[SCOI2010]序列操作 BZOJ1858 线段树

题目描述

lxhgww最近收到了一个01序列，序列里面包含了n个数，这些数要么是0，要么是1，现在对于这个序列有五种变换操作和询问操作：

0 a b 把[a, b]区间内的所有数全变成0

1 a b 把[a, b]区间内的所有数全变成1

2 a b 把[a,b]区间内的所有数全部取反，也就是说把所有的0变成1，把所有的1变成0

3 a b 询问[a, b]区间内总共有多少个1

4 a b 询问[a, b]区间内最多有多少个连续的1

对于每一种询问操作，lxhgww都需要给出回答，聪明的程序员们，你们能帮助他吗？

输入输出格式

输入格式：

输入数据第一行包括2个数，n和m，分别表示序列的长度和操作数目

第二行包括n个数，表示序列的初始状态

接下来m行，每行3个数，op, a, b，（0<=op<=4，0<=a<=b<n）表示对于区间[a, b]执行标号为op的操作

输出格式：

对于每一个询问操作，输出一行，包括1个数，表示其对应的答案

输入输出样例

输入样例#1：
复制

10 10
   0 0 0 1 1 0 1 0 1 1
   1 0 2
   3 0 5
   2 2 2
   4 0 4
   0 3 6
   2 3 7
   4 2 8
   1 0 5
   0 5 6
   3 3 9

输出样例#1： 复制

5
2
6
5

说明

对于30%的数据，1<=n, m<=1000

对于100%的数据，1<=n, m<=100000

很刺激的线段树题目；

注意赋值的操作的优先级>翻转的操作；

还有很多细节要注意；

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<string>
#include<cmath>
#include<map>
#include<set>
#include<vector>
#include<queue>
#include<bitset>
#include<ctime>
#include<deque>
#include<stack>
#include<functional>
#include<sstream>
//#include<cctype>
//#pragma GCC optimize(2)
using namespace std;
#define maxn 300005
#define inf 0x3f3f3f3f
#define INF 9999999999
#define rdint(x) scanf("%d",&x)
#define rdllt(x) scanf("%lld",&x)
#define rdult(x) scanf("%lu",&x)
#define rdlf(x) scanf("%lf",&x)
#define rdstr(x) scanf("%s",x)
typedef long long  ll;
typedef unsigned long long ull;
typedef unsigned int U;
#define ms(x) memset((x),0,sizeof(x))
const long long int mod = 1e9 + 7;
#define Mod 1000000000
#define sq(x) (x)*(x)
#define eps 1e-3
typedef pair<int, int> pii;
#define pi acos(-1.0)
const int N = 1005;
#define REP(i,n) for(int i=0;i<(n);i++)
typedef pair<int, int> pii;
inline ll rd() {
	ll x = 0;
	char c = getchar();
	bool f = false;
	while (!isdigit(c)) {
		if (c == '-') f = true;
		c = getchar();
	}
	while (isdigit(c)) {
		x = (x << 1) + (x << 3) + (c ^ 48);
		c = getchar();
	}
	return f ? -x : x;
}

ll gcd(ll a, ll b) {
	return b == 0 ? a : gcd(b, a%b);
}
ll sqr(ll x) { return x * x; }

/*ll ans;
ll exgcd(ll a, ll b, ll &x, ll &y) {
	if (!b) {
		x = 1; y = 0; return a;
	}
	ans = exgcd(b, a%b, x, y);
	ll t = x; x = y; y = t - a / b * y;
	return ans;
}
*/

ll qpow(ll a, ll b, ll c) {
	ll ans = 1;
	a = a % c;
	while (b) {
		if (b % 2)ans = ans * a%c;
		b /= 2; a = a * a%c;
	}
	return ans;
}

struct node {
	int sum;
	int Lw, Lb;// Lb:区间连续0的最大长度，Lw:连续1的最大长度
	int llw, rlw;//llb:区间左端点连续0的最大长度，llw:区间左端点连续1的最大长度；
	int llb, rlb;// rlb:区间右端点连续0的最大长度；rlw：区间右端点连续1的最大长度
	int lazy, rev;// lazy：是否全部变为1/0；rev：翻转标记
}tr[maxn<<2];
int n, m;
#define lson (rt<<1)
#define rson (rt<<1|1)
#define mid ((l+r)>>1)
void pushup(int l, int r, int rt) {
	tr[rt].sum = tr[lson].sum + tr[rson].sum;

	tr[rt].Lb = max(tr[lson].Lb, tr[rson].Lb);
	tr[rt].Lw = max(tr[lson].Lw, tr[rson].Lw);

	tr[rt].llb = tr[lson].llb;
	tr[rt].llw = tr[lson].llw;
	if (tr[lson].llw == mid - l + 1)tr[rt].llw += tr[rson].llw;
	if (tr[lson].llb == mid - l + 1)tr[rt].llb += tr[rson].llb;

	tr[rt].rlb = tr[rson].rlb;
	tr[rt].rlw = tr[rson].rlw;
	if (tr[rson].rlb == r - mid)tr[rt].rlb += tr[lson].rlb;
	if (tr[rson].rlw == r - mid)tr[rt].rlw += tr[lson].rlw;

	tr[rt].Lw = max(tr[rt].Lw, tr[lson].rlw + tr[rson].llw);
	tr[rt].Lb = max(tr[rt].Lb, tr[lson].rlb + tr[rson].llb);
}

