A way to solve 1547F(#731F) by implementation

Revision en11, by handsome_gay, 2021-07-10 23:35:28

As we know, if $$$x\neq 1$$$ and $$$x\neq y$$$, then either $$$gcd(x,y)=x$$$ or $$$gcd(x,y)<=\frac{x}{2}$$$. That means for each element $$$a_i$$$ in the array, it will change at most $$$log(a_i)$$$ times before it becomes $$$1$$$.

So we can implement the process, but for every round we only consider the element that will change (which means $$$a_i \neq 1$$$ and $$$a_i \neq a_{i+1}$$$), then we just do $$$O(N*log(a_i))$$$ times change.

How to find the elements that will change in the next round? We can see that elements will change in the next round, are only in the elements change in this round and their left element, so we just check them. The number of elements we check is $$$O(N*log(a_i))$$$ too.

solution

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  Rev. Lang. By When Δ Comment
en12 English handsome_gay 2021-07-10 23:37:23 50
en11 English handsome_gay 2021-07-10 23:35:28 1 Tiny change: 'q a_{i+1}$, then we ' -> 'q a_{i+1}$), then we '
en10 English handsome_gay 2021-07-10 23:31:33 7 Tiny change: ' y$, then $gcd(x,y)' -> ' y$, then either $gcd(x,y)'
en9 English handsome_gay 2021-07-10 23:31:10 16 Tiny change: ' $gcd(x,y)' -> ' $gcd(x,y)=x$ or $gcd(x,y)'
en8 English handsome_gay 2021-07-10 23:28:57 6 Tiny change: ' 1$ and $x>y$, then $' -> ' 1$ and $x\neq y$, then $'
en7 English handsome_gay 2021-07-10 23:25:20 6 Tiny change: ' 1$ and $x\neq y$, then $' -> ' 1$ and $x>y$, then $'
en6 English handsome_gay 2021-07-10 23:19:16 7 Tiny change: 'now, if $x!=1$ and $x\' -> 'now, if $x\neq 1$ and $x\'
en5 English handsome_gay 2021-07-10 23:18:54 29
en4 English handsome_gay 2021-07-10 20:31:28 11
en3 English handsome_gay 2021-07-10 20:30:02 12
en2 English handsome_gay 2021-07-10 20:29:06 48 Tiny change: '$ too.\n\n\n~~~~' -> '$ too.\n\n[submission:1010182]\n\n\n~~~~'
en1 English handsome_gay 2021-07-10 20:24:23 2399 Initial revision (published)