bzoj1597: [Usaco2008 Mar]土地购买

斜率优化dp。

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;
const int maxn = 50000 + 10;

struct Field {
    long long x,y;    
} t[maxn];
long long f[maxn],x[maxn],y[maxn];
int    q[maxn],l,r; 
int    n,cnt;

bool cmp(Field a,Field b) {
    return a.x > b.x || (a.x == b.x && a.y > b.y);
}


long long calc(int j,int i) {
    return f[j]+y[i]*x[j+1];
}

int main() {
    scanf("%d",&n); 
    for(int i=1;i<=n;i++) scanf("%lld%lld",&t[i].x,&t[i].y);
    sort(t+1,t+n+1,cmp);    
    for(int i=1;i<=n;i++) 
        if(t[i].y>y[cnt]) {
            cnt++;
            x[cnt]=t[i].x;
            y[cnt]=t[i].y;    
        }
    f[0]=0; q[r++]=0;
    for(int i=1;i<=cnt;i++) {
        while(l+1<r && calc(q[l+1],i)<calc(q[l],i)) l++; 
        f[i]=f[q[l]]+y[i]*x[q[l]+1];
        while(l+1<r && (f[q[r-1]]-f[q[r-2]])*(x[q[r-1]+1]-x[i+1]) > (f[i]-f[q[r-1]])*(x[q[r-2]+1]-x[q[r-1]+1])) r--;
        q[r++]=i; 
    }
    printf("%lld\n",f[cnt]);
    return 0;
}