金中高一康复训练5

打个A和D签到>_<，赛后补了F...

A

　　先把所有的山峰找出来，然后算一下前缀和$sum[i]$。如果k可以的话肯定满足第i*k段的和$sum[i]-sum[i-k]>=1$，这个k可以暴力枚举>_<，不要枚举1就行>_<

　　效率$O(∑i|1<=i<=n)$

　　效率不是很对？注意到，只有$i|n$的才能选，所以最多只有$\sqrt{n}$个选择>_<

　　

 1 #include<map>
 2 #include<set>
 3 #include<list>
 4 #include<cmath>
 5 #include<queue>
 6 #include<cstdio>
 7 #include<vector>
 8 #include<string>
 9 #include<cstring>
10 #include<iostream>
11 #include<algorithm>
12 using namespace std;
13 #define mp make_pair
14 #define ll long long
15 #define reg register
16 #define inf 0x7fffffff
17 #define MOD 1000000007
18 #define clr(a) memset(a,sizeof(a),0);
19 #define rep(i,l,r) for(reg int i=l;i<=r;i++)
20 #define dow(i,l,r) for(reg int i=l;i>=r;i--)
21 inline int read(){int x=0,f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;}
22 inline ll readl(){ll x=0,f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;}
23 template<class T>inline void print(T x){if(x/10!=0)print(x/10);putchar(x%10+'0');}
24 template<class T>inline void writeln(T x){if(x<0)putchar('-');x=abs(x);print(x);putchar('\n');}
25 template<class T>inline void write(T x){if(x<0)putchar('-');x=abs(x);print(x);}
26 template<class T>inline T power(T a,T b){T ans=1;while(b){if(b&1){ans=ans*a%MOD;}b>>=1;a=a*a%MOD;}return ans%MOD;}
27 /*================Header Template==============*/
28 int n,a[50005],sum[50005];
29 int main(){
30     n=read(); a[0]=inf; a[n+1]=inf;
31     rep(i,1,n) a[i]=read(); 
32     rep(i,1,n){
33         if(a[i]>a[i-1]&&(a[i]>a[i+1])) sum[i]=sum[i-1]+1;
34         else sum[i]=sum[i-1];
35     }
36 //    rep(i,1,n) cout<<sum[i]<<" ";
37     rep(k,1,n){
38         if(n%k)continue;
39         int flag=1;
40         for(reg int i=k;i<=n;i+=k) 
41             if((sum[i]-sum[i-k])); else flag=0;
42         if(flag) return writeln(n/k),0;
43     }
44     writeln(0);
45 }

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D

　　Trisolaris dalao好强啊>_<，我好弱啊...他给了我以下提示

　　“这道题，对每次区间修改打个标记，标记$r[i]=y,l[i]=x|x<=i<=y$，就避免了重复的合并>_<”

　　效率$O(nlogn)$

　　

 1 #include<map>
 2 #include<set>
 3 #include<list>
 4 #include<cmath>
 5 #include<queue>
 6 #include<cstdio>
 7 #include<vector>
 8 #include<string>
 9 #include<cstring>
10 #include<iostream>
11 #include<algorithm>
12 using namespace std;
13 #define mp make_pair
14 #define ll long long
15 #define reg register
16 #define inf 0x7fffffff
17 #define MOD 1000000007
18 #define clr(a) memset(a,sizeof(a),0);
19 #define rep(i,l,r) for(reg int i=l;i<=r;i++)
20 #define dow(i,l,r) for(reg int i=l;i>=r;i--)
21 inline int read(){int x=0,f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;}
22 inline ll readl(){ll x=0,f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;}
23 template<class T>inline void print(T x){if(x/10!=0)print(x/10);putchar(x%10+'0');}
24 template<class T>inline void writeln(T x){if(x<0)putchar('-');x=abs(x);print(x);putchar('\n');}
25 template<class T>inline void write(T x){if(x<0)putchar('-');x=abs(x);print(x);}
26 template<class T>inline T power(T a,T b){T ans=1;while(b){if(b&1){ans=ans*a%MOD;}b>>=1;a=a*a%MOD;}return ans%MOD;}
27 /*================Header Template==============*/
28 int num[200005],f[200005]; 
29 int find( int x ){ return (x == f[x]) ? x : f[x] = find( f[x] ); }
30 void uni(int x,int y){ 
31     int fx=find(x) , fy=find(y);
32     if(num[fx]>num[fy]){ num[fx]+=num[fy]; f[fy]=fx; }
33     else { num[fy]+=num[fx]; f[fx]=fy; }
34 }
35 int n,m,l[200005],r[200005];
36 int main(){
37     n=read();m=read();
38     rep(i,1,n) f[i]=i , num[i]=1 , l[i]=i , r[i]=i;
39     rep(i,1,m){
40         int st=read();
41         if(st==1){
42             int x=read() , y=read();
43             uni(x,y);
44         }else
45         if(st==2){
46             int x=read() , y=read();
47             rep(j,r[x],l[y]) uni(x,j);
48             rep(j,r[x],l[y]) r[j]=y,l[j]=x;
49         }else{
50             int x=read() , y=read();
51             puts((find(x)==find(y))?"YES":"NO");
52         }
53     }
54 }

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F

　　这题我怎么可能自己写出来QWQ

　　看了一下网上的题解...哦

　　原来，对于每次交换，$a[i]+i$是固定的，因为$i-1$的同时$a[i]+1$了>_<，所以对于每个点，$a[i]+i$肯定是不会变的

　　所以，定义$b[i]=a[i]+i$，排序之后去重，如果a[i]+i相同的话，那么交换了和没交换是一样的，比如样例2...　　

　　顺便还学会了$unique$：是个函数、用法：$t=unique(a+1,a+n+1)-a-1;$

　　效率：$O(nlogn)$

　　

 1 #include<map>
 2 #include<set>
 3 #include<list>
 4 #include<cmath>
 5 #include<queue>
 6 #include<cstdio>
 7 #include<vector>
 8 #include<string>
 9 #include<cstring>
10 #include<iostream>
11 #include<algorithm>
12 using namespace std;
13 #define mp make_pair
14 #define ll long long
15 #define reg register
16 #define inf 0x7fffffff
17 #define MOD 1000000007
18 #define clr(a) memset(a,sizeof(a),0);
19 #define rep(i,l,r) for(reg int i=l;i<=r;i++)
20 #define dow(i,l,r) for(reg int i=l;i>=r;i--)
21 inline int read(){int x=0,f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;}
22 inline ll readl(){ll x=0,f=1;char c=getchar();while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}return x*f;}
23 template<class T>inline void print(T x){if(x/10!=0)print(x/10);putchar(x%10+'0');}
24 template<class T>inline void writeln(T x){if(x<0)putchar('-');x=abs(x);print(x);putchar('\n');}
25 template<class T>inline void write(T x){if(x<0)putchar('-');x=abs(x);print(x);}
26 template<class T>inline T power(T a,T b){T ans=1;while(b){if(b&1){ans=ans*a%MOD;}b>>=1;a=a*a%MOD;}return ans%MOD;}
27 /*================Header Template==============*/
28 int main(){
29     int n=read(),a[200005]={0};
30     rep(i,1,n) a[i]=read() , a[i]+=i;
31     sort(a+1,a+n+1);
32     int t=unique(a+1,a+n+1)-a-1;
33     if(t==n) return puts("Happy"),0; else return puts("Sad"),0;
34      
35 }

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