CF321E Ciel and Gondolas Wqs二分 四边形不等式优化dp 决策单调性

//#include<bits\stdc++.h>
#include<iostream>
#include<iomanip>
#include<cstdio>
#include<cstring>
#include<string>
#include<ctime>
#include<cmath>
#include<cctype>
#include<cstdlib>
#include<queue>
#include<deque>
#include<stack>
#include<vector>
#include<algorithm>
#include<utility>
#include<bitset>
#include<set>
#include<map>
#define ll long long
#define db double
#define INF 10000000000000010ll
#define ldb long double
#define pb push_back
#define put_(x) printf("%d ",x);
#define get(x) x=read()
#define gt(x) scanf("%d",&x)
#define gi(x) scanf("%lf",&x)
#define put(x) printf("%d\n",x)
#define putl(x) printf("%lld\n",x)
#define gc(a) scanf("%s",a+1)
#define rep(p,n,i) for(RE int i=p;i<=n;++i)
#define go(x) for(int i=lin[x],tn=ver[i];i;tn=ver[i=nex[i]])
#define fep(n,p,i) for(RE int i=n;i>=p;--i)
#define vep(p,n,i) for(RE int i=p;i<n;++i)
#define pii pair<int,int>
#define mk make_pair
#define RE register
#define P 1000000007
#define gf(x) scanf("%lf",&x)
#define pf(x) ((x)*(x))
#define uint unsigned long long
#define ui unsigned
#define EPS 1e-8
#define sq sqrt
#define S second
#define F first
#define mod 998244353
using namespace std;
char buf[1<<15],*fs,*ft;
inline char getc()
{
    return (fs==ft&&(ft=(fs=buf)+fread(buf,1,1<<15,stdin),fs==ft))?0:*fs++;
}
inline int read()
{
    RE int x=0,f=1;RE char ch=getc();
    while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getc();}
    while(ch>=‘0‘&&ch<=‘9‘){x=((ll)x*10+ch-‘0‘)%mod;ch=getc();}
    return x*f;
}
const int MAXN=4010,G=3;
int n,k,l,r;
ll f[MAXN];
int sum[MAXN],pre[MAXN][MAXN];
int c[MAXN][MAXN],cnt[MAXN];
struct wy{int l,r,x;}q[MAXN];
inline int cost(int i,int j)
{
	return (sum[j]-c[i-1][j]*2+sum[i-1])>>1;
}
inline int pd(int x,int y,int z)
{
	if(f[x]+cost(x+1,z)<f[y]+cost(y+1,z))return 0;
	if(f[x]+cost(x+1,z)==f[y]+cost(y+1,z))return cnt[x]<cnt[y];
	return 1;
}
inline int calc(wy a,int x)
{
	int l=a.l,r=a.r+1;
	while(l<r)
	{
		int mid=(l+r)>>1;
		if(pd(a.x,x,mid))r=mid;
		else l=mid+1;
	}
	return r;
}
inline void calc(int x)
{
	q[l=r=1]=(wy){1,n,0};
	rep(1,n,i)
	{
		while(l<r&&q[l].r<i)++l;
		int w=q[l].x;++q[l].l;
		f[i]=f[w]+cost(w+1,i)+x;cnt[i]=cnt[w]+1;
		if(pd(q[r].x,i,n))
		{
			while(l<=r&&pd(q[r].x,i,q[r].l))--r;
			if(l>r){q[++r]=(wy){i+1,n,i};continue;}
			int w=calc(q[r],i);
			q[r].r=w-1;q[++r]=(wy){w,n,i};
		}
	}
}
int main()
{
	//freopen("1.in","r",stdin);
	get(n);get(k);
	rep(1,n,i)
	{
		rep(1,n,j)
		{
			int get(x);
			pre[i][j]=pre[i][j-1]+x;
			c[i][j]=c[i-1][j]+pre[i][j];
		}
		sum[i]=sum[i-1]+(pre[i][i]<<1);
	}
	int l=0,r=(sum[n]>>1)+1;
	while(l+1<r)
	{
		int mid=(l+r)>>1;
		calc(mid);
		if(cnt[n]>=k)l=mid;
		else r=mid;
	}
	calc(r);
	if(cnt[n]>=k)l=r;else calc(l);
	putl(f[n]-k*l);return 0;
}