dimanche 26 janvier 2020

getting difficulty while tracing this N queen problem code

I am new to Backtracking technique of solving problems,while learning N-queen problem i am unable to recognize what "if(board[row][i])" in issafe() function is returning. I mean after first loop in "bool solveNQUtil(int board[N][N], int col)" function the value of i and col become 0 and passed to "issafe()" to check if a queen can be placed on board[row][col]. Now in issafe() function i am unable to understand what is rest condition in which basis if statements and returning true or false. I really appreciate your help,Your kind words warmed my heart.. Thank you.

bool isSafe(int board[N][N], int row, int col) 
{ 
    int i, j; 

    /* Check this row on left side */
    for (i = 0; i < col; i++) 
        if (board[row][i]) 
            return false; 

    /* Check upper diagonal on left side */
    for (i = row, j = col; i >= 0 && j >= 0; i--, j--) 
        if (board[i][j]) 
            return false; 

    /* Check lower diagonal on left side */
    for (i = row, j = col; j >= 0 && i < N; i++, j--) 
        if (board[i][j]) 
            return false; 

    return true; 
} 



bool solveNQUtil(int board[N][N], int col) 
{ 
    /* base case: If all queens are placed 
      then return true */
    if (col >= N) 
        return true; 

    /* Consider this column and try placing 
       this queen in all rows one by one */
    for (int i = 0; i < N; i++) { 
        /* Check if the queen can be placed on 
          board[i][col] */
        if (isSafe(board, i, col)) { 
            /* Place this queen in board[i][col] */
            board[i][col] = 1; 

            /* recur to place rest of the queens */
            if (solveNQUtil(board, col + 1)) 
                return true; 

            /* If placing queen in board[i][col] 
               doesn't lead to a solution, then 
               remove queen from board[i][col] */
            board[i][col] = 0; // BACKTRACK 
        } 
    } 

    /* If the queen cannot be placed in any row in 
        this colum col  then return false */
    return false; 
} 


/* This function solves the N Queen problem using 
   Backtracking. It mainly uses solveNQUtil() to  
   solve the problem. It returns false if queens 
   cannot be placed, otherwise, return true and 
   prints placement of queens in the form of 1s. 
   Please note that there may be more than one 
   solutions, this function prints one  of the 
   feasible solutions.*/
bool solveNQ() 
{ 
    int board[N][N] = { { 0, 0, 0, 0 }, 
                        { 0, 0, 0, 0 }, 
                        { 0, 0, 0, 0 }, 
                        { 0, 0, 0, 0 } }; 

    if (solveNQUtil(board, 0) == false) { 
        printf("Solution does not exist"); 
        return false; 
    } 

    printSolution(board); 
    return true; 
} 

// driver program to test above function 
int main() 
{ 
    solveNQ(); 
    return 0; 
} 

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