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Task/N-queens-problem/SQL-PL/n-queens-problem.sql
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276
Task/N-queens-problem/SQL-PL/n-queens-problem.sql
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-- A column of a matrix.
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CREATE TYPE INTEGER_ARRAY AS INTEGER ARRAY[]@
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-- The whole matrix of any size.
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CREATE TYPE INTEGER_MATRIX AS INTEGER_ARRAY ARRAY[]@
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/**
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* Retrieves the value from a matrix at a specific position.
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*
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* IN X: Row number.
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* IN Y: Column number.
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* IN M: Matrix.
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* RETURN the integer value at that position.
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*/
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CREATE OR REPLACE FUNCTION GET_INTEGER_VALUE(
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IN X SMALLINT,
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IN Y SMALLINT,
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IN M INTEGER_MATRIX)
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RETURNS INTEGER
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F_GET_INTEGER_VALUE: BEGIN
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DECLARE A INTEGER_ARRAY;
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DECLARE RET INTEGER;
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SET A = M[X];
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SET RET = A[Y];
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RETURN RET;
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END F_GET_INTEGER_VALUE
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@
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/**
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* Establishes the given value at a specific position in the matrix.
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*
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* IN X: Row number.
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* IN Y: Column number.
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* INOUT M: Matrix.
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* IN VAL: Value to set in the matrix.
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*/
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CREATE OR REPLACE PROCEDURE SET_INTEGER_VALUE(
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IN X SMALLINT,
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IN Y SMALLINT,
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INOUT M INTEGER_MATRIX,
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IN VAL INTEGER)
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P_SET_INTEGER_VALUE: BEGIN
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DECLARE A INTEGER_ARRAY;
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SET A = M[X];
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SET A[Y] = VAL;
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SET M[X] = A;
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END P_SET_INTEGER_VALUE
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@
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/**
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* Initializes the matriz at a given size with the same value in all positions.
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*
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* INOUT M: Matrix.
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* IN X: Number of rows.
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* IN Y: Number of columns per row.
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* IN VAL: Value to set in the matrix.
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*/
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CREATE OR REPLACE PROCEDURE INIT_INTEGER_MATRIX(
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INOUT M INTEGER_MATRIX,
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IN X SMALLINT,
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IN Y SMALLINT,
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IN VAL INTEGER)
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P_INIT_INTEGER_MATRIX: BEGIN
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DECLARE I SMALLINT DEFAULT 1;
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DECLARE J SMALLINT;
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DECLARE A INTEGER_ARRAY;
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WHILE (I <= X) DO
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SET A = ARRAY[];
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SET J = 1;
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WHILE (J <= Y) DO
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SET A[J] = VAL;
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SET J = J + 1;
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END WHILE;
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SET M[I] = A;
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SET I = I + 1;
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END WHILE;
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END P_INIT_INTEGER_MATRIX
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@
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/**
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* Prints the content of the matrix to the standard output.
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*
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* INOUT M: Matrix.
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*/
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CREATE OR REPLACE PROCEDURE PRINT_INTEGER_MATRIX(
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IN M INTEGER_MATRIX)
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P_PRINT_INTEGER_MATRIX: BEGIN
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DECLARE I SMALLINT DEFAULT 1;
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DECLARE J SMALLINT;
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DECLARE X SMALLINT;
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DECLARE Y SMALLINT;
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DECLARE VAL INTEGER;
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DECLARE A INTEGER_ARRAY;
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DECLARE RET VARCHAR(256);
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SET X = CARDINALITY(M);
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CALL DBMS_OUTPUT.PUT_LINE('>>>>>');
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WHILE (I <= X) DO
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SET A = M[I];
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SET RET = '[';
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SET Y = CARDINALITY(A);
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SET J = 1;
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WHILE (J <= Y) DO
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SET VAL = A[J];
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SET RET = RET || VAL;
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SET J = J + 1;
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IF (J <= Y) THEN
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SET RET = RET || ',';
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END IF;
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END WHILE;
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SET RET = RET || ']';
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CALL DBMS_OUTPUT.PUT_LINE(RET);
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SET I = I + 1;
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END WHILE;
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CALL DBMS_OUTPUT.PUT_LINE('<<<<<');
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END P_PRINT_INTEGER_MATRIX
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@
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/**
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* Checks if a queen is safe in the given position.
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*
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* IN M: Matrix representing the chessboard.
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* IN ROW: Row of the queen.
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* IN COL: Column in the row for the queen.
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* IN SIZE: Size of the chessboard (max row, max col).
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* RETURNS true if the position is safe.
