CodeForce-798C Mike and gcd problem(贪心)
Mike has a sequence A = [a1, a2, ..., an] of length n. He considers the sequence B = [b1, b2, ..., bn] beautiful if the gcd of all its elements is bigger than 1, i.e. .
Mike wants to change his sequence in order to make it beautiful. In one move he can choose an index i (1 ≤ i < n), delete numbers ai, ai + 1 and put numbers ai - ai + 1, ai + ai + 1 in their place instead, in this order. He wants perform as few operations as possible. Find the minimal number of operations to make sequence A beautiful if it's possible, or tell him that it is impossible to do so.
is the biggest non-negative number d such that d divides bi for every i (1 ≤ i ≤ n).
Input
The first line contains a single integer n (2 ≤ n ≤ 100 000) — length of sequence A.
The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — elements of sequence A.
Output
Output on the first line "YES" (without quotes) if it is possible to make sequence A beautiful by performing operations described above, and "NO" (without quotes) otherwise.
If the answer was "YES", output the minimal number of moves needed to make sequence A beautiful.
Example
2
1 1
YES
1
3
6 2 4
YES
0
2
1 3
YES
1
Note
In the first example you can simply make one move to obtain sequence [0, 2] with .
In the second example the gcd of the sequence is already greater than 1.
题意:n个数,n<=1e5,操作:把a[i],a[i+1] 替换成 a[i]-a[i+1],a[i]+a[i+1],问至少要多少次操作才能让整个a数组的最大公约数gcd大于1.
由题目给出操作可知:当gcd(a,b)<=1时,进行操作为:
初始:a b
第一步:a-b a+b
第二步:-2b 2a
即两个数最多2步操作就能满足GCD==2。
对于两个偶数,要进行0步操作;对于两个奇数,要进行1步操作;对于一个奇数一个偶数,要进行2步操作。
先把所有“2个奇数成对”的情况计数+1并把两个奇数更新为偶数,然后在重新判断所有“1个奇数1个偶数成对”的情况计数+2。
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a[200050],n,num=0;
ll gcd(ll a,ll b){
return b==0?a:gcd(b,a%b);
}
int main(){
cin>>n;
for(int i=1;i<=n;i++)
scanf("%lld",&a[i]);
ll ans=gcd(abs(a[1]),abs(a[2]));
for(int i=3;i<=n;i++)\
ans=gcd(ans,abs(a[i]));
if(ans>1) cout<<"YES"<<endl<<0<<endl;
else
{
for(int i=1;i<n;i++)
if(a[i]%2&&a[i+1]%2)
a[i]=0,a[i+1]=0,num++;
for(int i=1;i<n;i++)
if((a[i]%2&&a[i+1]%2==0)||(a[i]%2==0&&a[i]%2))
a[i]=0,a[i+1]=0,num+=2;
cout<<"YES"<<endl<<num<<endl;
}
return 0;
}
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