Magnet Puzzle
We are given a set of bipolar magnets, each domino-shaped. The objective is to place magnets on an M × N board, which satisfies a set of conditions where both M and N are not odd.
For instance, the following problem has the solution on its right:
Each 2 × 1 or 1 × 2 grid in the board can contain a magnet or empty. The blank entry will be indicated by X's, and the magnet will be represented by + and - (For the positive and negative end, respectively). The digits along the board’s left and top sides represent the count of + squares in corresponding rows or columns. Similarly, those along the right and bottom show the total number of - signs in particular rows or columns. Rows and columns for which no number is mentioned can have any number of + or - signs. The puzzle solution must also satisfy the constraint that no two adjacent squares can have the same sign. But diagonally joined squares can have the same sign.
Examples:
Here, top[], bottom[], left[], right[] arrays indicates the count of + or - along the top (+), bottom (-), left (+), and right (-) edges, respectively. The value of -1 indicate any number of + or - signs.
The rules[][] matrix can contain any T, B, L, or R character. T indicates its top end for a vertical slot in the board, and B indicates the bottom end. L indicates the left end, and R indicates the right end for a horizontal slot in the board.
Input:
top[] = [1, -1, -1, 2, 1, -1]
bottom[] = [2, -1, -1, 2, -1, 3]
left[] = [2, 3, -1, -1, -1]
right[] = [-1, -1, -1, 1, -1]
Rules[][] =
[L R L R T T]
[L R L R B B]
[T T T T L R]
[B B B B T T]
[L R L R B B]
Output:
+ – + – X –
– + – + X +
X X + – + –
X X – + X +
– + X X X –
Input:
top[] = [2, -1, -1]
bottom[] = [-1, -1, 2]
left[] = [-1, -1, 2, -1]
right[] = [0, -1, -1, -1]
Rules[][] =
[T T T]
[B B B]
[T L R]
[B L R]
Output:
+ X +
– X –
+ – +
– + –
top[] = [1, -1, -1, 2, 1, -1]
bottom[] = [2, -1, -1, 2, -1, 3]
left[] = [2, 3, -1, -1, -1]
right[] = [-1, -1, -1, 1, -1]
Rules[][] =
[L R L R T T]
[L R L R B B]
[T T T T L R]
[B B B B T T]
[L R L R B B]
Output:
+ – + – X –
– + – + X +
X X + – + –
X X – + X +
– + X X X –
Input:
top[] = [2, -1, -1]
bottom[] = [-1, -1, 2]
left[] = [-1, -1, 2, -1]
right[] = [0, -1, -1, -1]
Rules[][] =
[T T T]
[B B B]
[T L R]
[B L R]
Output:
+ X +
– X –
+ – +
– + –
The idea is to use backtracking. We start from the first cell of the rules matrix and check for every horizontal and vertical slot. If the horizontal or vertical slot contains L and R or T and B, respectively, put ('+', '-') or ('-', '+') accordingly in the slot and recursively checks if they lead to the solution or not. If the solution is found with the required configuration, print the solution matrix; if none of the above solutions work, return false from the function.