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*/
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CREATE OR REPLACE FUNCTION IS_SAFE(
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IN M INTEGER_MATRIX,
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IN ROW SMALLINT,
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IN COL SMALLINT,
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IN SIZE SMALLINT)
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MODIFIES SQL DATA
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RETURNS BOOLEAN
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F_IS_SAFE: BEGIN
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DECLARE I SMALLINT;
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DECLARE J SMALLINT;
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DECLARE VAL INTEGER;
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-- Debug purposes.
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--CALL SET_INTEGER_VALUE(ROW, COL, M, -1);
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--CALL PRINT_INTEGER_MATRIX(M);
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--CALL SET_INTEGER_VALUE(ROW, COL, M, 0);
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SET I = 1;
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WHILE (I <= COL) DO
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SET VAL = GET_INTEGER_VALUE(ROW, I, M);
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IF (VAL = 1) THEN
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RETURN FALSE;
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END IF;
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SET I = I + 1;
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END WHILE;
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SET I = ROW;
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SET J = COL;
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WHILE (I >= 1 AND J >= 1) DO
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SET VAL = GET_INTEGER_VALUE(I, J, M);
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IF (VAL = 1) THEN
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CALL SET_INTEGER_VALUE(ROW, COL, M, 0);
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RETURN FALSE;
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END IF;
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SET I = I - 1;
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SET J = J - 1;
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END WHILE;
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SET I = ROW;
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SET J = COL;
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WHILE (J >= 1 AND I <= SIZE) DO
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SET VAL = GET_INTEGER_VALUE(I, J, M);
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IF (VAL = 1) THEN
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RETURN FALSE;
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END IF;
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SET I = I + 1;
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SET J = J - 1;
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END WHILE;
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RETURN TRUE;
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END F_IS_SAFE
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@
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/**
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* Dummy procedure for the recurssion.
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*
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* IN SIZE: Size of the chessboard (max row, max col).
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* IN COL: Column to analyse.
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* OUT RET: True if it was possible to put all queens
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*/
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CREATE OR REPLACE PROCEDURE SOLVE_N_QUEENS(
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INOUT M INTEGER_MATRIX,
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IN SIZE SMALLINT,
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IN COL SMALLINT,
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OUT RET BOOLEAN)
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P_SOLVE_N_QUEENS: BEGIN
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END P_SOLVE_N_QUEENS
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@
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/**
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* Solves the n-queens algoritm.
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*
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* IN SIZE: Size of the chessboard (max row, max col).
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* IN COL: Column to analyse.
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* OUT RET: True if it was possible to put all queens
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*/
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CREATE OR REPLACE PROCEDURE SOLVE_N_QUEENS(
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INOUT M INTEGER_MATRIX,
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IN SIZE SMALLINT,
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IN COL SMALLINT,
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OUT RET BOOLEAN)
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MODIFIES SQL DATA
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P_SOLVE_N_QUEENS: BEGIN
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DECLARE I SMALLINT;
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DECLARE SAFE BOOLEAN;
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DECLARE SOLVED BOOLEAN;
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-- Debug purposes.
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--CALL PRINT_INTEGER_MATRIX(M);
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SET RET = FALSE;
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IF (COL > SIZE) THEN
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SET RET = TRUE;
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ELSE
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SET I = 1;
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WHILE (I <= SIZE AND NOT RET) DO
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SET SAFE = IS_SAFE(M, I, COL, SIZE);
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IF (SAFE) THEN
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CALL SET_INTEGER_VALUE(I, COL, M, 1);
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CALL SOLVE_N_QUEENS(M, SIZE, COL + 1, SOLVED);
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IF (SOLVED) THEN
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SET RET = TRUE;
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ELSE
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CALL SET_INTEGER_VALUE(I, COL, M, 0); -- Backtrack.
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END IF;
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END IF;
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SET I = I + 1;
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END WHILE;
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END IF;
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END P_SOLVE_N_QUEENS
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@
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/**
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* Main procedure to solve the n-queen algoritm.
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*
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* IN SIZE: Size of the chessboard. The bigger it is, the more time it takes.
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*/
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CREATE OR REPLACE PROCEDURE N_QUEENS(
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IN SIZE SMALLINT)
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P_N_QUEENS: BEGIN
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DECLARE M INTEGER_MATRIX;
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DECLARE SOL BOOLEAN DEFAULT FALSE;
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CALL INIT_INTEGER_MATRIX(M, SIZE, SIZE, 0);
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CALL SOLVE_N_QUEENS(M, SIZE, 1, SOL);
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IF (SOL = TRUE) THEN
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CALL PRINT_INTEGER_MATRIX(M);
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ELSE
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CALL DBMS_OUTPUT.PUT_LINE('Solution does not exist.');
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END IF;
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END P_N_QUEENS
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@
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--#SET TERMINATOR ;
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-- Activates the standard output for the current session.
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SET SERVEROUTPUT ON;
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CALL N_QUEENS(4);
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CALL N_QUEENS(8);
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CALL N_QUEENS(16);
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