[BZOJ2388]旅行规划

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <algorithm>
#include <cmath>
using namespace std;

const int BufferSize = 1 << 16;
char buffer[BufferSize], *Head, *Tail;
inline char Getchar() {
	if(Head == Tail) {
		int l = fread(buffer, 1, BufferSize, stdin);
		Tail = (Head = buffer) + l;
	}
	return *Head++;
}
int read() {
	int x = 0, f = 1; char c = Getchar();
	while(!isdigit(c)){ if(c == ‘-‘) f = -1; c = Getchar(); }
	while(isdigit(c)){ x = x * 10 + c - ‘0‘; c = Getchar(); }
	return x * f;
}

#define maxn 100010
#define maxbl 320
#define oo (1ll << 60)
#define LL long long

int n, cb, st[maxbl], en[maxbl], blid[maxn];
LL Sa[maxn], addv[maxbl], K[maxbl], cp[maxbl];

struct Vec {
	LL x, y;
	
	Vec() {}
	Vec(LL _, LL __): x(_), y(__) {}
	
	Vec operator + (const Vec& t) const { return Vec(x + t.x, y + t.y); }
	Vec operator - (const Vec& t) const { return Vec(x - t.x, y - t.y); }
	LL operator ^ (const Vec& t) const { return x * t.y - y * t.x; }
} poly[maxbl][maxbl];

void pushdown(int bl) {
	for(int i = st[bl]; i <= en[bl]; i++) Sa[i] += addv[bl] + K[bl] * (i - st[bl] + 1);
	addv[bl] = K[bl] = 0;
	return ;
}
void build_poly(int bl) {
	cp[bl] = 0;
	for(int i = st[bl]; i <= en[bl]; i++) {
		while(cp[bl] > 1 && (poly[bl][cp[bl]] - poly[bl][cp[bl]-1] ^ Vec(i - st[bl] + 1, Sa[i]) - poly[bl][cp[bl]]) >= 0) cp[bl]--;
		poly[bl][++cp[bl]] = Vec(i - st[bl] + 1, Sa[i]);
	}
	return ;
}
void update(int ql, int qr, int k) {
	if(blid[ql] == blid[qr]) {
		int b = blid[ql];
		pushdown(b);
		for(int i = ql; i <= qr; i++) Sa[i] += (LL)k * (i - ql + 1);
		for(int i = qr + 1; i <= en[b]; i++) Sa[i] += (LL)k * (qr - ql + 1);
		build_poly(b);
	}
	else {
		int b = blid[ql];
		pushdown(b);
		for(int i = ql; i <= en[b]; i++) Sa[i] += (LL)k * (i - ql + 1);
		build_poly(b);
		
		b = blid[qr];
		pushdown(b);
		for(int i = st[b]; i <= qr; i++) Sa[i] += (LL)k * (i - ql + 1);
		for(int i = qr + 1; i <= en[b]; i++) Sa[i] += (LL)k * (qr - ql + 1);
		build_poly(b);
		
		for(int i = blid[ql] + 1; i <= blid[qr] - 1; i++) {
			addv[i] += (LL)k * (st[i] - ql);
			K[i] += k;
		}
	}
	for(int i = blid[qr] + 1; i <= cb; i++) addv[i] += (LL)k * (qr - ql + 1);
	return ;
}
LL getans(int bl, int p) {
	if(p > cp[bl]) return -oo;
	return poly[bl][p].x * K[bl] + poly[bl][p].y + addv[bl];
}
LL query(int ql, int qr) {
	LL ans = -oo;
	if(blid[ql] == blid[qr]) {
		int b = blid[ql];
		pushdown(b); build_poly(b);
		for(int i = ql; i <= qr; i++) ans = max(ans, Sa[i]);
		return ans;
	}
	int b = blid[ql];
	pushdown(b); build_poly(b);
	for(int i = ql; i <= en[b]; i++) ans = max(ans, Sa[i]);
	
	b = blid[qr];
	pushdown(b); build_poly(b);
	for(int i = st[b]; i <= qr; i++) ans = max(ans, Sa[i]);
	
	for(int i = blid[ql] + 1; i <= blid[qr] - 1; i++) {
		int l = 1, r = cp[i];
		while(l < r) {
			int mid = l + r >> 1;
			if(getans(i, mid) <= getans(i, mid + 1)) l = mid + 1;
			else r = mid;
		}
		ans = max(ans, getans(i, l));
	}
	
	return ans;
}

int main() {
	n = read();
	for(int i = 1; i <= n; i++) Sa[i] = Sa[i-1] + read();
	
	int m = sqrt(n + .5);
	for(int i = 1; i <= n; i++) {
		int bl = (i - 1) / m + 1; cb = max(cb, bl);
		blid[i] = bl;
		if(!st[bl]) st[bl] = i; en[bl] = i;
	}
	for(int i = 1; i <= cb; i++) build_poly(i);
	
	int q = read();
	while(q--) {
		int tp = read();
		if(!tp) {
			int ql = read(), qr = read(), k = read();
			update(ql, qr, k);
		}
		else {
			int ql = read(), qr = read();
			printf("%lld\n", query(ql, qr));
		}
	}
	
	return 0;
}