Following is the C++, Java, and Python implementation of the idea:
C++
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 |
#include <iostream> using namespace std; // `M × N` matrix #define M 5 #define N 6 // Utility function to print solution void printSolution(char board[M][N]) { for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) { cout << board[i][j] << " "; } cout << endl; } } // Utility function to count the total number of characters `ch` in current column `j` int countInColumns(char board[N][N], char ch, int j) { int count = 0; for (int i = 0; i < M; i++) { if (board[i][j] == ch) { count++; } } return count; } // Utility function to count the total number of characters `ch` in current row `i` int countInRow(char board[N][N], char ch, int i) { int count = 0; for (int j = 0; j < N; j++) { if (board[i][j] == ch) { count++; } } return count; } // Function to check if it is safe to put `ch` at `board[row][col]` bool isSafe(char board[N][N], int row, int col, char ch, int top[], int left[], int bottom[], int right[]) { // check for adjacent cells if ((row - 1 >= 0 && board[row - 1][col] == ch) || (col + 1 < N && board[row][col + 1] == ch) || (row + 1 < M && board[row + 1][col] == ch) || (col - 1 >= 0 && board[row][col - 1] == ch)) { return false; } // count character `ch` in the current row int rowCount = countInRow(board, ch, row); // count character `ch` in the current column int colCount = countInColumns(board, ch, col); // if the given character is `+`, check `top[]` and `left[]` if (ch == '+') { // check top if (top[col] != -1 && colCount >= top[col]) { return false; } // check left if (left[row] != -1 && rowCount >= left[row]) { return false; } } // if the given character is `-`, check `bottom[]` and `right[]` if (ch == '-') { // check bottom if (bottom[col] != -1 && colCount >= bottom[col]) { return false; } // check left if (right[row] != -1 && rowCount >= right[row]) { return false; } } return true; } // Function to validate the configuration of an output board bool validateConfiguration(char board[N][N], int top[], int left[], int bottom[], int right[]) { // check top for (int i = 0; i < N; i++) { if (top[i] != -1 && countInColumns(board, '+', i) != top[i]) { return false; } } // check left for (int j = 0; j < M; j++) { if (left[j] != -1 && countInRow(board, '+', j) != left[j]) { return false; } } // check bottom for (int i = 0; i < N; i++) { if (bottom[i] != -1 && countInColumns(board, '-', i) != bottom[i]) { return false; } } // check right for (int j = 0; j < M; j++) { if (right[j] != -1 && countInRow(board, '-', j) != right[j]) { return false; } } return true; } // The main function to solve the Bipolar Magnets puzzle bool solveMagnetPuzzle(char board[N][N], int row, int col, int top[], int left[], int bottom[], int right[], char rules[M][N]) { // if the last cell is reached if (row >= M - 1 && col >= N - 1) { if (validateConfiguration(board, top, left, bottom, right)) { return true; } return false; } // if the last column of the current row is already processed, // go to the next row, the first column if (col >= N) { col = 0; row = row + 1; } // if the current cell contains `R` or `B` (end of horizontal // or vertical slot), recur for the next cell if (rules[row][col] == 'R' || rules[row][col] == 'B') { if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } } // if horizontal slot contains `L` and `R` if (rules[row][col] == 'L' && rules[row][col + 1] == 'R') { // put (`+`, `-`) pair and recur if (isSafe(board, row, col, '+', top, left, bottom, right) && isSafe(board, row, col + 1, '-', top, left, bottom, right)) { board[row][col] = '+'; board[row][col + 1] = '-'; if (solveMagnetPuzzle(board, row, col + 2, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row][col + 1] = 'X'; } // put (`-`, `+`) pair and recur if (isSafe(board, row, col, '-', top, left, bottom, right) && isSafe(board, row, col + 1, '+', top, left, bottom, right)) { board[row][col] = '-'; board[row][col + 1] = '+'; if (solveMagnetPuzzle(board, row, col + 2, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row][col + 1] = 'X'; } } // if vertical slot contains `T` and `B` if (rules[row][col] == 'T' && rules[row + 1][col] == 'B') { // put (`+`, `-`) pair and recur if (isSafe(board, row, col, '+', top, left, bottom, right) && isSafe(board, row + 1, col, '-', top, left, bottom, right)) { board[row][col] = '+'; board[row + 1][col] = '-'; if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row + 1][col] = 'X'; } // put (`-`, `+`) pair and recur if (isSafe(board, row, col, '-', top, left, bottom, right) && isSafe(board, row + 