题意：查询区间中位数
思路：模板题，相当于区间第K大的数，主席树可以水过，但划分树是正解。但还没搞明白划分树，先上模板
1 #include <iostream>
2 #include <cstdio>
3 #include <cmath>
4 #include <cstring>
5 #include <cstdlib>
6 #include <string>
7 #include <vector>
8 #include <algorithm>
9 #include <set>
10 #define repu(i,a,b) for(int i=a;i<b;i++)
11 using namespace std;
12 #define N 1000010
13 #define ll long long
14 #define _cle(m, a) memset(m, a, sizeof(m))
15 const int MAXN = 100010;
16 const int M = MAXN * 30;
17 int n,q,m,tot;
18 int a[MAXN], t[MAXN];
19 int T[MAXN], lson[M], rson[M], c[M];
20 void Init_Hash()
21 {
22 for(int i = 1; i <= n; i++)
23 t[i] = a[i];
24 sort(t+1,t+1+n);
25 m = unique(t+1,t+1+n) -t-1;
26 }
27 int build(int l, int r)
28 {
29 int root = tot++;
30 c[root] = 0;
31 if(l != r)
32 {
33 int mid = (l+r)>>1;
34 lson[root] = build(l,mid);
35 rson[root] = build(mid+1,r);
36 }
37 return root;
38 }
39 int Hash(int x)
40 {
41 return lower_bound(t+1,t+1+m,x) - t;
42 }
43 int update(int root, int pos, int val)
44 {
45 int newroot = tot++, tmp = newroot;
46 c[newroot] = c[root] + val;
47 int l = 1, r = m;
48 while(l < r)
49 {
50 int mid = (l+r)>>1;
51 if(pos <= mid)
52 {
53 lson[newroot] = tot++;
54 rson[newroot] = rson[root];
55 newroot = lson[newroot];
56 root = lson[root];
57 r = mid;
58 }
59 else
60 {
61 rson[newroot] = tot++;
62 lson[newroot] = lson[root];
63 newroot = rson[newroot];
64 root = rson[root];
65 l = mid+1;
66 }
67 c[newroot] = c[root] + val;
68 }
69 return tmp;
70 }
71 int query(int left_root, int right_root, int k)
72 {
73 int l = 1, r = m;
74 while( l < r)
75 {
76 int mid = (l+r)>>1;
77 if(c[lson[left_root]] -c[lson[right_root]] >= k )
78 {
79 r = mid;
80 left_root = lson[left_root];
81 right_root = lson[right_root];
82 }
83 else
84 {
85 l = mid + 1;
86 k -= c[lson[left_root]] - c[lson[right_root]];
87 left_root = rson[left_root];
88 right_root = rson[right_root];
89 }
90 }
91 return l;
92 }
93 int main()
94 {
95 //freopen("in.txt","r", stdin);
96 //freopen("out.txt","w", stdout);
97 int kase = 1;
98 while(scanf("%d",&n) == 1)
99 {
100 tot = 0;
101 for(int i = 1; i <= n; i++)
102 scanf("%d",&a[i]);
103 Init_Hash();
104 T[n+1] = build(1,m);
105 for(int i = n; i ; i--)
106 {
107 int pos = Hash(a[i]);
108 T[i] = update(T[i+1],pos,1);
109 }
110 printf("Case %d:\n",kase++);
111 scanf("%d",&q);
112 while(q--)
113 {
114 int l,r,k;
115 scanf("%d%d",&l,&r);
116 k = (r-l)/2+1;
117 printf("%d\n",t[query(T[l],T[r+1],k)]);
118 }
119 }
120 return 0;
121 }
主席树
先上KB模板
1 //划分树
2 #include<cstdio>
3 #include<cstring>
4 #include<algorithm>
5 using namespace std;
6 const int MAXN=100010;
7 int tree[20][MAXN];//表示每层每个位置的值
8 int sorted[MAXN];//已经排序好的数
9 int toleft[20][MAXN];//toleft[p][i]表示第i层从1到i有数分入左边
10 void build(int l,int r,int dep){
11 if(l==r)return;
12 int mid=(l+r)>>1;
13 int same=mid-l+1;//表示等于中间值而且被分入左边的个数
14 for(int i=l;i<=r;i++)//注意是l,不是one
15 if(tree[dep][i]<sorted[mid]) same--;
16 int lpos=l;
17 int rpos=mid+1;
18 for(int i=l;i<=r;i++){
19 if(tree[dep][i]<sorted[mid]) tree[dep+1][lpos++]=tree[dep][i];
20 else if(tree[dep][i]==sorted[mid]&&same>0){
21 tree[dep+1][lpos++]=tree[dep][i];
22 same--;
23 }
24 else tree[dep+1][rpos++]=tree[dep][i];
25 toleft[dep][i]=toleft[dep][l-1]+lpos-l;
26 }
27 build(l,mid,dep+1);
28 build(mid+1,r,dep+1);
29 }
30 //查询区间第k大的数,[L,R]是大区间,[l,r]是要查询的小区间
31 int query(int L,int R,int l,int r,int dep,int k){
32 if(l==r)return tree[dep][l];
33 int mid=(L+R)>>1;
34 int cnt=toleft[dep][r]-toleft[dep][l-1];
35 if(cnt>=k){
36 int newl=L+toleft[dep][l-1]-toleft[dep][L-1];int newr=newl+cnt-1;
37 return query(L,mid,newl,newr,dep+1,k);
38 }
39 else{
40 int newr=r+toleft[dep][R]-toleft[dep][r],newl=newr-(r-l-cnt);
41 return query(mid+1,R,newl,newr,dep+1,k-cnt);
42 }
43 }
44 int main(){
45 int n,m,t=0;
46 while(~scanf("%d",&n)){
47 memset(tree,0,sizeof(tree));
48 for(int i=1;i<=n;i++){
49 scanf("%d",&tree[0][i]);
50 sorted[i]=tree[0][i];
51 }
52 sort(sorted+1,sorted+n+1);
53 build(1,n,0);
54 scanf("%d",&m);
55 printf("Case %d:\n",++t);
56 int s,t,k;
57 while(m--){
58 scanf("%d%d",&s,&t);
59 k=(t-s+2)/2;
60 printf("%d\n",query(1,n,s,t,0,k));
61 }
62 }
63 return 0;
64 }
划分树
时间： 2024-10-25 10:19:27