主席树（区间第k小的数）

Posted 2022-08-20 zxz666

题目链接： https://www.luogu.org/problem/P3834

首先要离散化，然后主席树模板。

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 #define mid (l+r)/2
 5 using namespace std;
 6 
 7 const int N = 200010;
 8 int n, q, m, cnt = 0;
 9 int a[N], b[N], T[N];
10 int sum[N<<5], L[N<<5], R[N<<5];
11 
12 inline int build(int l, int r)
13 
14     int rt = ++ cnt;
15     sum[rt] = 0;
16     if (l < r)
17         L[rt] = build(l, mid);
18         R[rt] = build(mid+1, r);
19     
20     return rt;
21 
22 
23 inline int update(int pre, int l, int r, int x)
24 
25     int rt = ++ cnt;
26     L[rt] = L[pre]; R[rt] = R[pre]; sum[rt] = sum[pre]+1;
27     if (l < r)
28         if (x <= mid) L[rt] = update(L[pre], l, mid, x);
29         else R[rt] = update(R[pre], mid+1, r, x);
30     
31     return rt;
32 
33 
34 inline int query(int u, int v, int l, int r, int k)
35 
36     if (l >= r) return l;
37     int x = sum[L[v]] - sum[L[u]];
38     if (x >= k) return query(L[u], L[v], l, mid, k);
39     else return query(R[u], R[v], mid+1, r, k-x);
40 
41 
42 int main()
43 
44     scanf("%d%d", &n, &q);
45     for (int i = 1; i <= n; i ++)
46         scanf("%d", &a[i]);
47         b[i] = a[i];
48     
49     sort(b+1, b+1+n);
50     m = unique(b+1, b+1+n)-b-1;
51     T[0] = build(1, m);
52     for (int i = 1; i <= n; i ++)
53         int t = lower_bound(b+1, b+1+m, a[i])-b;
54         T[i] = update(T[i-1], 1, m, t);
55     
56     while (q --)
57         int x, y, z;
58         scanf("%d%d%d", &x, &y, &z);
59         int t = query(T[x-1], T[y], 1, m, z);
60         printf("%d\n", b[t]);
61     
62     return 0;
63