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%斜率优化%

作者:互联网

站在巨人肩上!

以后怎么用:

        但凡出现dp得分计算公式中有平方,可以化简成为:

                ​​​​​​​        ​​​​​​​        ​​​​​​​        \small \frac{Y(i)-Y(j)}{X(i)-X(j)}

        的形式就可以用斜率优化

斜率优化的精髓就在将上面的公式求出来,并且利用单调队列

#include<cstdio>

using namespace std;

int n,L;
long long C[100100];
long long dp[100100];

inline long long A(int x){return (long long)C[x];}
inline long long g(int x){return (long long)A(x)+L;}
inline long double slope(int j,int k){return (long double)(dp[j]-dp[k]+g(j)*g(j)-g(k)*g(k))/(A(j)-A(k))*1.0;}

int q[100100];
int h,t;

int main(void)
{
	scanf("%d %d",&n,&L);L++;
	for(int i=1;i<=n;i++){
		scanf("%lld",&C[i]);
		C[i]+=C[i-1]+1;
	}
//	h=1;
//	t++;
//	q[t]=0;
	for(int i=1;i<=n;i++){
		while(h<t && slope(q[h],q[h+1])<=2ll*C[i])h++;
		dp[i]=dp[q[h]]+(long long)(A(i)-A(q[h])-L)*(A(i)-A(q[h])-L);
		while(h<t && slope(q[t-1],q[t])>=slope(q[t-1],i))t--;
		t++;q[t]=i;
	}
	printf("%lld",dp[n]);
}

标签:return,int,100100,long,斜率,inline,优化,dp
来源: https://blog.csdn.net/wallyIII/article/details/120205777