BZOJ1563 NOI2009诗人小G(动态规划+决策单调性)

  设f[i]为前i行的最小不协调度,转移枚举这一行从哪开始,显然有f[i]=min{f[j]+abs(s[i]-s[j]+i-j-1-m)p}。大胆猜想有决策单调性就好了。证明看起来很麻烦,从略。注意需要全程long double。

#include<bits/stdc++.h>
using namespace std;
int read()
{
int x=,f=;char c=getchar();
while (c<''||c>'') {if (c=='-') f=-;c=getchar();}
while (c>=''&&c<='') x=(x<<)+(x<<)+(c^),c=getchar();
return x*f;
}
#define N 100010
#define inf 1000000000000000001ll
#define ll long long
#define ld long double
int T,n,m,p,a[N],from[N],stk[N],L[N],R[N],top;
ld f[N];
char s[N][];
void print(int n)
{
if (n==) return;
print(from[n]);
for (int i=from[n]+;i<n;i++) printf("%s ",s[i]);
puts(s[n]);
}
ld ksm(ld a,int k)
{
ld s=;
for (;k;k>>=,a*=a) if (k&) s*=a;
return s;
}
ld calc(int i,int j){return f[j]+ksm(abs(a[i]-a[j]-m),p);}
int main()
{
#ifndef ONLINE_JUDGE
freopen("c.in","r",stdin);
freopen("c.out","w",stdout);
const char LL[]="%I64d\n";
#else
const char LL[]="%lld\n";
#endif
T=read();
while (T--)
{
n=read(),m=read()+,p=read();
for (int i=;i<=n;i++) scanf("%s",s[i]),a[i]=a[i-]+strlen(s[i]);
for (int i=;i<=n;i++) f[i]=inf,a[i]+=i;
stk[top=]=;L[]=,R[]=n;
for (int i=;i<=n;i++)
{
int l=,r=top;
while (l<=r)
{
int mid=l+r>>;
if (R[mid]>=i) from[i]=stk[mid],r=mid-;
else l=mid+;
}
f[i]=calc(i,from[i]);
while (L[top]>i&&calc(L[top],i)<calc(L[top],stk[top])) top--;
l=max(L[top],i+),r=R[top];int x=R[top]+;
while (l<=r)
{
int mid=l+r>>;
if (calc(mid,i)<calc(mid,stk[top])) x=mid,r=mid-;
else l=mid+;
}
R[top]=x-;if (x<=n) stk[++top]=i,L[top]=x,R[top]=n;
}
if (f[n]<inf) printf(LL,(ll)f[n]),print(n);
else puts("Too hard to arrange");
for (int i=;i<=;i++) putchar('-');if (T) printf("\n");
}
return ;
}
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