By: newkid

newkid — Fri, 25 Jun 2010 19:20:21 +0000
11GR2:
WITH n AS (SELECT ROWNUM-1 rn FROM DUAL CONNECT BY ROWNUM<=10)
,o AS (SELECT '+' op FROM DUAL UNION ALL SELECT '-' op FROM DUAL UNION ALL SELECT NULL FROM DUAL)
,t(num,tot,expr,op) AS (
  SELECT 0 as num, 0 as tot, '' AS expr, '' AS op FROM DUAL
  UNION ALL
  SELECT n.rn
        ,DECODE(o.op,'+',t.tot+n.rn,'-',t.tot-n.rn,DECODE(t.op,'+',t.tot-t.num+t.num*10+n.rn,t.tot+t.num-t.num*10-n.rn))
        ,t.expr||o.op||n.rn
        ,o.op
    FROM n,t,o
   WHERE t.num = n.rn-1 AND (o.op IS NOT NULL OR t.op IS NOT NULL)
   )
SELECT expr||'='||tot AS OUTPUT 
FROM t
WHERE num=9 AND tot=1;

other solutions wihtout recursive WITH:

WITH t AS(
SELECT '+' X FROM DUAL UNION ALL
SELECT '-' X FROM DUAL UNION ALL
SELECT ''  X FROM DUAL)
,t2 AS (
SELECT * 
  FROM (SELECT ROWNUM id,t.x||
                         1||t1.x||
                         2||t2.x||
                         3||t3.x||
                         4||t4.x||
                         5||t5.x||
                         6||t6.x||
                         7||t7.x||
                         8||t8.x||
                         9 y
       FROM t,t t1,t t2,t t3,t t4,t t5,t t6,t t7,t t8
      WHERE t.x IN ('-','+')
      )
WHERE REPLACE(y,123)=y AND
      REPLACE(y,234)=y AND
      REPLACE(y,345)=y AND
      REPLACE(y,456)=y AND
      REPLACE(y,567)=y AND
      REPLACE(y,678)=y AND
      REPLACE(y,789)=y
)
SELECT LTRIM(y,'+')
  FROM (SELECT id,y,REGEXP_SUBSTR(y,'[+-]',1,rn) op,REGEXP_SUBSTR(y,'[^+-]+',1,rn) num
         FROM t2,(SELECT ROWNUM rn FROM DUAL CONNECT BY ROWNUM<=9)
        )
GROUP BY id,y 
HAVING SUM(DECODE(op,'+',num,-num))=1
;


WITH t AS(
SELECT n,op
  FROM (SELECT '+' op FROM DUAL UNION ALL
        SELECT '-' op FROM DUAL UNION ALL
        SELECT ''  op FROM DUAL)
       ,(SELECT ROWNUM n FROM DUAL CONNECT BY ROWNUM<=9)
WHERE n>1 OR op IN ('+','-')
)
,t2 AS (
SELECT ROWNUM id, REPLACE(SYS_CONNECT_BY_PATH(op||n,'@'),'@') y
  FROM t
WHERE n=9
START WITH n=1 
CONNECT BY n= PRIOR n+1 AND (op IS NOT NULL OR PRIOR op IS NOT NULL)
)
SELECT LTRIM(y,'+')
  FROM (SELECT id,y,REGEXP_SUBSTR(y,'[+-]',1,rn) op,REGEXP_SUBSTR(y,'[^+-]+',1,rn) num
          FROM t2,(SELECT ROWNUM rn FROM DUAL CONNECT BY ROWNUM<=9)
        )
GROUP BY id,y 
HAVING SUM(DECODE(op,'+',num,-num))=1
;


WITH t AS(
SELECT n,op
  FROM (SELECT '+' op FROM DUAL UNION ALL
        SELECT '-' op FROM DUAL UNION ALL
        SELECT '~'  op FROM DUAL)
       ,(SELECT ROWNUM n FROM DUAL CONNECT BY ROWNUM<=9)
WHERE n>1 OR op IN ('+','-')
)
,t2 AS (
SELECT ROWNUM id, REPLACE(SYS_CONNECT_BY_PATH(op||n,'@'),'@') y
      ,DECODE(op,'+',n,'-',-n,DECODE(PRIOR op,'+',- (PRIOR n)+ (PRIOR n)*10 +n, (PRIOR n)- (PRIOR n)*10 -n)) val
  FROM t
WHERE n=9
START WITH n=1 
CONNECT BY n= PRIOR n+1 AND (op <>'~' OR PRIOR op <>'~')
)
SELECT LTRIM(REPLACE(t2.y,'~'),'+')
  FROM t2,(SELECT ROWNUM n FROM DUAL CONNECT BY ROWNUM<=9)
GROUP BY t2.y
HAVING SUM(DECODE(SUBSTR(y,(n-1)*2+1,1),'+',n,'-',-n,DECODE(SUBSTR(y,(n-2)*2+1,1),'+',-(n-1)+(n-1)*10+n,(n-1)-(n-1)*10-n )))=1;
Comments on: How to solve the 123456789 Equation Puzzle in SQL

By: newkid
