[BZOJ1597]土地购买 斜率优化

dp方程较难想

 

#include<cstdio>
#include<algorithm>

using namespace std;

int top=0,x[50010],y[50010];
long long dp[50010];
int q[50010],n;

struct S{
    long long int x,y;
}s[50010];

bool cmp(S a,S b)
{
    if(a.x==b.x)
        return a.y<b.y;
    else 
        return a.x<b.x;
}

double slope(int j,int k)
{
    return double((dp[j]-dp[k])/(y[k+1]-y[j+1]));
} 

int main()
{
    scanf("%d",&n);
    
    for(int i=1;i<=n;i++)
        scanf("%lld %lld",&s[i].x,&s[i].y);
    
    sort(s+1,s+1+n,cmp);
    
    for(int i=1;i<=n;i++)
    {
        while(top && s[i].y>=y[top]) top--;
        x[++top]=s[i].x;
        y[top]=s[i].y;
    }
    int head=0,tail=0;
    for(int i=1;i<=top;i++)
    {
        while(head<tail && slope(q[head+1],q[head])<x[i]) head++;
        dp[i]=dp[q[head]]+x[i]*y[q[head]+1];
        while(head<tail && slope(q[tail],q[tail-1])>slope(i,q[tail])) tail--;
        q[++tail]=i;
//        printf("%d,",dp[i]);
    }
    
    printf("%lld",dp[top]);
    
    return 0;
} 

int相乘如果结果超出int，会出错。