1, col, '+', top, left, bottom, right)) { board[row][col] = '-'; board[row + 1][col] = '+'; if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row + 1][col] = 'X'; } } // ignore the current cell and recur if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } // if no solution is possible, return false return false; } void solveMagnetPuzzle(int top[], int left[], int bottom[], int right[], char rules[M][N]) { // to store the result char board[M][N]; // initialize all cells by `X` for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) { board[i][j] = 'X'; } } // start from `(0, 0)` cell if (!solveMagnetPuzzle(board, 0, 0, top, left, bottom, right, rules)) { cout << "Solution does not exist"; return; } // print result if the given configuration is solvable printSolution(board); } int main() { // indicates the count of `+` or `-` along the top (+), bottom (-), // left (+), and right (-) edges, respectively. // Value of -1 indicate any number of `+` or `-` signs int top[N] = { 1, -1, -1, 2, 1, -1 }; int bottom[N] = { 2, -1, -1, 2, -1, 3 }; int left[M] = { 2, 3, -1, -1, -1 }; int right[M] = { -1, -1, -1, 1, -1 }; // rules matrix char rules[M][N] = { { 'L', 'R', 'L', 'R', 'T', 'T' }, { 'L', 'R', 'L', 'R', 'B', 'B' }, { 'T', 'T', 'T', 'T', 'L', 'R' }, { 'B', 'B', 'B', 'B', 'T', 'T' }, { 'L', 'R', 'L', 'R', 'B', 'B' } }; solveMagnetPuzzle(top, left, bottom, right, rules); return 0; } |
Java
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 |
import java.util.Arrays; class Main { // `M × N` matrix private static final int M = 5; private static final int N = 6; // Utility function to print solution private static void printSolution(char[][] board) { for (var r: board) { System.out.println(Arrays.toString(r)); } } // Utility function to count the total number of characters `ch` in // current column `j` private static int countInColumns(char[][] board, char ch, int j) { int count = 0; for (int i = 0; i < M; i++) { if (board[i][j] == ch) { count++; } } return count; } // Utility function to count the total number of characters `ch` in // current row `i` private static int countInRow(char[][] board, char ch, int i) { int count = 0; for (int j = 0; j < N; j++) { if (board[i][j] == ch) { count++; } } return count; } // Function to check if it is safe to put `ch` at `board[row][col]` private static boolean isSafe(char[][] board, int row, int col, char ch, int[] top, int[] left, int[] bottom, int[] right) { // check for adjacent cells if ((row - 1 >= 0 && board[row - 1][col] == ch) || (col + 1 < N && board[row][col + 1] == ch) || (row + 1 < M && board[row + 1][col] == ch) || (col - 1 >= 0 && board[row][col - 1] == ch)) { return false; } // count character `ch` in the current row int rowCount = countInRow(board, ch, row); // count character `ch` in the current column int colCount = countInColumns(board, ch, col); // if the given character is `+`, check `top[]` and `left[]` if (ch == '+') { // check top if (top[col] != -1 && colCount >= top[col]) { return false; } // check left if (left[row] != -1 && rowCount >= left[row]) { return false; } } // if the given character is `-`, check `bottom[]` and `right[]` if (ch == '-') { // check bottom if (bottom[col] != -1 && colCount >= bottom[col]) { return false; } // check left if (right[row] != -1 && rowCount >= right[row]) { return false; } } return true; } // Function to validate the configuration of an output board private static boolean validateConfiguration(char[][] board, int[] top, int[] left, int[] bottom, int[] right) { // check top for (int i = 0; i < N; i++) { if (top[i] != -1 && countInColumns(board, '+', i) != top[i]) { return false; } } // check left for (int j = 0; j < M; j++) { if (left[j] != -1 && countInRow(board, '+', j) != left[j]) { return false; } } // check bottom for (int i = 0; i < N; i++) { if (bottom[i] != -1 && countInColumns(board, '-', i) != bottom[i]) { return false; } } // check right for (int j = 0; j < M; j++) { if (right[j] != -1 && countInRow(board, '-', j) != right[j]) { return false; } } return true; } // The main function to solve the Bipolar Magnets puzzle private static boolean solveMagnetPuzzle(char[][] board, int row, int col, int[] top, int[] left, int[] bottom, int[] right, char[][] rules) { // if the last cell is reached if (row >= M - 1 && col >= N - 1) { return validateConfiguration(board, top, left, bottom, right); } // if the last column of the current row is already processed, // go to the next row, the first column if (col >= N) { col = 0; row = row + 1; } // if the current cell contains `R` or `B` (end of horizontal // or vertical slot), recur