• luogu P2617 Dynamic Rankings(分块,n <= 1e4)


    嘟嘟嘟

    带修改区间第k大。

    然而某谷把数据扩大到了1e5,所以用分块现在只能得50分。

    分块怎么做呢?很暴力的。

    基本思想还是块内有序,块外暴力统计。

    对于修改,直接重排修改的数所在块,时间复杂度O(√nlogn√n)。

    对于询问,二分答案,然后在每个块内再二分统计小于mid的数有几个,块外暴力统计,时间复杂度O(m * log1e9 * √nlog√n),所以只能过1e4。

      1 #include<cstdio>
      2 #include<iostream>
      3 #include<cmath>
      4 #include<algorithm>
      5 #include<cstring>
      6 #include<cstdlib>
      7 #include<cctype>
      8 #include<vector>
      9 #include<stack>
     10 #include<queue>
     11 using namespace std;
     12 #define enter puts("") 
     13 #define space putchar(' ')
     14 #define Mem(a, x) memset(a, x, sizeof(a))
     15 #define rg register
     16 typedef long long ll;
     17 typedef double db;
     18 const int INF = 0x3f3f3f3f;
     19 const db eps = 1e-8;
     20 const int maxn = 1e5 + 5;
     21 const int maxb = 320;
     22 inline ll read()
     23 {
     24   ll ans = 0;
     25   char ch = getchar(), last = ' ';
     26   while(!isdigit(ch)) {last = ch; ch = getchar();}
     27   while(isdigit(ch)) {ans = (ans << 1) + (ans << 3) + ch - '0'; ch = getchar();}
     28   if(last == '-') ans = -ans;
     29   return ans;
     30 }
     31 inline void write(ll x)
     32 {
     33   if(x < 0) x = -x, putchar('-');
     34   if(x >= 10) write(x / 10);
     35   putchar(x % 10 + '0');
     36 }
     37 
     38 int n, q, a[maxn];
     39 char c[2];
     40 
     41 int S, Cnt = 0, blo[maxn], lb[maxn], rb[maxn];
     42 int b[maxb][maxb];
     43 void init()
     44 {
     45   S = sqrt(n);
     46   Cnt = n % S ? n / S + 1: n / S;
     47   for(rg int i = 1; i <= Cnt; ++i) lb[i] = rb[i - 1] + 1, rb[i] = lb[i] + S - 1;
     48   rb[Cnt] = n;
     49   for(rg int i = 1, j = 1; i <= n; ++i) blo[i] = j, j += (i == rb[j]);
     50   for(rg int i = 1, cb = 0; i <= Cnt; ++i, cb = 0)
     51     {
     52       for(rg int j = lb[i]; j <= rb[i]; ++j) b[i][++cb] = a[j];
     53       sort(b[i] + 1, b[i] + cb + 1);
     54     }
     55 }
     56 inline void update(const int& x, const int& k)
     57 {
     58   a[x] = k;
     59   int t = blo[x], cb = 0;
     60   for(rg int i = lb[t]; i <= rb[t]; ++i) b[t][++cb] = a[i];
     61   sort(b[t] + 1, b[t] + cb + 1);
     62 }
     63 inline int judge(const int& L, const int& R, const int& x, const int& k)
     64 {
     65   int l = blo[L], r = blo[R], ret = 0;
     66   if(l == r)
     67     {
     68       for(rg int i = L; i <= R; ++i) ret += (a[i] < x);
     69       return ret < k;
     70     }
     71   for(rg int i = l + 1; i < r; ++i)
     72     {
     73       int tp = lower_bound(b[i] + 1, b[i] + rb[i] - lb[i] + 2, x) - b[i] - 1;
     74       if(tp < 1) tp = 0;
     75       if(tp > rb[i] - lb[i]) tp = rb[i] - lb[i] + 1;
     76       ret += tp;
     77     }
     78   for(rg int i = L; i <= rb[l]; ++i) ret += (a[i] < x);
     79   for(rg int i = lb[r]; i <= R; ++i) ret += (a[i] < x);
     80   return ret < k;
     81 }
     82 
     83 int main()
     84 {
     85   n = read(), q = read();
     86   for(rg int i = 1; i <= n; ++i) a[i] = read();
     87   init();
     88   for(rg int i = 1; i <= q; ++i)
     89     {
     90       scanf("%s", c);
     91       if(c[0] == 'C')
     92     {
     93       int x = read(), y = read();
     94       update(x, y);
     95     }
     96       else
     97     {
     98       int L = read(), R = read(), k = read();
     99       int l = 0, r = 1e9;
    100       while(l < r)
    101         {
    102           int mid = (l + r + 1) >> 1;
    103           if(judge(L, R, mid, k)) l = mid;
    104           else r = mid - 1;
    105         }
    106       write(l), enter;
    107     }
    108     }
    109   return 0;
    110 }
    View Code
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  • 原文地址:https://www.cnblogs.com/mrclr/p/9870719.html
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