"BZOJ-3156" Defense preparation DP + slope optimization

3156: Defense Readiness Time Limit:10 SEC Memory limit:512 MB
submit:951 solved:446
[Submit] [Status] [Discuss] Description Input

The first behavior of an integer n indicates the total length of the front.

The second row of n integers, and the first integer represents the cost of placing the guard tower in position I ai.

Output

A total of one integer that represents the minimum front cost value.

Sample Input10
2 3 1 5 4 5 6 3 1 2
Sample Output18
HINT

1<=n<=10^6,1<=ai<=10^9

Source

katharon+ #1

Solution

Slope optimization DP

The plan is shifted from behind? Flip the sequence.

Then there is the transfer equation $DP [I]=min (dp[i],dp[j]+sum[i-1]-sum[j]-(i-j-1) *j+a[i]$

Then the slope is optimized, the comparison is bare, and then you can

Notable places:

Transfer, $i =1$ in advance to deal with it.

When calculating the answer, note that a long long or else will wa into a dog.

Code

#include <iostream>#include<cstdio>#include<algorithm>#include<cstring>#include<cmath>using namespacestd;intRead () {intx=0, f=1;CharCh=GetChar ();  while(ch<'0'|| Ch>'9') {if(ch=='-') f=-1; Ch=GetChar ();}  while(ch>='0'&& ch<='9') {x=x*Ten+ch-'0'; Ch=GetChar ();} returnx*F;}#defineMAXN 1000100intN,A[MAXN];intQue[maxn],l,r;Long LongDp[maxn],sumid[maxn],ans;DoubleSlopeLong LongILong Longj) {return(Double) (DP[I]-DP[J]-SUMID[I]+SUMID[J]+I-J+I*I-J*J)/(Double) (I-j);}intMain () {n=read (); Ans= (Long Long)1<< -;  for(intJ=m; i>=1; i--) a[i]=read ();  for(intI=1; i<=n; i++) sumid[i]=sumid[i-1]+i; dp[1]=a[1]; que[1]=1; L=r=1;  for(intTmp,i=2; i<=n; i++)        {             while(L<r && Slope (que[l],que[l+1]) <i) l++; TMP=Que[l]; Dp[i]=dp[tmp]+sumid[i-1]-sumid[tmp]-(i-tmp-1) *tmp+A[i];  while(L<r && Slope (que[r],i) <slope (que[r-1],QUE[R]) r--; que[++r]=i; }     for(intI=1; i<=n; i++) Ans=min (ans,dp[i]+sumid[n]-sumid[i]-(Long Long) (n-i) *i); printf ("%lld\n", ans); return 0;}

The above mentioned WA into a dog ... Mdzz

"BZOJ-3156" Defense preparation DP + slope optimization