Minimal steps down to 1: Difference between revisions
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(→{{header|Haskell}}: added Haskell solution) |
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Line 510:
λ> task2 [Div 2, Div 3, Sub 2] [1..2000]
17: (((((((((((1699-2)-2)/3-2)-2)/3-2)-2)/3-2)-2)/3-2)-2)/3-2)/3</pre>
=={{header|J}}==
Implementation:
<lang J>step=: {{
~.((#~ 1<:]),y-/m),(#~ (=<.)),y%/n
}}
steps=: {{
m step n^:(1 - 1 e. ])^:a:
}}
show=: {{
k=.,:,:0 0 1
m=.,m [ n=.,n
for_ok.}.|.m steps n y do.
last=.{:"2 k
subs=. (1,.m,.0)+"2]0 0 1*"1 last+"1 0/m
divs=. (2,.n,.0)+"2]0 0 1*"1 last*"1 0/n
next=. subs,"2 divs
k=. (,({:"1 next)e.ok)#,/k,"2 1/"2 next
end.
;@((<":y),_2 }. ,)"2((' -/'{~{.);":@{:)"1 }:"1 |."2 k
}}
taskA=: {{
for_j. 1+i.10 do.
echo j,&":': ',(_1+#x steps y j),&":' steps.'
echo x show y j
echo ''
end.
}}
taskB=: {{
echo 'considering positive integers up to ',":m
tallies=. _1+#@(x steps y)every 1+i.m
echo (>./tallies) ,&": ' steps: ',&": 1+I.(=>./)tallies
echo ''
}}
task=: 2e4 taskB, 2e3 taskB, taskA
</lang>
Task examples:
<lang J> 1 task 2 3
1: 0 steps.
1
2: 1 steps.
2-1
2/2
3: 1 steps.
3/3
4: 2 steps.
4/2-1
4/2/2
4-1/3
5: 3 steps.
5-1/2-1
5-1/2/2
5-1-1/3
6: 2 steps.
6/3-1
6/3/2
6/2/3
7: 3 steps.
7-1/3-1
7-1/3/2
7-1/2/3
8: 3 steps.
8/2/2-1
8/2/2/2
8/2-1/3
9: 2 steps.
9/3/3
10: 3 steps.
10-1/3/3
considering positive integers up to 2000
14 steps: 863 1079 1295 1439 1511 1583 1607 1619 1691 1727 1823 1871 1895 1907 1919 1943
considering positive integers up to 20000
20 steps: 12959 15551 17279 18143 19439
2 task 2 3
1: 0 steps.
1
2: 1 steps.
2/2
3: 1 steps.
3-2
3/3
4: 2 steps.
4-2/2
4/2/2
5: 2 steps.
5-2-2
5-2/3
6: 2 steps.
6/2-2
6/3/2
6/2/3
7: 3 steps.
7-2-2-2
7-2-2/3
8: 3 steps.
8-2/2-2
8/2-2/2
8/2/2/2
8-2/3/2
8-2/2/3
9: 2 steps.
9/3-2
9/3/3
10: 3 steps.
10/2-2-2
10/2-2/3
considering positive integers up to 2000
17 steps: 1699
considering positive integers up to 20000
24 steps: 19681</lang>
=={{header|Java}}==
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