线段树（最值）

实现的功能：区间加、区间赋最值、区间和查询、区间最值查询

时间复杂度：单次操作O(log^2(n))

N5e5,Q5e5->LOJ 1.2s/200MB

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
class MxSegTree{
    struct data{
        ll mx,mx2,cntmax,lazymax; //最大值，次大值，最大值个数，最大值标记
        ll mn,mn2,cntmin,lazymin; //最小值，次小值，最小值个数，最小值标记
        ll lazyadd,sum; // 增加标记，区间和
        data(){mx=mx2=-INF;mn=mn2=INF;cntmax=cntmin=0;lazymax=-INF;lazymin=INF;lazyadd=0;sum=0;}
    };
    vector<data> tree;
    vector<ll> *arr;
    long n,n5,root,end;

    void push_add(ll cl, ll cr, ll p,ll v){
        tree[p].sum += (cr - cl + 1) * v;
        tree[p].mx += v, tree[p].mn += v;
        if (tree[p].mx2 != -INF) tree[p].mx2 += v;
        if (tree[p].mn2 != INF) tree[p].mn2 += v;
        if (tree[p].lazymax != -INF) tree[p].lazymax += v;
        if (tree[p].lazymin != INF) tree[p].lazymin += v;
        tree[p].lazyadd += v;
    }
    void push_min(ll p, ll tg){
        if (tree[p].mx <= tg) return;
        tree[p].sum += (tg * 1ll - tree[p].mx) * tree[p].cntmax;
        if (tree[p].mn2 == tree[p].mx) tree[p].mn2 = tg;  
        if (tree[p].mn == tree[p].mx) tree[p].mn = tg;  
        if (tree[p].lazymax > tg) tree[p].lazymax = tg; 
        tree[p].mx = tg, tree[p].lazymin = tg;
    }
    void push_max(ll p, ll tg){
        if (tree[p].mn > tg) return;
        tree[p].sum += (tg * 1ll - tree[p].mn) * tree[p].cntmin;
        if (tree[p].mx2 == tree[p].mn) tree[p].mx2 = tg;
        if (tree[p].mx == tree[p].mn) tree[p].mx = tg;
        if (tree[p].lazymin < tg) tree[p].lazymin = tg;
        tree[p].mn = tg, tree[p].lazymax = tg;
    }
    //用子节点维护当前节点信息
    void push_up(ll p) {
        tree[p].sum = tree[p * 2].sum + tree[p * 2 + 1].sum;
        if (tree[p * 2].mx == tree[p * 2 + 1].mx) {
            tree[p].mx = tree[p * 2].mx, tree[p].cntmax = tree[p * 2].cntmax + tree[p * 2 + 1].cntmax;
            tree[p].mx2 = max(tree[p * 2].mx2, tree[p * 2 + 1].mx2);
        } else if (tree[p * 2].mx > tree[p * 2 + 1].mx) {
            tree[p].mx = tree[p * 2].mx, tree[p].cntmax = tree[p * 2].cntmax;
            tree[p].mx2 = max(tree[p * 2].mx2, tree[p * 2 + 1].mx);
        } else {
            tree[p].mx = tree[p * 2 + 1].mx, tree[p].cntmax = tree[p * 2 + 1].cntmax;
            tree[p].mx2 = max(tree[p * 2].mx, tree[p * 2 + 1].mx2);
        }
        if (tree[p * 2].mn == tree[p * 2 + 1].mn) {
            tree[p].mn = tree[p * 2].mn, tree[p].cntmin = tree[p * 2].cntmin + tree[p * 2 + 1].cntmin;
            tree[p].mn2 = min(tree[p * 2].mn2, tree[p * 2 + 1].mn2);
        } else if (tree[p * 2].mn < tree[p * 2 + 1].mn) {
            tree[p].mn = tree[p * 2].mn, tree[p].cntmin = tree[p * 2].cntmin;
            tree[p].mn2 = min(tree[p * 2].mn2, tree[p * 2 + 1].mn);
        } else {
            tree[p].mn = tree[p * 2 + 1].mn, tree[p].cntmin = tree[p * 2 + 1].cntmin;
            tree[p].mn2 = min(tree[p * 2].mn, tree[p * 2 + 1].mn2);
        }
    }
    //下放标记
    void push_down(ll cl, ll cr, ll p) { 
        ll cm = cl + (cr - cl) / 2;
        if(tree[p].lazyadd) push_add(cl, cm, p * 2, tree[p].lazyadd), push_add(cm + 1, cr, p * 2 + 1, tree[p].lazyadd);
        if(tree[p].lazymax != -INF) push_max(p * 2, tree[p].lazymax), push_max(p * 2 + 1, tree[p].lazymax);
        if(tree[p].lazymin != INF) push_min(p * 2, tree[p].lazymin), push_min(p * 2 + 1, tree[p].lazymin);
        tree[p].lazyadd = 0, tree[p].lazymax = -INF, tree[p].lazymin = INF;
    }

    void build(ll s, ll t, ll p) {
        tree[p].lazymax = -INF, tree[p].lazymin = INF;
        if (s == t) {
            tree[p].sum = tree[p].mx = tree[p].mn = (*arr)[s];
            tree[p].mx2 = -INF, tree[p].mn2 = INF;
            tree[p].cntmax = tree[p].cntmin = 1;
            return;
        }
        ll m = s + (t - s) / 2;
        build(s, m, p * 2);
        build(m + 1, t, p * 2 + 1);
        push_up(p);
    }

