {[incr i]==1} {
set grid [my Solve $grid {*}$start 0]
return
}
return -code error "solution not possible"
}
method solution {} {return $grid}
}
proc parsePuzzle {str} {
foreach line [split $str "\n"] {
if {[string trim $line] eq ""} continue
lappend rows [lmap {- c} [regexp -all -inline {(.)\s?} $line] {
string map {" " -1 "." -1} $c
}]
}
set len [tcl::mathfunc::max {*}[lmap r $rows {llength $r}]]
for {set i 0} {$i < [llength $rows]} {incr i} {
while {[llength [lindex $rows $i]] < $len} {
lset rows $i end+1 -1
}
}
return $rows
}
proc showPuzzle {grid name} {
foreach row $grid {foreach cell $row {incr c [expr {$cell>=0}]}}
set len [string length $c]
set u [string repeat "_" $len]
puts "$name with $c cells"
foreach row $grid {
puts [format " %s" [join [lmap c $row {
format "%*s" $len [if {$c==-1} list elseif {$c==0} {set u} {set c}]
}]]]
}
}
set puzzle [parsePuzzle {
. 0 0 . 0 0 .
0 0 0 0 0 0 0
0 0 0 0 0 0 0
. 0 0 0 0 0 .
. . 0 0 0 . .
. . . 1 . . .
}]
showPuzzle $puzzle "Input"
HopidoSolver create hop $puzzle
hop solve
showPuzzle [hop solution] "Output"
```
{{out}}
```txt
Input with 27 cells
__ __ __ __
__ __ __ __ __ __ __
__ __ __ __ __ __ __
__ __ __ __ __
__ __ __
1
Output with 27 cells
3 6 23 7
27 11 14 26 10 13 25
5 17 20 4 16 19 22
2 9 12 24 8
15 18 21
1
```
## zkl
This solution uses the code from [[Solve_a_Numbrix_puzzle#zkl]]
```zkl
hi:= // 0==empty cell, X==not a cell
#<<<
" X 0 0 X 0 0 X
0 0 0 0 0 0 0
0 0 0 0 0 0 0
X 0 0 0 0 0 X
X X 0 0 0 X X
X X X 0 X X X";
#<<<
adjacent:=T( T(-3,0),
T(-2,-2), T(-2,2),
T(0,-3), T(0,3),
T(2,-2), T(2,2),
T(3,0) );
puzzle:=Puzzle(hi,adjacent);
puzzle.print_board();
puzzle.solve();
println();
puzzle.print_board();
println();
```
{{out}}
```txt
Number of cells = 27
__ __ __ __
__ __ __ __ __ __ __
__ __ __ __ __ __ __
__ __ __ __ __
__ __ __
__
1 8 2 9
12 24 21 13 25 22 14
19 6 3 18 7 4 27
16 11 23 15 10
20 5 26
17
```
[[Category:Puzzles]]