BZOJ 1935 园丁的烦恼

园丁的烦恼

题解:如果 x 和 y 足够小的话, 我们就可以用2维树状数组去单点修改,区间查询去计算答案。但是现在 x 和 y 都足够大, 我们没办法去这样操作。

现在我们转换思路,按 x 为第一权重, y 为第二权重去排序, 这样我们就可以只用一颗树状数组去维护 x到当前为止y的数目。

然后对于查询来说,我们把一个矩阵的查询分为4次查询, 用差分的思想维护。还是和树状数组2维查询区间的时候,对于一个矩阵(x1,y1)(左下角的点) (x2,y2)(右上角的点), 我们把这个查询拆成4个点

即到(x1-1,y1-1),(x2,y2)为止所出现的点的数目加到对应的答案里,然后删掉到(x1-1,y2), (x2,y1-1)为止出现的数目。这样对于这个矩阵我们就计算完了答案。

代码:

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 #define Fopen freopen("_in.txt","r",stdin); freopen("_out.txt","w",stdout);
 4 #define LL long long
 5 #define ULL unsigned LL
 6 #define fi first
 7 #define se second
 8 #define pb emplace_back
 9 #define lson l,m,rt<<1
10 #define rson m+1,r,rt<<1|1
11 #define lch(x) tr[x].son[0]
12 #define rch(x) tr[x].son[1]
13 #define max3(a,b,c) max(a,max(b,c))
14 #define min3(a,b,c) min(a,min(b,c))
15 typedef pair<int,int> pll;
16 const int inf = 0x3f3f3f3f;
17 const LL INF = 0x3f3f3f3f3f3f3f3f;
18 const LL mod =  (int)1e9+7;
19 const int N = 3e6 + 100;
20 const int M = 1e7 + 100;
21 int tree[M];
22 inline int lowbit(int x){
23     return x & (-x);
24 }
25 void Add(int x){
26     for(int i = x; i < M; i+=lowbit(i))
27         tree[i] += 1;
28 }
29 int Query(int x){
30     int ret = 0;
31     for(int i = x; i; i -= lowbit(i)){
32         ret += tree[i];
33     }
34     return ret;
35 }
36 int ans[N];
37 struct Node{
38     int x, y, op, id;
39     bool operator< (const Node & node) const{
40         if(x != node.x) return x < node.x;
41         if(y != node.y) return y < node.y;
42         return op < node.op;
43     }
44 }A[N];
45 int tot = 0;
46 void nownode(int x, int y, int op, int id){
47     tot++;
48     //if(id) cout << x << " " << y << " " << op << " " << id << endl;
49     A[tot].x = x;
50     A[tot].y = y;
51     A[tot].op = op;
52     A[tot].id = id;
53 }
54 int main(){
55     int n, m, x, y, x1, y1, id, op;
56     scanf("%d%d", &n, &m);
57     for(int i = 1; i <= n; i++){
58         scanf("%d%d", &x, &y);
59         ++x;
60         ++y;
61         nownode(x, y, 0, 0);
62     }
63     for(int i = 1; i <= m; i++){
64         scanf("%d%d%d%d", &x, &y, &x1, &y1);
65         ++x; ++y; ++x1; ++y1;
66         nownode(x1, y1, 1, i);
67         nownode(x-1, y-1, 1, i);
68         nownode(x-1, y1, 2, i);
69         nownode(x1, y-1, 2, i);
70     }
71     sort(A+1, A+1+tot);
72     for(int i = 1; i <= tot; i++){
73         y = A[i].y;id = A[i].id, op = A[i].op;
74         //cout << y << " " << id << " " << op << endl;
75         if(!op) Add(y);
76         else if(op == 1) ans[id] += Query(y);
77         else ans[id] -= Query(y);
78     }
79     for(int i = 1; i <= m; i++){
80         printf("%d
", ans[i]);
81     }
82     return 0;
83 }
View Code
原文地址:https://www.cnblogs.com/MingSD/p/9745210.html