CF372C Watching Fireworks is Fun [单调队列]

把 \(b_i - |a_i - x|\) 的 \(b_i\) 提出来然后单调队列就没了。

// clang-format off
// powered by c++11
// by Isaunoya
#include<bits/stdc++.h>
#define rep(i,x,y) for(register int i=(x);i<=(y);++i)
#define Rep(i,x,y) for(register int i=(x);i>=(y);--i)
using namespace std;
using db=double;
using ll=long long;
using uint=unsigned int;
using ull=unsigned long long;
using pii=pair<int,int>;
#define Tp template
#define fir first
#define sec second
Tp<class T>void cmax(T&x,const T&y) {
		if(x<y)x=y;
}
Tp<class T>void cmin(T&x,const T&y) {
		if(x>y)x=y;
}
#define all(v) v.begin(),v.end()
#define sz(v) ((int)v.size())
#define pb emplace_back
Tp<class T>void sort(vector<T>&v) {
		sort(all(v));
}
Tp<class T>void reverse(vector<T>&v) {
		reverse(all(v));
}
Tp<class T>void unique(vector<T>&v) {
		sort(all(v)),v.erase(unique(all(v)),v.end());
}
inline void reverse(string&s) {
	reverse(s.begin(),s.end());
}
const int SZ=1<<23|233;
struct FILEIN {
	char qwq[SZ],*S=qwq,*T=qwq,ch;
#ifdef __WIN64
#define GETC getchar
#else
	inline char GETC() {
		return(S==T)&&(T=(S=qwq)+fread(qwq,1,SZ,stdin),S==T)?EOF:*S++;
	}
#endif
	inline FILEIN&operator>>(char&c) {
		while(isspace(c=GETC()));
		return*this;
	} inline FILEIN&operator>>(string&s) {
		s.clear();
		while(isspace(ch=GETC()));
		if(!~ch)return*this;
		s=ch;
		while(!isspace(ch=GETC())&&~ch)s+=ch;
		return*this;
	}
	inline FILEIN&operator>>(char*str) {
		char*cur=str;
		while(*cur)*cur++=0;
		cur=str;
		while(isspace(ch=GETC()));
		if(!~ch)return*this;
		*cur=ch;
		while(!isspace(ch=GETC())&&~ch)*++cur=ch;
		*++cur=0;
		return*this;
	}
	Tp<class T>inline void read(T&x) {
			bool f=0;
			while((ch=GETC())<48&&~ch)f^=(ch==45);
			x=~ch?(ch^48):0;
			while((ch=GETC())>47)x=x*10+(ch^48);
			x=f?-x:x;
	}
	inline FILEIN&operator>>(int&x) {
		return read(x),*this;
	} inline FILEIN&operator>>(ll&x) {
		return read(x),*this;
	} inline FILEIN&operator>>(uint&x) {
		return read(x),*this;
	} inline FILEIN&operator>>(ull&x) {
		return read(x),*this;
	}
	inline FILEIN&operator>>(double&x) {
		read(x);
		bool f=x<0;
		x=f?-x:x;
		if(ch^'.')return*this;
		double d=0.1;
		while((ch=GETC())>47)x+=d*(ch^48),d*=.1;
		return x=f?-x:x,*this;
	}
} in;
struct FILEOUT {
	const static int LIMIT=1<<22;
	char quq[SZ],ST[233];
	int sz,O,pw[233];
	FILEOUT() {
		set(7);
		rep(i,pw[0]=1,9)pw[i]=pw[i-1]*10;
	}~FILEOUT() {
		flush();
	}
	inline void flush() {
		fwrite(quq,1,O,stdout),fflush(stdout),O=0;
	}
	inline FILEOUT&operator<<(char c) {
		return quq[O++]=c,*this;
	} inline FILEOUT&operator<<(string str) {
		if(O>LIMIT)flush();
		for(char c:str)quq[O++]=c;
		return*this;
	}
	inline FILEOUT&operator<<(char*str) {
		if(O>LIMIT)flush();
		char*cur=str;
		while(*cur)quq[O++]=(*cur++);
		return*this;
	}
	Tp<class T>void write(T x) {
			if(O>LIMIT)flush();
			if(x<0) {
				quq[O++]=45;
				x=-x;
			}
			do {
				ST[++sz]=x%10^48;
				x/=10;
			} while(x);
			while(sz)quq[O++]=ST[sz--];
	}
	inline FILEOUT&operator<<(int x) {
		return write(x),*this;
	} inline FILEOUT&operator<<(ll x) {
		return write(x),*this;
	} inline FILEOUT&operator<<(uint x) {
		return write(x),*this;
	} inline FILEOUT&operator<<(ull x) {
		return write(x),*this;
	}
	int len,lft,rig;
	void set(int l) {
		len=l;
	} inline FILEOUT&operator<<(double x) {
		bool f=x<0;
		x=f?-x:x,lft=x,rig=1.*(x-lft)*pw[len];
		return write(f?-lft:lft),quq[O++]='.',write(rig),*this;
	}
} out;
#define int long long
struct Math {
	vector<int>fac,inv;
	int mod;
	void set(int n,int Mod) {
		fac.resize(n+1),inv.resize(n+1),mod=Mod;
		rep(i,fac[0]=1,n)fac[i]=fac[i-1]*i%mod;
		inv[n]=qpow(fac[n],mod-2);
		Rep(i,n-1,0)inv[i]=inv[i+1]*(i+1)%mod;
	}
	int qpow(int x,int y) {
		int ans=1;
		for(; y; y>>=1,x=x*x%mod)if(y&1)ans=ans*x%mod;
		return ans;
	} int C(int n,int m) {
		if(n<0||m<0||n<m)return 0;
		return fac[n]*inv[m]%mod*inv[n-m]%mod;
	}
	int gcd(int x,int y) {
		return!y?x:gcd(y,x%y);
	} int lcm(int x,int y) {
		return x*y/gcd(x,y);
	}
} math;
// clang-format on

int n, m, d;
const int maxn = 2e5 + 52;
int t[2], f[2][maxn], q[maxn];
int ans = 1e18;

signed main() {
	//code begin.
	in >> n >> m >> d;
	int p = 0, sum = 0;
	rep(i , 1 , m) {
		int a, b;
		in >> a >> b >> t[p ^ 1];
		sum += b;
		int len = (t[p ^ 1] - t[p]) * d;
		int head = 1, tail = 0;
		rep(j , 1 , n) {
			while(head <= tail && q[head] < j - len)
				++ head;
			while(head <= tail && f[p][q[tail]] > f[p][j])
				-- tail;
			q[++ tail] = j;
			f[p ^ 1][j] = f[p][q[head]] + abs(a - j);

		}

		head = 1, tail = 0;
		Rep(j , n , 1) {
			while(head <= tail && q[head] > j + len)
				++ head;
			while(head <= tail && f[p][q[tail]] > f[p][j])
				-- tail;
			q[++ tail] = j;
			cmin(f[p ^ 1][j], f[p][q[head]] + abs(a - j));
		}
		p ^= 1;
	}
	rep(i , 1 , n) cmin(ans, f[p][i]);
	out << sum - ans << '\n';
	return 0;
	//code end.
}