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  • POJ-2104 K-th Number CDQ分治

    题目传送门

    题意:给你一个序列,长度为n,m次询问,询问一段区间的第k大。

    题解:CDQ分治,对整个值域进行分治。每次取一个mid, 计算出整个区间内mid <= 的数目,如果 num >= k, 那么就可以第k大的数一定落在[ l, mid]之间, 否者就会落在 [mid+1, r]之间, 然后我们继续递归二分下去,直到 l == r 那么就找到第k大了。

    代码:

      1 #include<cstdio>
      2 #include<algorithm>
      3 #include<vector>
      4 #include<queue>
      5 #include<iostream>
      6 #include<cstring>
      7 using namespace std;
      8 #define Fopen freopen("_in.txt","r",stdin); freopen("_out.txt","w",stdout);
      9 #define LL long long
     10 #define ULL unsigned LL
     11 #define fi first
     12 #define se second
     13 #define pb push_back
     14 #define lson l,m,rt<<1
     15 #define rson m+1,r,rt<<1|1
     16 #define lch(x) tr[x].son[0]
     17 #define rch(x) tr[x].son[1]
     18 #define max3(a,b,c) max(a,max(b,c))
     19 #define min3(a,b,c) min(a,min(b,c))
     20 typedef pair<int,int> pll;
     21 const int inf = 0x3f3f3f3f;
     22 const LL INF = 0x3f3f3f3f3f3f3f3f;
     23 const LL mod =  (int)1e9+7;
     24 const int N = 2e5 + 100;
     25 int n;
     26 struct Node{
     27     int op;
     28     int L, R;
     29     int x, id;
     30 }A[N], lf[N], ri[N];
     31 int tot = 0;
     32 void NowNode(int op, int L, int R, int x, int id){
     33     ++tot;
     34     A[tot].op = op; A[tot].L = L; A[tot].R = R;
     35     A[tot].x = x; A[tot].id = id;
     36 }
     37 int ans[N];
     38 int tree[N];
     39 int Mn = inf, Mx = 0;
     40 void Add(int x, int v){
     41     for(int i = x; i <= n; i += i & (-i)){
     42         tree[i] += v;
     43     }
     44 }
     45 int Query(int x){
     46     int ret = 0;
     47     for(int i = x; i; i -= i&(-i)){
     48         ret += tree[i];
     49     }
     50     return ret;
     51 }
     52 void cdq(int Lval, int Rval, int st, int ed){
     53     if(Lval > Rval || st > ed) return ;
     54     if(Lval == Rval){
     55         for(int i = st; i <= ed; i++)
     56             if(A[i].op == 1) ans[A[i].id] = Lval;
     57         return ;
     58     }
     59     int mid = Lval + Rval >> 1;
     60 
     61     int lsz = 0, rsz = 0;
     62     for(int i = st; i <= ed; i++){
     63         int op = A[i].op, x = A[i].x, L = A[i].L, R = A[i].R, id = A[i].id;
     64         if(op == 0){
     65             if(x <= mid){
     66                 Add(A[i].id, 1);
     67                 lf[++lsz] = A[i];
     68             }
     69             else ri[++rsz] = A[i];
     70         }
     71         else if(A[i].op == 1){
     72             int num = Query(R) - Query(L-1);
     73             if(num >= x) lf[++lsz] = A[i];
     74             else {
     75                 A[i].x -= num;
     76                 ri[++rsz] = A[i];
     77             }
     78         }
     79     }
     80     for(int i = 1; i <= lsz; i++) {
     81 
     82         if(lf[i].op == 0) {
     83             Add(lf[i].id, -1);
     84         }
     85         A[st + i - 1] = lf[i];
     86     }
     87     for(int i = 1; i <= rsz; i++) A[st + lsz + i - 1] = ri[i];
     88     cdq(Lval, mid, st, st+lsz-1);
     89     cdq(mid+1, Rval, st+lsz, ed);
     90 }
     91 int main(){
     92     int m, val, l, r;
     93     scanf("%d%d", &n, &m);
     94     for(int i = 1; i <= n; i++){
     95         scanf("%d", &val);
     96         NowNode(0,0,0,val,i);
     97         Mn = min(Mn, val);
     98         Mx = max(Mx, val);
     99     }
    100     for(int i = 1; i <= m; i++){
    101         scanf("%d%d%d", &l, &r, &val);
    102         NowNode(1,l,r,val,i);
    103     }
    104     cdq(Mn,Mx,1,n+m);
    105     for(int i = 1; i <= m; i++){
    106         printf("%d
    ", ans[i]);
    107     }
    108     return 0;
    109 }
    View Code
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  • 原文地址:https://www.cnblogs.com/MingSD/p/9749542.html
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