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Commit f460e32

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florist-notessoubh1k
authored andcommitted
Backtrack Problems (#87)
* BackTracking Implementation * _knights tour_ will PR this later * delete_knightsTour * Delete Sudoku.cpp * Delete nQueen.cpp * Backtrack
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// A Backtracking program in C++ to solve Sudoku problem
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#include <stdio.h>
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// UNASSIGNED is used for empty cells in sudoku grid
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#define UNASSIGNED 0
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// N is used for size of Sudoku grid. Size will be NxN
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#define N 9
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// This function finds an entry in grid that is still unassigned
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bool FindUnassignedLocation(int grid[N][N], int &row, int &col);
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// Checks whether it will be legal to assign num to the given row,col
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bool isSafe(int grid[N][N], int row, int col, int num);
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/* Takes a partially filled-in grid and attempts to assign values to
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all unassigned locations in such a way to meet the requirements
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for Sudoku solution (non-duplication across rows, columns, and boxes) */
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bool SolveSudoku(int grid[N][N])
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{
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int row, col;
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// If there is no unassigned location, we are done
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if (!FindUnassignedLocation(grid, row, col))
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return true; // success!
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// consider digits 1 to 9
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for (int num = 1; num <= 9; num++)
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{
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// if looks promising
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if (isSafe(grid, row, col, num))
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{
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// make tentative assignment
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grid[row][col] = num;
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// return, if success, yay!
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if (SolveSudoku(grid))
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return true;
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// failure, unmake & try again
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grid[row][col] = UNASSIGNED;
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}
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}
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return false; // this triggers backtracking
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}
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/* Searches the grid to find an entry that is still unassigned. If
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found, the reference parameters row, col will be set the location
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that is unassigned, and true is returned. If no unassigned entries
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remain, false is returned. */
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bool FindUnassignedLocation(int grid[N][N], int &row, int &col)
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{
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for (row = 0; row < N; row++)
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for (col = 0; col < N; col++)
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if (grid[row][col] == UNASSIGNED)
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return true;
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return false;
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}
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/* Returns a boolean which indicates whether any assigned entry
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in the specified row matches the given number. */
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bool UsedInRow(int grid[N][N], int row, int num)
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{
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for (int col = 0; col < N; col++)
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if (grid[row][col] == num)
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return true;
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return false;
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}
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/* Returns a boolean which indicates whether any assigned entry
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in the specified column matches the given number. */
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bool UsedInCol(int grid[N][N], int col, int num)
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{
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for (int row = 0; row < N; row++)
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if (grid[row][col] == num)
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return true;
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return false;
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}
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/* Returns a boolean which indicates whether any assigned entry
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within the specified 3x3 box matches the given number. */
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bool UsedInBox(int grid[N][N], int boxStartRow, int boxStartCol, int num)
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{
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for (int row = 0; row < 3; row++)
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for (int col = 0; col < 3; col++)
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if (grid[row+boxStartRow][col+boxStartCol] == num)
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return true;
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return false;
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}
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/* Returns a boolean which indicates whether it will be legal to assign
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num to the given row,col location. */
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bool isSafe(int grid[N][N], int row, int col, int num)
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{
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/* Check if 'num' is not already placed in current row,
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current column and current 3x3 box */
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return !UsedInRow(grid, row, num) &&
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!UsedInCol(grid, col, num) &&
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!UsedInBox(grid, row - row%3 , col - col%3, num);
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}
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/* A utility function to print grid */
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void printGrid(int grid[N][N])
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{
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for (int row = 0; row < N; row++)
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{
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for (int col = 0; col < N; col++)
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printf("%2d", grid[row][col]);
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printf("\n");
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}
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}
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/* Driver Program to test above functions */
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int main()
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{
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// 0 means unassigned cells
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int grid[N][N] = {{3, 0, 6, 5, 0, 8, 4, 0, 0},
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{5, 2, 0, 0, 0, 0, 0, 0, 0},
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{0, 8, 7, 0, 0, 0, 0, 3, 1},
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{0, 0, 3, 0, 1, 0, 0, 8, 0},
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{9, 0, 0, 8, 6, 3, 0, 0, 5},
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{0, 5, 0, 0, 9, 0, 6, 0, 0},
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{1, 3, 0, 0, 0, 0, 2, 5, 0},
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{0, 0, 0, 0, 0, 0, 0, 7, 4},
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{0, 0, 5, 2, 0, 6, 3, 0, 0}};
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if (SolveSudoku(grid) == true)
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printGrid(grid);
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else
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printf("No solution exists");
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return 0;
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}
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/* C/C++ program to solve N Queen Problem using backtracking */
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#define N 4
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#include<stdio.h>
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/* A utility function to print solution */
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void printSolution(int board[N][N])
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{
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for (int i = 0; i < N; i++)
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{
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for (int j = 0; j < N; j++)
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printf(" %d ", board[i][j]);
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printf("\n");
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}
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}
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/* A utility function to check if a queen can
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be placed on board[row][col]. Note that this
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function is called when "col" queens are
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already placed in columns from 0 to col -1.
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So we need to check only left side for
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attacking queens */
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bool isSafe(int board[N][N], int row, int col)
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{
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int i, j;
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/* Check this row on left side */
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for (i = 0; i < col; i++)
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if (board[row][i])
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return false;
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/* Check upper diagonal on left side */
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for (i=row, j=col; i>=0 && j>=0; i--, j--)
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if (board[i][j])
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return false;
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/* Check lower diagonal on left side */
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for (i=row, j=col; j>=0 && i<N; i++, j--)
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if (board[i][j])
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return false;
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return true;
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}
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/* A recursive utility function to solve N Queen problem */
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bool solveNQUtil(int board[N][N], int col)
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{
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/* base case: If all queens are placed then return true */
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if (col >= N)
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return true;
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/* Consider this column and try placing this queen in all rows one by one */
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for (int i = 0; i < N; i++)
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{
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/* Check if queen can be placed on board[i][col] */
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if ( isSafe(board, i, col) )
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{
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/* Place this queen in board[i][col] */
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board[i][col] = 1;
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/* recur to place rest of the queens */
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if ( solveNQUtil(board, col + 1) )
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return true;
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/* If placing queen in board[i][col] doesn't lead to a solution, then remove queen from board[i][col] */
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board[i][col] = 0; // BACKTRACK
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}
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}
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/* If queen can not be place in any row in this colum col then return false */
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return false;
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}
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/* This function solves the N Queen problem using
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Backtracking. It mainly uses solveNQUtil() to
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solve the problem. It returns false if queens
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cannot be placed, otherwise return true and
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prints placement of queens in the form of 1s.
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Please note that there may be more than one
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solutions, this function prints one of the
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feasible solutions.*/
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bool solveNQ()
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{
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int board[N][N] = { {0, 0, 0, 0},
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{0, 0, 0, 0},
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{0, 0, 0, 0},
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{0, 0, 0, 0}
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};
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if ( solveNQUtil(board, 0) == false )
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{
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printf("Solution does not exist");
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return false;
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}
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printSolution(board);
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return true;
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}
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// driver program to test above function
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int main()
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{
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solveNQ();
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return 0;
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}

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