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NQueenProblem.java(file created)
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| 1 | + | // Java program to solve N Queen Problem using backtracking | |
| 2 | + | ||
| 3 | + | public class NQueenProblem { | |
| 4 | + | final int N = 4; | |
| 5 | + | ||
| 6 | + | // A utility function to print solution | |
| 7 | + | void printSolution(int board[][]) | |
| 8 | + | { | |
| 9 | + | for (int i = 0; i < N; i++) { | |
| 10 | + | for (int j = 0; j < N; j++) { | |
| 11 | + | if (board[i][j] == 1) | |
| 12 | + | System.out.print("Q "); | |
| 13 | + | else | |
| 14 | + | System.out.print(". "); | |
| 15 | + | } | |
| 16 | + | System.out.println(); | |
| 17 | + | } | |
| 18 | + | } | |
| 19 | + | ||
| 20 | + | // A utility function to check if a queen can | |
| 21 | + | // be placed on board[row][col]. Note that this | |
| 22 | + | // function is called when "col" queens are already | |
| 23 | + | // placeed in columns from 0 to col -1. So we need | |
| 24 | + | // to check only left side for attacking queens | |
| 25 | + | boolean isSafe(int board[][], int row, int col) | |
| 26 | + | { | |
| 27 | + | int i, j; | |
| 28 | + | ||
| 29 | + | // Check this row on left side | |
| 30 | + | for (i = 0; i < col; i++) | |
| 31 | + | if (board[row][i] == 1) | |
| 32 | + | return false; | |
| 33 | + | ||
| 34 | + | // Check upper diagonal on left side | |
| 35 | + | for (i = row, j = col; i >= 0 && j >= 0; i--, j--) | |
| 36 | + | if (board[i][j] == 1) | |
| 37 | + | return false; | |
| 38 | + | ||
| 39 | + | // Check lower diagonal on left side | |
| 40 | + | for (i = row, j = col; j >= 0 && i < N; i++, j--) | |
| 41 | + | if (board[i][j] == 1) | |
| 42 | + | return false; | |
| 43 | + | ||
| 44 | + | return true; | |
| 45 | + | } | |
| 46 | + | ||
| 47 | + | // A recursive utility function to solve N | |
| 48 | + | // Queen problem | |
| 49 | + | boolean solveNQUtil(int board[][], int col) | |
| 50 | + | { | |
| 51 | + | // Base case: If all queens are placed | |
| 52 | + | // then return true | |
| 53 | + | if (col >= N) | |
| 54 | + | return true; | |
| 55 | + | ||
| 56 | + | // Consider this column and try placing | |
| 57 | + | // this queen in all rows one by one | |
| 58 | + | for (int i = 0; i < N; i++) { | |
| 59 | + | ||
| 60 | + | // Check if the queen can be placed on | |
| 61 | + | // board[i][col] | |
| 62 | + | if (isSafe(board, i, col)) { | |
| 63 | + | ||
| 64 | + | // Place this queen in board[i][col] | |
| 65 | + | board[i][col] = 1; | |
| 66 | + | ||
| 67 | + | // Recur to place rest of the queens | |
| 68 | + | if (solveNQUtil(board, col + 1) == true) | |
| 69 | + | return true; | |
| 70 | + | ||
| 71 | + | // If placing queen in board[i][col] | |
| 72 | + | // doesn't lead to a solution then | |
| 73 | + | // remove queen from board[i][col] | |
| 74 | + | board[i][col] = 0; // BACKTRACK | |
| 75 | + | } | |
| 76 | + | } | |
| 77 | + | ||
| 78 | + | // If the queen can not be placed in any row in | |
| 79 | + | // this column col, then return false | |
| 80 | + | return false; | |
| 81 | + | } | |
| 82 | + | ||
| 83 | + | // This function solves the N Queen problem using | |
| 84 | + | // Backtracking. It mainly uses solveNQUtil () to | |
| 85 | + | // solve the problem. It returns false if queens | |
| 86 | + | // cannot be placed, otherwise, return true and | |
| 87 | + | // prints placement of queens in the form of 1s. | |
| 88 | + | // Please note that there may be more than one | |
| 89 | + | // solutions, this function prints one of the | |
| 90 | + | // feasible solutions. | |
| 91 | + | boolean solveNQ() | |
| 92 | + | { | |
| 93 | + | int board[][] = { { 0, 0, 0, 0 }, | |
| 94 | + | { 0, 0, 0, 0 }, | |
| 95 | + | { 0, 0, 0, 0 }, | |
| 96 | + | { 0, 0, 0, 0 } }; | |
| 97 | + | ||
| 98 | + | if (solveNQUtil(board, 0) == false) { | |
| 99 | + | System.out.print("Solution does not exist"); | |
| 100 | + | return false; | |
| 101 | + | } | |
| 102 | + | ||
| 103 | + | printSolution(board); | |
| 104 | + | return true; | |
| 105 | + | } | |
| 106 | + | ||
| 107 | + | // Driver program to test above function | |
| 108 | + | public static void main(String args[]) | |
| 109 | + | { | |
| 110 | + | NQueenProblem Queen = new NQueenProblem(); | |
| 111 | + | Queen.solveNQ(); | |
| 112 | + | } | |
| 113 | + | } | |
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