Do not cross section, can be seen that the sections forming the tree structure, then building the tree, provided F [u] [i] is the probability of u plus up interval maximum value of i, the transfer is \ (F [u] [i] = p [u] * \ prod f [v] [mxu-mxv-1] + (1-p [u]) * \ prod f [v] [mxu-mxv] \)
Note that for a rational choice contribution method, scan on the line, do not tune blind-half year ......
#include<iostream>
#include<cstdio>
#include<vector>
#include<algorithm>
using namespace std;
const int N=500005;
int n,m,a[N+1],st[N][20],b[N],mx;
double f[5005][5005];
bool vis[N+1];
vector<int>v[N<<1];
struct qwe
{
int l,r;
double p;
}q[N<<1];
bool cmp(qwe a,qwe b)
{
return a.l<b.l||(a.l==b.l&&a.r>b.r);
}
int read()
{
int r=0,f=1;
char p=getchar();
while(p>'9'||p<'0')
{
if(p=='-')
f=-1;
p=getchar();
}
while(p>='0'&&p<='9')
{
r=r*10+p-48;
p=getchar();
}
return r*f;
}
int build(int u,int fa,int ql,int qr,int w)
{
if(u)
v[fa].push_back(u);
vis[u]=1;
int x=-1;
for(int l=w,r;l<=m;l=r)
{
if(qr<q[l].r)
{
x=l;
break;
}
r=build(l,u,q[l].l,q[l].r,l+1);
}
return x==-1?m+1:x;
}
int ques(int l,int r)
{
if(l>r)
return 0;
int x=b[r-l+1];
return max(st[l][x],st[r-(1<<x)+1][x]);
}
void dfs(int u,int fa)
{
if(v[u].empty())
{
f[u][0]=1.0-q[u].p;
for(int i=1;i<=m*2;i++)
f[u][i]=1.0;
return;
}
int w=ques(q[u].l,q[u].r);
for(int i=0;i<v[u].size();i++)
dfs(v[u][i],u);
for(int i=0;i<=m;i++)
{
double x=1,y=1;
for(int j=0;j<v[u].size();j++)
x*=f[v[u][j]][min(m+1,w+i-1-ques(q[v[u][j]].l,q[v[u][j]].r))],y*=f[v[u][j]][min(m+1,w+i-ques(q[v[u][j]].l,q[v[u][j]].r))];
f[u][i]=(i?q[u].p:0)*x+(1.0-q[u].p)*y;
}
f[u][m+1]=1;
return ;
}
int main()
{
n=read(),m=read();
for(int i=1;i<=n;i++)
st[i][0]=a[i]=read(),mx=max(mx,a[i]);
if(mx>m)
for(int i=1;i<=n;i++)
st[i][0]=a[i]=max(0,a[i]+m-mx);
for(int i=2;i<=n;i++)
b[i]=b[i>>1]+1;
for(int j=1;j<=18;j++)
for(int i=1;i+(1<<j)-1<=n;i++)
st[i][j]=max(st[i][j-1],st[i+(1<<(j-1))][j-1]);
for(int i=1;i<=m;i++)
q[i].l=read(),q[i].r=read(),scanf("%lf",&q[i].p);
sort(q+1,q+m+1,cmp);
q[0].l=1,q[0].r=n,q[0].p=0;
build(0,-1,1,n,1);
dfs(0,-1);
double ans=mx;
for(int i=1;i<=m;i++)
ans+=(f[0][i]-f[0][i-1])*i;
printf("%.8lf\n",ans);
return 0;
}