HZOI20190822模拟29题解

题面：https://www.cnblogs.com/Juve/articles/11396238.html

下面开始一句话题解：

A：爬山：

二分答案，check即可

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#define int long long
using namespace std;
const int mod=1e9+7;
int n,d,a,b,l,r,mid,ans;
bool check(int m){
	int p=abs(m-a),q=abs(m-b),x,y;
	if(p%d==0) x=p/d;
	else x=p/d+1;
	if(q%d==0) y=q/d;
	else y=q/d+1;
	if(x+y<=n-1) return 1;
	return 0;
}
signed main(){
	scanf("%lld%lld%lld%lld",&n,&d,&a,&b);
	if(d==0){
		printf("%lld\n",max(a,b));
		return 0;
	}
	l=min(a,b)-n*d,r=max(a,b)+n*d;
	ans=max(a,b);
	while(l<=r){
		mid=(l+r)>>1;
		if(check(mid))
			ans=max(ans,mid),l=mid+1;
		else r=mid-1;
	}
	printf("%lld\n",ans);
	return 0;
}

B：学数数：

离散化，单调栈，前缀和

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#include<stack>
#define int long long
using namespace std;
const int MAXN=1e5+5;
int n,q,a[MAXN],b[MAXN],k,cnt,sum[MAXN];
int sta[MAXN],top=0,l[MAXN],r[MAXN];
char op[5];
signed main(){
	scanf("%lld%lld",&n,&q);
	for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
	memcpy(b,a,sizeof(a));
	sort(b+1,b+n+1);
	cnt=unique(b+1,b+n+1)-b-1;
	for(int i=1;i<=n;i++){
		while(top!=0&&a[sta[top]]<=a[i]) top--;
		if(top==0) l[i]=1;
		else l[i]=sta[top]+1;
		sta[++top]=i;
	}
	top=0;
	for(int i=n;i>=1;i--){
		while(top!=0&&a[sta[top]]<a[i]) top--;
		if(top==0) r[i]=n;
		else r[i]=sta[top]-1;
		sta[++top]=i;
	}
	for(int i=1;i<=n;i++){
		int pos=lower_bound(b+1,b+cnt+1,a[i])-b;
		sum[pos]+=(i-l[i]+1)*(r[i]-i+1);
	}
	for(int i=2;i<=n;i++) sum[i]+=sum[i-1];
	while(q--){
		scanf("%s%lld",op,&k);
		if(op[0]=='='){
			int x=upper_bound(b+1,b+cnt+1,k)-b-1;
			int y=lower_bound(b+1,b+cnt+1,k)-b;
			if(x==y) printf("%lld\n",sum[x]-sum[x-1]);
			else puts("0");
		}else if(op[0]=='<'){
			int x=lower_bound(b+1,b+cnt+1,k)-b-1;
			printf("%lld\n",sum[x]);
		}else{
			int x=upper_bound(b+1,b+cnt+1,k)-b-1;
			printf("%lld\n",sum[cnt]-sum[x]);
		}
	}
	return 0;
}

C：七十和十七

推一个公式即可，加上快速幂

#include<cstdio>
#include<iostream>
#include<algorithm>
#define int long long
using namespace std;
const int MAXN=1e5+5;
const int mod=1e9+7;
int f[MAXN],n,bit[MAXN];
int q_pow(int a,int b,int p){
	int res=1;
	while(b){
		if(b&1) res=1ll*res*a%p;
		a=1ll*a*a%p;
		b>>=1;
	}
	return res%mod;
}
signed main(){
	scanf("%lld",&n);
	bit[0]=1;
	for(int i=1;i<=n;i++) bit[i]=(bit[i-1]*2)%mod;
	for(int i=1;i<=n;i++)
		f[i]=(f[i-1]+(bit[i-1]-1)%mod*q_pow(i,mod-2,mod)%mod)%mod;
	printf("%lld\n",f[n]);
	return 0;
}