Codeforces 474E - Pillars

一眼看上去非常像最长不下降子序列。

然后比赛的时候对每个答案长度为k的序列，维护最后一个数的最大值和最小值。

当时不知道为什么认为从长度最长倒推至前面不会太长，于是心满意足地敲了个O(n^2)。结果T了。。。

正确的做法应该用线段树维护，搜起来就是log（n）,总的就是O(N*logN);

用非递归的方法写的

只用了77ms

#include <iostream>
#include <cstdio>
using namespace std;

#define ll long long

const int INF = 300009;

struct node {
ll key;
int pos;
} dtmin[INF], dtmax[INF];
ll n, d, t, x, M;
ll pre[INF];
int f[INF], ans[INF], namax[INF], namin[INF];

inline int Searchmax (int x, ll k) {
while (dtmax[x].key - k >= d) {
if (x > M) return dtmax[x].pos;
if (dtmax[x << 1 | 1].key - k >= d) x = x << 1 | 1;
else
x = x << 1;
}
return 0;
}
inline int Searchmin (int x, ll k) {
while (k - dtmin[x].key >= d) {
if (x > M) return dtmin[x].pos;
if (k - dtmin[x << 1 | 1].key >= d) x = x << 1 | 1;
else
x = x << 1;
}
return 0;
}

inline void modify (int x, ll k, int i) {
if (dtmax[x + M].key < k) namax[x] = i, dtmax[x + M].key = k;
for (int t = x + M; dtmax[t >> 1].key < k && t > 0; t >>= 1)
dtmax[t >> 1] = dtmax[t];

if (dtmin[x + M].key > k) namin[x] = i, dtmin[x + M].key = k;
for (int t = x + M; dtmin[t >> 1].key > k && t > 0; t >>= 1)
dtmin[t >> 1]  = dtmin[t];
}

int main() {
ios::sync_with_stdio (false);
cin >> n >> d;
cin>>x;
M = n;
int tem = 0;
for (int k = M; k; tem++, k >>= 1) ;
M = 1 << tem;
for (int i = 0; i < (M << 1) + 10; i++) {
dtmax[i].key = 0 , dtmin[i].key = (1LL << 60);
dtmax[i].pos = i - M, dtmin[i].pos = i - M;
}
dtmax[1].key = dtmin[1].key = x;
t = f[1] = 1;
modify (t, x, 1);
for (int i = 2,k; i <= n; i++) {
cin >> x;
if (k = Searchmax (1, x) )
if (f[i] < k + 1)
f[i] = k  + 1, pre[i] = namax[k];

if ((k = Searchmin (1, x)))
if (f[i] < k + 1)
f[i] = k  + 1, pre[i] = namin[k];

if (f[i] > t) t = f[i];
if (f[i] == 0)   f[i] = 1;
modify (f[i], x, i);
}
cout << t << endl;
int p = -1;
for (int i = 1; i <= n; i++)  if (f[i] == t) { p = i; break; }
for (int i = t; i; i--)
ans[i] = p, p = pre[p];
for (int i = 1; i <= t; i++)
cout << ans[i] << ' ';
}

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