CodeForces - 1355E Restorer Distance (三分)

题意：n根杆子，每根杆子由一定数量的砖组成，现要使这些砖一样高，添加一块砖花费A，去掉一块砖花费B，移动一块砖花费C，求最小花费

通过观察可知最终所有杆子的高度与花费的关系是个凸函数，三分高度找极值点即可（其实就是二分斜率）

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=1e5+10;
const ll inf=0x3f3f3f3f3f3f3f3fll;
int n,A,R,M,a[N],mx;
ll solve(int h) {
    ll x=0,y=0;
    for(int i=1; i<=n; ++i) {
        if(a[i]>h)x+=a[i]-h;
        else y+=h-a[i];
    }
    if(x>=y)return M*y+R*(x-y);
    else return M*x+A*(y-x);
}
ll tri(int l,int r) {
    while(r-l>1) {
        int mid=(l+r)>>1;
        if(solve(mid)<solve(mid+1))r=mid;
        else l=mid+1;
    }
    return min(solve(l),solve(r));
}
int main() {
    scanf("%d%d%d%d",&n,&A,&R,&M);
    M=min(M,A+R);
    for(int i=1; i<=n; ++i)scanf("%d",&a[i]);
    mx=0;
    for(int i=1; i<=n; ++i)mx=max(mx,a[i]);
    printf("%lld\n",tri(0,mx));
    return 0;
}