bzoj4355 Play with sequence（吉司机线段树）题解

Posted 2022-10-22 kirinsb

题意：

已知\(n\)个数字，进行以下操作：

• \(1.\)区间\([L,R]\) 赋值为\(x\)
• \(2.\)区间\([L,R]\) 赋值为\(max(a[i] + x, 0)\)
• \(3.\)区间\([L,R]\) 询问\(0\)个数

已知初始值\(\geq 0\)，\(x\geq0\)。

思路：

吉司机线段树。
操作\(1\)可以直接打覆盖标记。
操作\(2\)可以分为两步：区间加\(x\)，然后取区间\(max(a[i],0)\)。
操作\(3\)只要维护最小值的个数，因为不管怎么操作最后的值都\(\geq0\)，然后查询的时候判最小值是不是\(0\)。
注意覆盖的时候，要把次小值初始化为\(INF\)。

代码：

#include<map>
#include<set>
#include<queue>
#include<cmath>
#include<stack>
#include<ctime>
#include<vector>
#include<cstdio>
#include<string>
#include<cstring>
#include<sstream>
#include<iostream>
#include<algorithm>
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
const int maxn = 5e5 + 5;
const int MAXM = 3e6;
const ll MOD = 998244353;
const ull seed = 131;
const ll INF = 1e16;

#define lson (rt << 1)
#define rson (rt << 1 | 1)
int a[maxn];
ll Min[maxn << 2], sMin[maxn << 2], add[maxn << 2], cov[maxn << 2];
int Minlen[maxn << 2];
inline void pushup(int rt)
    if(Min[lson] > Min[rson])
        Min[rt] = Min[rson];
        Minlen[rt] = Minlen[rson];
        sMin[rt] = min(sMin[rson], Min[lson]);
    
    if(Min[lson] < Min[rson])
        Min[rt] = Min[lson];
        Minlen[rt] = Minlen[lson];
        sMin[rt] = min(sMin[lson], Min[rson]);
    
    if(Min[lson] == Min[rson])
        Min[rt] = Min[lson];
        Minlen[rt] = Minlen[lson] + Minlen[rson];
        sMin[rt] = min(sMin[lson], sMin[rson]);
    

inline void pushdown(int rt, int l, int r)
    int m = (l + r) >> 1;
    if(cov[rt] != -1)
        Min[lson] = Min[rson] = cov[rt];
        sMin[lson] = sMin[rson] = INF;  //careful！！！！
        cov[lson] = cov[rson] = cov[rt];
        add[lson] = add[rson] = 0;
        Minlen[lson] = m - l + 1;
        Minlen[rson] = r - m;
        cov[rt] = -1;
    
    if(add[rt])
        Min[lson] += add[rt], sMin[lson] += add[rt];
        Min[rson] += add[rt], sMin[rson] += add[rt];
        add[lson] += add[rt], add[rson] += add[rt];
        add[rt] = 0;
    
    if(Min[lson] < Min[rt])
        if(sMin[lson] == Min[lson]) sMin[lson] = Min[rt];
        Min[lson] = Min[rt];
    
    if(Min[rson] < Min[rt])
        if(sMin[rson] == Min[rson]) sMin[rson] = Min[rt];
        Min[rson] = Min[rt];
    

void build(int l, int r, int rt)
    cov[rt] = -1, add[rt] = 0;
    if(l == r)
        Min[rt] = a[l];
        sMin[rt] = INF;
        Minlen[rt] = 1;
        return;
    
    int m = (l + r) >> 1;
    build(l, m, lson);
    build(m + 1, r, rson);
    pushup(rt);

void cover(int L, int R, int l, int r, ll v, int rt)
    if(L <= l && R >= r)
        cov[rt] = v;
        add[rt] = 0;
        Min[rt] = v;
        sMin[rt] = INF; //careful！！！！
        Minlen[rt] = r - l + 1;
        return;
    
    pushdown(rt, l, r);
    int m = (l + r) >> 1;
    if(L <= m)
        cover(L, R, l, m, v, lson);
    if(R > m)
        cover(L, R, m + 1, r, v, rson);
    pushup(rt);

void update(int L, int R, int l, int r, ll v, int rt)
    if(L <= l && R >= r)
        Min[rt] += v;
        sMin[rt] += v;
        add[rt] += v;
        return;
    
    pushdown(rt, l, r);
    int m = (l + r) >> 1;
    if(L <= m)
        update(L, R, l, m, v, lson);
    if(R > m)
        update(L, R, m + 1, r, v, rson);
    pushup(rt);

void Less(int L, int R, int l, int r, ll v, int rt)
    if(Min[rt] >= v) return;
    if(L <= l && R >= r && sMin[rt] > v)   //>保证Minlen不变
        Min[rt] = v;
        return;
    
    pushdown(rt, l, r);
    int m = (l + r) >> 1;
    if(L <= m)
        Less(L, R, l, m, v, lson);
    if(R > m)
        Less(L, R, m + 1, r, v, rson);
    pushup(rt);

int querySum(int L, int R, int l, int r, int rt)
    if(L <= l && R >= r)
        return Min[rt] == 0? Minlen[rt] : 0;
    
    pushdown(rt, l, r);
    int m = (l + r) >> 1;
    int ret = 0;
    if(L <= m)
        ret += querySum(L, R, l, m, lson);
    if(R > m)
        ret += querySum(L, R, m + 1, r, rson);
    return ret;

inline bool read(int &num)
    char in;
    bool IsN=false;
    in = getchar();
    if(in == EOF) return false;
    while(in != '-' && (in < '0' || in > '9')) in = getchar();
    if(in == '-') IsN = true; num = 0;
    else num = in - '0';
    while(in = getchar(),in >= '0' && in <= '9')
            num *= 10, num += in-'0';
    
    if(IsN) num = -num;
    return true;

int main()
    int n, m;
    read(n), read(m);
    for(int i = 1; i <= n; i++) read(a[i]);
    build(1, n, 1);
    while(m--)
        int l, r, x, op;
        read(op), read(l), read(r);
        if(op < 3) read(x);
        if(op == 1) cover(l, r, 1, n, x, 1);
        else if(op == 2) update(l, r, 1, n, x, 1), Less(l, r, 1, n, 0, 1);
        else printf("%d\n", querySum(l, r, 1, n, 1));
    
    return 0;