void down(int l, int r, int rt) {
	int lazy = tr[rt].lazy, rev = tr[rt].rev;
	int L1 = mid - l + 1, L2 = r - mid;
	tr[rt].lazy = -1;
	if (lazy == 0) {
		tr[lson] = node { 0, 0, L1, 0, 0, L1, L1, 0, 0 };
		tr[rson] = node{ 0,0,L2,0,0,L2,L2,0,0 };
	}
	else if (lazy == 1) {
		tr[lson] = node{ L1,L1,0,L1,L1,0,0,1,0 };
		tr[rson] = node{ L2,L2,0,L2,L2,0,0,1,0 };
	}
	if (rev) {
		tr[rt].rev = 0;
		int sum = tr[lson].sum;
		int Lw = tr[lson].Lw, Lb = tr[lson].Lb;
		int llw = tr[lson].llw, llb = tr[lson].llb;
		int rlw = tr[lson].rlw, rlb = tr[lson].rlb;
		tr[lson].sum = L1 - sum;
		tr[lson].Lw = Lb; tr[lson].Lb = Lw;
		tr[lson].llw = llb; tr[lson].rlw = rlb;
		tr[lson].llb = llw; tr[lson].rlb = rlw;
		tr[lson].rev ^= 1;

		sum = tr[rson].sum;
		Lw = tr[rson].Lw; Lb = tr[rson].Lb;
		llw = tr[rson].llw; llb = tr[rson].llb;
		rlw = tr[rson].rlw; rlb = tr[rson].rlb;
		tr[rson].sum = L2 - sum;
		tr[rson].Lw = Lb; tr[rson].Lb = Lw;
		tr[rson].llw = llb; tr[rson].rlw = rlb;
		tr[rson].llb = llw; tr[rson].rlb = rlw;
		tr[rson].rev ^= 1;

	}
}

void build(int l, int r, int rt) {
	tr[rt].lazy = -1;
	if (l == r) {
		int x; rdint(x);
		tr[rt] = node{ x,x,(x ^ 1),x,x,(x ^ 1),(x ^ 1),-1,0 };
		return;
	}
	build(l, mid, lson); build(mid + 1, r, rson);
	pushup(l, r, rt);
}

void upd1(int l, int r, int rt, int L, int R) {
	if (L <= l && r <= R) {
		int LL = r - l + 1;
		tr[rt] = node{ 0,0,LL,0,0,LL,LL,0,0 };
		return;
	}
	if (l > R || r < L)return;
	down(l, r, rt);
	upd1(l, mid, lson, L, R); upd1(mid + 1, r, rson, L, R);
	pushup(l, r, rt);
}

void upd2(int l, int r, int rt, int L, int R) {
	if (L <= l && r <= R) {
		int LL = r - l + 1;
		tr[rt] = node{ LL,LL,0,LL,LL,0,0,1,0 };
		return;
	}
	if (l > R || r < L)return;
	down(l, r, rt);
	upd2(l, mid, lson, L, R); upd2(mid + 1, r, rson, L, R);
	pushup(l, r, rt);
}

void upd3(int l, int r, int rt, int L, int R) {
	if (L <= l && r <= R) {
		int LL = r - l + 1, sum = tr[rt].sum, Lw = tr[rt].Lw, Lb = tr[rt].Lb;
		int llw = tr[rt].llw, llb = tr[rt].llb;
		int rlw = tr[rt].rlw, rlb = tr[rt].rlb;
		tr[rt] = node{ LL - sum,Lb,Lw,llb,rlb,llw,rlw,tr[rt].lazy,(tr[rt].rev ^ 1) };
		return;
	}
	if (l > R || r < L)return;
	down(l, r, rt);
	upd3(l, mid, lson, L, R);
	upd3(mid + 1, r, rson, L, R);
	pushup(l, r, rt);
}

int query1(int l, int r, int rt, int L, int R) {
	if (L <= l && r <= R)return tr[rt].sum;
	if (l > R || r < L)return 0;
	down(l, r, rt);
	return query1(l, mid, lson, L, R) + query1(mid + 1, r, rson, L, R);
}

node query2(int l, int r, int rt, int L, int R) {
	if (L <= l && r <= R)return tr[rt];
	if (l > R || r < L)return node{ 0 };
	down(l, r, rt);
	node LL = query2(l, mid, lson, L, R), RR = query2(mid + 1, r, rson, L, R), ans;
	ans.sum = LL.sum + RR.sum;
	ans.Lw = max(LL.Lw, RR.Lw);
	ans.Lb = max(LL.Lb, RR.Lb);
	ans.llw = LL.llw, ans.rlw = RR.rlw;
	ans.llb = LL.llb, ans.rlb = RR.rlb;
	if (LL.llb == mid - l + 1)ans.llb += RR.llb;
	if (LL.llw == mid - l + 1)ans.llw += RR.llw;
	if (RR.rlb == r - mid)ans.rlb += LL.rlb;
	if (RR.rlw == r - mid)ans.rlw += LL.rlw;
	ans.Lw = max(ans.Lw, LL.rlw + RR.llw);
	ans.Lb = max(ans.Lb, LL.rlb + RR.llb);
	return ans;
}

int main()
{
	//ios::sync_with_stdio(0);
	rdint(n); rdint(m);
	build(1, n, 1);
	while (m--) {
		int op, a, b;
		rdint(op); rdint(a); rdint(b);
		a++; b++;
		if (op == 0)upd1(1, n, 1, a, b);
		if (op == 1)upd2(1, n, 1, a, b);
		if (op == 2)upd3(1, n, 1, a, b);
		if (op == 3)cout << query1(1, n, 1, a, b) << endl;
		if (op == 4)cout << query2(1, n, 1, a, b).Lw << endl;
	}
	return 0;
}