for the next cell if (rules[row][col] == 'R' || rules[row][col] == 'B') { if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } } // if horizontal slot contains `L` and `R` if (rules[row][col] == 'L' && rules[row][col + 1] == 'R') { // put (`+`, `-`) pair and recur if (isSafe(board, row, col, '+', top, left, bottom, right) && isSafe(board, row, col + 1, '-', top, left, bottom, right)) { board[row][col] = '+'; board[row][col + 1] = '-'; if (solveMagnetPuzzle(board, row, col + 2, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row][col + 1] = 'X'; } // put (`-`, `+`) pair and recur if (isSafe(board, row, col, '-', top, left, bottom, right) && isSafe(board, row, col + 1, '+', top, left, bottom, right)) { board[row][col] = '-'; board[row][col + 1] = '+'; if (solveMagnetPuzzle(board, row, col + 2, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row][col + 1] = 'X'; } } // if vertical slot contains `T` and `B` if (rules[row][col] == 'T' && rules[row + 1][col] == 'B') { // put (`+`, `-`) pair and recur if (isSafe(board, row, col, '+', top, left, bottom, right) && isSafe(board, row + 1, col, '-', top, left, bottom, right)) { board[row][col] = '+'; board[row + 1][col] = '-'; if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row + 1][col] = 'X'; } // put (`-`, `+`) pair and recur if (isSafe(board, row, col, '-', top, left, bottom, right) && isSafe(board, row + 1, col, '+', top, left, bottom, right)) { board[row][col] = '-'; board[row + 1][col] = '+'; if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } // if it doesn't lead to a solution, backtrack board[row][col] = 'X'; board[row + 1][col] = 'X'; } } // ignore the current cell and recur if (solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules)) { return true; } // if no solution is possible, return false return false; } public static void solveMagnetPuzzle(int[] top, int[] left, int[] bottom, int[] right, char[][] rules) { // to store the result char[][] board = new char[M][N]; // initialize all cells by `X` for (int i = 0; i < M; i++) { Arrays.fill(board[i], 'X'); } // start from `(0, 0)` cell if (!solveMagnetPuzzle(board, 0, 0, top, left, bottom, right, rules)) { System.out.println("Solution does not exist"); return; } // print result if the given configuration is solvable printSolution(board); } public static void main(String[] args) { // indicates the count of `+` or `-` along the top (+), bottom (-), // left (+), and right (-) edges, respectively. // value of -1 indicate any number of `+` or `-` signs final int[] top = { 1, -1, -1, 2, 1, -1 }; final int[] bottom = { 2, -1, -1, 2, -1, 3 }; final int[] left = { 2, 3, -1, -1, -1 }; final int[] right = { -1, -1, -1, 1, -1 }; // rules matrix char[][] rules = { { 'L', 'R', 'L', 'R', 'T', 'T' }, { 'L', 'R', 'L', 'R', 'B', 'B' }, { 'T', 'T', 'T', 'T', 'L', 'R' }, { 'B', 'B', 'B', 'B', 'T', 'T' }, { 'L', 'R', 'L', 'R', 'B', 'B' } }; solveMagnetPuzzle(top, left, bottom, right, rules); } } |
Python
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 |
# Utility function to print solution def printSolution(board): for i in range(M): for j in range(N): print(board[i][j], end=' ') print() # Utility function to count the total number of characters `ch` in current column `j` def countInColumns(board, ch, j): count = 0 for i in range(M): if board[i][j] == ch: count = count + 1 return count # Utility function to count the total number of characters `ch` in current row `i` def countInRow(board, ch, i): count = 0 for j in range(N): if board[i][j] == ch: count = count + 1 return count # Function to check if it is safe to put `ch` at `board[row][col]` def isSafe(board, row, col, ch, top, left, bottom, right): # check for adjacent cells if ((row - 1 >= 0 and board[row - 1][col] == ch) or (col + 1 < N and board[row][col + 1] == ch) or (row + 1 < M and board[row + 1][col] == ch) or (col - 1 >= 0 and board[row][col - 1] == ch)): return False # count character `ch` in the current row rowCount = countInRow(board, ch, row) # count character `ch` in the current column colCount = countInColumns(board, ch, col) # if the given character is `+`, check `top[]` and `left[]` if ch == '+': # check top if top[col] != -1 and colCount >= top[col]: return False # check left if left[row] != -1 and rowCount >= left[row]: return False # if the given character is `-`, check `bottom[]` and `right[]` if ch == '-': # check bottom if bottom[col] != -1 and colCount >= bottom[col]: return False # check left if right[row] != -1 and rowCount >= right[row]: return False return True # Function to validate the configuration of an output board def