线段树单点修改区间修改单点查询值区间查询最大值最小值区间和之模板

Posted 2021-03-11 st-lovaer

毕生所学。

 1 const int N = 2e5 + 10;
 2 #define lson rt << 1      // == rt * 2     左儿子
 3 #define rson rt << 1 | 1  // == rt * 2 + 1 右儿子
 4 #define int_mid int mid = tree[rt].l + tree[rt].r >> 1
 5 int a[N]; // 初始值
 6 struct node {
 7     int l, r;
 8     ll val, lazy;
 9 } tree[N * 4];
10 void push_up(int rt) {
11     //tree[rt].val = min(tree[lson].val, tree[rson].val);
12     //tree[rt].val = max(tree[lson].val, tree[rson].val);
13     tree[rt].val = tree[lson].val + tree[rson].val;
14 }
15 void push_down(int rt) {
16     if (tree[rt].lazy) {
17         tree[lson].lazy += tree[rt].lazy;
18         tree[rson].lazy += tree[rt].lazy;
19         //{ // 维护最大最小值
20         //    tree[lson].val += tree[rt].lazy;
21         //    tree[rson].val += tree[rt].lazy;
22         //}
23         { // 维护和
24             int l = tree[rt].l, r = tree[rt].r;
25             int mid = l + r >> 1;
26             tree[lson].val += 1ll * (mid - l + 1) * tree[rt].lazy;
27             tree[rson].val += 1ll * (r - mid) * tree[rt].lazy;
28         }
29         tree[rt].lazy = 0;
30     }
31 }
32 void build(int rt, int l, int r) { // 建树
33     tree[rt].l = l, tree[rt].r = r;
34     tree[rt].lazy = 0;
35     if (l == r) {
36         tree[rt].val = a[l]; // 给定一个初始值
37         return;
38     } else {
39         int mid = l + r >> 1; // (l + r) / 2
40         build(lson, l, mid);
41         build(rson, mid + 1, r);
42         push_up(rt);
43     }
44 }
45  
46 void update_point(int rt, int pos, ll val) { // 单点更新
47     if (tree[rt].l == tree[rt].r && pos == tree[rt].l) {
48         tree[rt].val += val;
49         return;
50     }
51     int_mid;
52     if (pos <= mid) update_point(lson, pos, val);
53     else update_point(rson, pos, val);
54     push_up(rt);
55 }
56  
57 void update_interval(int rt, int l, int r, ll val) { // 区间更新
58     if (l <= tree[rt].l && r >= tree[rt].r) {
59         tree[rt].lazy += val;
60         //tree[rt].val += val; // 维护最大最小值
61         tree[rt].val += 1ll * (tree[rt].r - tree[rt].l + 1) * val; // 维护和 
62         return;
63     }
64     push_down(rt);
65     int_mid;
66     if (l <= mid) update_interval(lson, l, r, val);
67     if (r > mid) update_interval(rson, l, r, val);
68     push_up(rt);
69 }
70  
71 ll query_point(int rt, int pos) { // 单点查询
72     if (tree[rt].l == tree[rt].r && tree[rt].l == pos)
73         return tree[rt].val;
74     push_down(rt);
75     int_mid;
76     if (pos <= mid) query_point(lson, pos);
77     else query_point(rson, pos);
78 }
79  
80 ll query_interval(int rt, int l, int r) { // 区间查询
81     if (l <= tree[rt].l && r >= tree[rt].r)
82         return tree[rt].val;
83     push_down(rt);
84     int_mid;
85     if (r <= mid) return query_interval(lson, l, r);
86     else if (l > mid) return query_interval(rson, l, r);
87     else {
88         //return min(query_interval(lson, l, mid), query_interval(rson, mid + 1, r));
89         //return max(query_interval(lson, l, mid), query_interval(rson, mid + 1, r));
90         return query_interval(lson, l, mid) + query_interval(rson, mid + 1, r);
91     }
92 }