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

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 }