[HEOI2016/TJOI2016]排序

嘟嘟嘟


首先这题的暴力是十分好写的,而且据说能得不少分。
正解写起来不难,就是不太好想。


根据做题经验,我想到了给这个序列转化成01序列,但是接下来我就不会了。还是看了题解。
因为查询只有一个数,所以可以二分答案:把大于等于mid的数标记成1,小于mid的数为0.这样排序就是区间赋值了,线段树可做。
那怎么检验mid是否正确呢?其实这个是有单调性的:如果二分的是1,那么很显然最后位置(q)上一定是1,随着二分的值变大,位置(q)上是1的可能性就越小。这大抵就是二分的单调性?
(这只能算是感性理解吧)
或者说如果第(Q)位是1,那么答案就是([mid, R]),否则就是([L, mid - 1])

#include<cstdio>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<vector>
#include<stack>
#include<queue>
using namespace std;
#define enter puts("") 
#define space putchar(' ')
#define Mem(a, x) memset(a, x, sizeof(a))
#define In inline
typedef long long ll;
typedef double db;
const int INF = 0x3f3f3f3f;
const db eps = 1e-8;
const int maxn = 1e5 + 5;
inline ll read()
{
  ll ans = 0;
  char ch = getchar(), last = ' ';
  while(!isdigit(ch)) last = ch, ch = getchar();
  while(isdigit(ch)) ans = (ans << 1) + (ans << 3) + ch - '0', ch = getchar();
  if(last == '-') ans = -ans;
  return ans;
}
inline void write(ll x)
{
  if(x < 0) x = -x, putchar('-');
  if(x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}

int n, m, Q, a[maxn];
bool b[maxn];
struct Node
{
  int op, L, R;
}q[maxn];

int l[maxn << 2], r[maxn << 2], sum[maxn << 2], lzy[maxn << 2];
In void build(int L, int R, int now)
{
  l[now] = L, r[now] = R;
  lzy[now] = -1;
  if(L == R) {sum[now] = b[L]; return;}
  int mid = (L + R) >> 1;
  build(L, mid, now << 1);
  build(mid + 1, R, now << 1 | 1);
  sum[now] = sum[now << 1] + sum[now << 1 | 1];
}
In void change(int now, int flg)
{
  sum[now] = (r[now] - l[now] + 1) * flg;
  lzy[now] = flg;
}
In void pushdown(int now)
{
  if(~lzy[now])
    {
      change(now << 1, lzy[now]), change(now << 1 | 1, lzy[now]);
      lzy[now] = -1;
    }
}
In void update(int L, int R, int now, int flg)
{
  if(L > R) return;
  if(l[now] == L && r[now] == R) {change(now, flg); return;}
  pushdown(now);
  int mid = (l[now] + r[now]) >> 1;
  if(R <= mid) update(L, R, now << 1, flg);
  else if(L > mid) update(L, R, now << 1 | 1, flg);
  else update(L, mid, now << 1, flg), update(mid + 1, R, now << 1 | 1, flg);
  sum[now] = sum[now << 1] + sum[now << 1 | 1];
}
In int query(int L, int R, int now)
{
  if(l[now] == L && r[now] == R) return sum[now];
  pushdown(now);
  int mid = (l[now] + r[now]) >> 1;
  if(R <= mid) return query(L, R, now << 1);
  else if(L > mid) return query(L, R, now << 1 | 1);
  else return query(L, mid, now << 1) + query(mid + 1, R, now << 1 | 1);
}

In bool judge(int x)
{
  for(int i = 1; i <= n; ++i) b[i] = (a[i] >= x);
  build(1, n, 1);
  for(int i = 1; i <= m; ++i)
    {
      int tp = query(q[i].L, q[i].R, 1);
      if(!q[i].op)
	{
	  update(q[i].L, q[i].R - tp, 1, 0);
	  update(q[i].R - tp + 1, q[i].R, 1, 1);
	}
      else
	{
	  update(q[i].L, q[i].L + tp - 1, 1, 1);
	  update(q[i].L + tp, q[i].R, 1, 0);	  
	}
    }
  return query(Q, Q, 1);
}

int main()
{
  n = read(), m = read();
  for(int i = 1; i <= n; ++i) a[i] = read();
  for(int i = 1; i <= m; ++i) q[i].op = read(), q[i].L = read(), q[i].R = read();
  Q = read();
  int L = 1, R = n;
  while(L < R)
    {
      int mid = (L + R + 1) >> 1;
      if(judge(mid)) L = mid;
      else R = mid - 1;
    }
  write(L), enter;
  return 0;
}
原文地址:https://www.cnblogs.com/mrclr/p/10554598.html