validateConfiguration(board, top, left, bottom, right): # check top for i in range(N): if top[i] != -1 and countInColumns(board, '+', i) != top[i]: return False # check left for j in range(M): if left[j] != -1 and countInRow(board, '+', j) != left[j]: return False # check bottom for i in range(N): if bottom[i] != -1 and countInColumns(board, '-', i) != bottom[i]: return False # check right for j in range(M): if right[j] != -1 and countInRow(board, '-', j) != right[j]: return False return True # The main function to solve the Bipolar Magnets puzzle def solveMagnetPuzzle(board, row, col, top, left, bottom, right, rules): # if the last cell is reached if row >= M - 1 and col >= N - 1: return validateConfiguration(board, top, left, bottom, right) # if the last column of the current row is already processed, # go to the next row, the first column if col >= N: col = 0 row = row + 1 # if the current cell contains `R` or `B` (end of horizontal # or vertical slot), recur for the next cell if rules[row][col] == 'R' or rules[row][col] == 'B': if solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules): return True # if the horizontal slot contains `L` and `R` if rules[row][col] == 'L' and rules[row][col + 1] == 'R': # put (`+`, `-`) pair and recur if (isSafe(board, row, col, '+', top, left, bottom, right) and isSafe(board, row, col + 1, '-', top, left, bottom, right)): board[row][col] = '+' board[row][col + 1] = '-' if solveMagnetPuzzle(board, row, col + 2, top, left, bottom, right, rules): return True # if it doesn't lead to a solution, backtrack board[row][col] = 'X' board[row][col + 1] = 'X' # put (`-`, `+`) pair and recur if (isSafe(board, row, col, '-', top, left, bottom, right) and isSafe(board, row, col + 1, '+', top, left, bottom, right)): board[row][col] = '-' board[row][col + 1] = '+' if solveMagnetPuzzle(board, row, col + 2, top, left, bottom, right, rules): return True # if it doesn't lead to a solution, backtrack board[row][col] = 'X' board[row][col + 1] = 'X' # if the vertical slot contains `T` and `B` if rules[row][col] == 'T' and rules[row + 1][col] == 'B': # put (`+`, `-`) pair and recur if (isSafe(board, row, col, '+', top, left, bottom, right) and isSafe(board, row + 1, col, '-', top, left, bottom, right)): board[row][col] = '+' board[row + 1][col] = '-' if solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules): return True # if it doesn't lead to a solution, backtrack board[row][col] = 'X' board[row + 1][col] = 'X' # put (`-`, `+`) pair and recur if (isSafe(board, row, col, '-', top, left, bottom, right) and isSafe(board, row + 1, col, '+', top, left, bottom, right)): board[row][col] = '-' board[row + 1][col] = '+' if solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules): return True # if it doesn't lead to a solution, backtrack board[row][col] = 'X' board[row + 1][col] = 'X' # ignore the current cell and recur if solveMagnetPuzzle(board, row, col + 1, top, left, bottom, right, rules): return True # if no solution is possible, return false return False def magnetPuzzle(top, left, bottom, right, rules): # to store the result # initialize all cells by `X` board = [['X' for x in range(N)] for y in range(M)] # start from `(0, 0)` cell if not solveMagnetPuzzle(board, 0, 0, top, left, bottom, right, rules): print("Solution does not exist") return # print result if the given configuration is solvable printSolution(board) if __name__ == '__main__': # indicates the count of `+` or `-` along the top (+), bottom (-), # left (+), and right (-) edges, respectively. # value of -1 indicate any number of `+` or `-` signs top = [1, -1, -1, 2, 1, -1] bottom = [2, -1, -1, 2, -1, 3] left = [2, 3, -1, -1, -1] right = [-1, -1, -1, 1, -1] # rules matrix rules = [ ['L', 'R', 'L', 'R', 'T', 'T'], ['L', 'R', 'L', 'R', 'B', 'B'], ['T', 'T', 'T', 'T', 'L', 'R'], ['B', 'B', 'B', 'B', 'T', 'T'], ['L', 'R', 'L', 'R', 'B', 'B'] ] # `M × N` matrix (M, N) = (len(rules), len(rules[0])) magnetPuzzle(top, left, bottom, right, rules) |
Output:
+ – + – X –
– + – + X +
X X + – + –
X X – + X +
– + X X X –
+ – + – X –
– + – + X +
X X + – + –
X X – + X +
– + X X X –
The time complexity of the above solution is exponential and requires additional space for the recursion (call stack).
This question is taken from – https://people.eecs.berkeley.edu/~hilfingr/programming-contest/f2012-contest.pdf
Thanks for reading.
To share your code in the comments, please use our online compiler that supports C, C++, Java, Python, JavaScript, C#, PHP, and many more popular programming languages.
Like us? Refer us to your friends and support our growth. Happy coding :)