BZOJ-1911 特别行动队
DP+斜率优化
就不再多说了。。。还是基础的斜率优化。。。
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var
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n,i,s,t,a,b,c,xa,xb,xc:longint;
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num,dp,xl,sum,s2:array[0..1000005] of int64;
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begin
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read(n,xa,xb,xc);
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for i:=1 to n do read(num[i]);
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for i:=1 to n do sum[i]:=sum[i-1]+num[i];
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s:=1;t:=1;
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for i:=1 to n do
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begin
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while s<t do
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begin
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a:=xl[s];
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b:=xl[s+1];
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if 2*xa*sum[i] < (s2[b]-s2[a])/(sum[b]-sum[a]) then
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begin
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xl[s]:=0;inc(s);
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end
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else break;
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end;
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a:=xl[s];
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dp[i]:=dp[a]+xa*sqr(sum[i]-sum[a])+xb*(sum[i]-sum[a])+xc;
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s2[i]:=dp[i]+xa*sqr(sum[i])-xb*sum[i];
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inc(t);
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xl[t]:=i;
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while t-s>1 do
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begin
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a:=xl[t-2];b:=xl[t-1];c:=xl[t];
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if (s2[b]-s2[a])/(sum[b]-sum[a]) < (s2[b]-s2[c])/(sum[b]-sum[c]) then
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begin
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xl[t-1]:=xl[t];xl[t]:=0;dec(t);
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end
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else break;
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end;
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end;
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write(dp[n]);
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end.
