斜率优化DP 【pascal】



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Time Limit: 9000/3000 MS (Java/Others)    Memory Limit: 131072/65536 K (Java/Others)


[align=left]Problem Description[/align]
Zero has an old printer that doesn't work well sometimes. As it is antique, he still like to use it to print articles. But it is too old to work for a long time and it will certainly wear and tear, so Zero use a cost to evaluate this
degree.

One day Zero want to print an article which has N words, and each word i has a cost Ci to be printed. Also, Zero know that print k words in one line will cost



M is a const number.

Now Zero want to know the minimum cost in order to arrange the article perfectly.
 
 

[align=left]Input[/align]
There are many test cases. For each test case, There are two numbers N and M in the first line (0 ≤ n ≤
500000, 0 ≤ M ≤ 1000). Then, there are N numbers in the next 2 to N + 1 lines. Input are terminated by EOF.
 
 

[align=left]Output[/align]
A single number, meaning the mininum cost to print the article.
 
 

[align=left]Sample Input[/align]

5 5 5 9 5 7 5

 
 

[align=left]Sample Output[/align]

230

 
 

[align=left]Author[/align]
Xnozero
 

var

  sum,dp,q:array[0..600000] of longint;

  n,m,i,l,r:longint;
function up(i,j:longint):longint;

begin

  up:=dp[i]+sqr(sum[i])-dp[j]-sqr(sum[j]);

end;
function down(i,j:longint):longint;

begin

  down:=sum[i]-sum[j];

end;
begin

  readln(n,m);

  q[0]:=0;dp[0]:=0;

  for i:=1 to n do begin

    readln(sum[i]);

    sum[i]:=sum[i]+sum[i-1];

  end;

  l:=0;r:=1;

  for i:=1 to n do begin

    while (l+1<r) and (up(q[l],q[l+1])>=2*sum[i]*down(q[l],q[l+1])) do inc(l);

    dp[i]:=dp[q[l]]+(sum[i]-sum[q[l]])*(sum[i]-sum[q[l]])+m;

    while (l+1<r) and (up(q[r-2],q[r-1])*down(q[r-1],i)>=up(q[r-1],i)*down(q[r-2],q[r-1]))

    do dec(r);

    inc(r);

    q[r]:=i;

  end;

  writeln(dp[n-2]-dp[0]-1);

  readln;

end.