    void range_add(ll l, ll r, ll v, ll cl, ll cr, ll p) {
        if(cl > r || cr < l) return;
        if (l <= cl && cr <= r) return push_add(cl, cr, p, v);
        ll cm = cl + (cr - cl) / 2;
        push_down(cl, cr, p);
        if (l <= cm) range_add(l, r, v, cl, cm, p * 2);
        if (r > cm) range_add(l, r, v, cm + 1, cr, p * 2 + 1);
        push_up(p);
    }
    void range_min(ll l, ll r, ll v, ll cl, ll cr, ll p) {
        if(cl > r || cr < l || tree[p].mx <= v) return;
        if (l <= cl && cr <= r && tree[p].mx2 < v) return push_min(p, v);
        ll cm = cl + (cr - cl) / 2;
        push_down(cl, cr, p);
        if (l <= cm) range_min(l, r, v, cl, cm, p * 2);
        if (r > cm) range_min(l, r, v, cm + 1, cr, p * 2 + 1);
        push_up(p);
    }
    void range_max(ll l, ll r, ll v, ll cl, ll cr, ll p) {
        if(cl > r || cr < l || tree[p].mn >= v) return;
        if (l <= cl && cr <= r && tree[p].mn2 > v) return push_max(p, v);
        ll cm = cl + (cr - cl) / 2;
        push_down(cl, cr, p);
        if (l <= cm) range_max(l, r, v, cl, cm, p * 2);
        if (r > cm) range_max(l, r, v, cm + 1, cr, p * 2 + 1);
        push_up(p);
    }
    
    ll query_sum(ll l, ll r, ll cl, ll cr, ll p) {
        if(cl > r || cr < l) return 0;
        if (l <= cl && cr <= r) return tree[p].sum;
        ll cm = cl + (cr - cl) / 2;
        ll sum = 0;
        push_down(cl, cr, p);
        if (l <= cm) sum += query_sum(l, r, cl, cm, p * 2);
        if (r > cm) sum += query_sum(l, r, cm + 1, cr, p * 2 + 1);
        return sum;
    }
    ll query_max(ll l, ll r, ll cl, ll cr, ll p) {
        if(cl > r || cr < l) return -INF;
        if (l <= cl && cr <= r) return tree[p].mx;
        ll cm = cl + (cr - cl) / 2;
        ll mx = -INF;
        push_down(cl, cr, p);
        if (l <= cm) mx = max(mx, query_max(l, r, cl, cm, p * 2));
        if (r > cm) mx = max(mx, query_max(l, r, cm + 1, cr, p * 2 + 1));
        return mx;
    }
    ll query_min(ll l, ll r, ll cl, ll cr, ll p) {
        if(cl > r || cr < l) return INF;
        if (l <= cl && cr <= r) return tree[p].mn;
        ll cm = cl + (cr - cl) / 2;
        ll mn = INF;
        push_down(cl, cr, p);
        if (l <= cm) mn = min(mn, query_min(l, r, cl, cm, p * 2));
        if (r > cm) mn = min(mn, query_min(l, r, cm + 1, cr, p * 2 + 1));
        return mn;
    }

public:
    explicit MxSegTree(vector<ll> v) {
        n = v.size();
        n5 = n * 5;
        end = n - 1;
        root = 1;
        arr = &v;
        tree.resize(n5);
        build(0, end, 1);
        arr = nullptr;
    }
    // 区间加，O(logn)
    void range_add(ll l, ll r, ll v) { range_add(l, r, v, 0, end, root); }
    // 区间内和k取min，O(log^2(n))
    void range_min(ll l, ll r, ll v) { range_min(l, r, v, 0, end, root); }
    // 区间内和k取max，O(log^2(n))
    void range_max(ll l, ll r, ll v) { range_max(l, r, v, 0, end, root); }
    // 查询区间和，O(logn)
    ll query_sum(ll l, ll r) { return query_sum(l, r, 0, end, root); }
    // 查询区间最大值，O(logn)
    ll query_max(ll l, ll r) { return query_max(l, r, 0, end, root); }
    // 查询区间最小值，O(logn)
    ll query_min(ll l, ll r) { return query_min(l, r, 0, end, root); }
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    ll n,q;cin >> n;
    vector<ll> v(n);
    for(auto &i:v) cin >> i;
    MxSegTree st(v);
    cin >> q;
    ll op,x,y,k;
    while(q--){
        cin >> op;
        if(op == 1){
            cin >> x >> y >> k;
            st.range_add(x-1,y-1,k);
        }else if(op == 2){
            cin >> x >> y >> k;
            st.range_max(x-1,y-1,k);
        }else if(op == 3){
            cin >> x >> y >> k;
            st.range_min(x-1,y-1,k);
        }else if(op == 4){
            cin >> x >> y;
            cout << st.query_sum(x-1,y-1) << endl;
        }else if(op == 5){
            cin >> x >> y;
            cout << st.query_max(x-1,y-1) << endl;
        }else{
            cin >> x >> y;
            cout << st.query_min(x-1,y-1) << endl;
        }
    }
    return 0;
}