2022 PUZZLEUP

solomon_007

#3

SQL>
SQL> with t as (select to_number(column_value) n from xmltable('1 to 4'))
  2  select count(*)
  3   from ( select level lvl,replace(sys_connect_by_path(n,','),',') nNum
  4            from t
  5          connect by level <= (select sum(n) from t)
  6        ) a
  7   where regexp_count(nNum,1,1) <= 1
  8     and regexp_count(nNum,2,1) <= 2
  9     and regexp_count(nNum,3,1) <= 3
10     and regexp_count(nNum,4,1) <= 4
11  /

  COUNT(*)
----------
     38847

这个先排列完再过滤，纯粹玩一下，很慢！ connect by 的写法好像很难将 regexp_count的判断放到 CONNECT BY 子句中，因为前面的sys_connect_by_path 函数在这个子句中不支持，要是支持就没问题

solomon_007

newkid 发表于 2022-11-2 21:32
#3 FOUR DIGITS How many positive integers are there where only the digits 1, 2, 3 and 4 are used and ...

牛蛙这几天炒股亏得好惨！

〇〇

newkid 发表于 2022-11-4 02:37
暴力法，和你们差不多：with n as (select level n from dual connect by level

从1-9只有用公式才能算出来

〇〇

newkid 发表于 2022-11-4 02:37
暴力法，和你们差不多：with n as (select level n from dual connect by level

改写错在哪里
with recursive f(n,f) as (  ------- 构造阶乘表
select 0,1
union all
select n+1,f*(n+1) from f where n<10
)
,t(n,s,f) as (
select 1,lv-1,1 from (values(1,2))s(lv)
union all
select t.n+1,t.s+f.n,t.f*f.f
  from t
       ,f
where t.n<4 and f.n<=t.n+1
)     
select sum(f.f/t.f) from t,f where t.n=4 and t.s>0 and t.s=f.n;

sum
----
4024

〇〇

〇〇 发表于 2022-11-4 11:50
改写错在哪里with recursive f(n,f) as (  ------- 构造阶乘表select 0,1 union allselect n+1,f*(n+1) fro ...

对values语法不熟悉导致

with recursive f(n,f) as (  ------- 构造阶乘表
select 0,1
union all
select n+1,f*(n+1) from f where n<10
)
,t(n,s,f) as (
select 1,lv-1,1 from (values(1),(2))s(lv)
union all
select t.n+1,t.s+f.n,t.f*f.f
  from t
       ,f
where t.n<4 and f.n<=t.n+1
)     
select sum(f.f/t.f) from t,f where t.n=4 and t.s>0 and t.s=f.n;

〇〇

还是算不出1-9,
D select factorial(45)a;
Error: Out of Range Error: Overflow in HUGEINT multiplication!
postgres=# select factorial(45)a;
                             a
-----------------------------------------------------------
119622220865480194561963161495657715064383733760000000000

〇〇

〇〇 发表于 2022-11-4 13:05
还是算不出1-9,D select factorial(45)a;Error: Out of Range Error: Overflow in HUGEINT multiplication! ...

终于把1-9算出来了，公式都用了10秒

with recursive f(n,f) as (  ------- 构造阶乘表
select n, factorial(n) from generate_series(0,45) m(n)
)
,t(n,s,f) as (
select 1,lv-1,1*f.f from (values(1),(2))s(lv),f where f.n=1
union all
select t.n+1,t.s+f.n,t.f*f.f
  from t
       ,f
where t.n<9 and f.n<=t.n+1
)
select sum(f.f/t.f) from t,f where t.n=9 and t.s>0 and t.s=f.n;
                            sum
-----------------------------------------------------------
189295112473714316327855615439169023.00000000000000000000
(1 行记录)


时间：9179.060 ms (00:09.179)
如果把最后一行的=9改为=4
            sum
----------------------------
38847.00000000000000000000
(1 行记录)


时间：5503.563 ms (00:05.504)

newkid

徽章已转给两位。
这道题还有改善余地，比如说四个数的使用次数分别是1,2,3,2的情形和1,2,2,3的计算结果是一样的，可以合并，但是目前也没有什么好办法把它们列举出来。

newkid

#4 THREE CIRCLES

Two circles of the same size and different colors are placed randomly on a computer screen. These circles can be in one of 4 different states:



1. The circles are not touching.
2. The circles are tangent, i.e. touching at a single point.
3. The circles are overlapping, the first one is on top.
4. The circles are overlapping, the second one is on top.

How many different states are there for 3 circles with different colors?

Notes:
*All three circles should be seen on the screen and considered two-dimensional.
*The circles have a well defined order (top/bottom), e.g. if the first circle is on top of the second and the second circle is on top of the third, the third circle cannot be on top of the first.

电脑屏幕上随机放置两个大小相同、颜色不同的圆圈。这些圆圈可以处于 4 种不同状态之一：

1. 两圆没有接触。
2. 两圆相切，即在一个点相接。
3. 两圆交叠，第一个在上面。
4. 两圆交叠，第二个在上面。

3个不同颜色的圆圈有多少种不同的状态？

注意：
*所有三个圆圈都应该可以在屏幕上看到并被认为是二维的。
*圆圈有明确的顺序（上/下），例如, 假设第一个圆圈在第二个圆圈的上面，而第二个圆圈在第三个圆圈的上面，则第三个圆圈不能在第一个圆圈的下面。

------------
这道题2017出过：
http://www.itpub.net/thread-2090903-1-2.html

283楼。

newkid

#5 ONE AND TWO

You will generate a number using only the digits 1 and 2. Our condition is that no sequence of 3 or more digits consecutively repeats two times. How many digits is the largest number satisfying this condition?

Note: The sequence “xxxx” cannot be included in the number because “xxx” repeats twice.


你仅使用数字 1 和 2 生成一个数字。我们的条件是任何连续3个或更多数字的序列都不重复出现。满足这个条件的最大数是多少位？

注意：数字中不能包含“xxxx”序列，因为“xxx”重复了两次。

------------
原文表达不清，consecutively应该是说连续的数字，而不是连续出现。我已经在翻译时做了纠正。

对付这种油腻的题目，就得写一个油腻的SQL。