BZOJ 3675: [Apio2014]序列分割

难度在于认识到顺序是没有关系的

斜率优化

#include<cstdio>
#include<algorithm>
using namespace std;
int n,m,K,Sum[100005],a[100005];
long long F[2][100005];
struct node{
	long long k,b;
}stack[1000005];
double check(node a,node b){
	return ((double)a.b-b.b)/(b.k-a.k);
}
int main(){
	scanf("%d%d",&m,&K);
	for (int i=1; i<=m; i++) {
		int x;
		scanf("%d",&x);
		if (x) a[++n]=x;
	}
	for (int i=1; i<=n; i++) Sum[i]=Sum[i-1]+a[i];
	for (int k=1; k<=K; k++){
		for (int i=0; i<=n; i++) F[k%2][i]=0;
		int head=1,tail=0;
		for (int i=0; i<=n; i++){
			node line=(node){Sum[i],F[(k-1)%2][i]-1ll*Sum[i]*Sum[i]};
			while (tail-head>0 && check(stack[tail],stack[tail-1])>check(stack[tail],line)) tail--;
			stack[++tail]=line;
			while (tail-head>0 && check(stack[head],stack[head+1])<Sum[i]) head++;
			F[k%2][i]=stack[head].k*Sum[i]+stack[head].b;
		}
	}
	printf("%lld\n",F[K%2][n]);
	return 0;
}