/* Slow solution to the task Treasure hunt
* Author: Jakub Radoszewski
* Date: 10.06.2011
* Time complexity: O(#calls * log^2(#calls + #nodes)).
* Description: the explicit nodes are renumbered.
*/
#include <utility>
#include <vector>
#include <utility>
#include <algorithm>
#include <cassert>
using namespace std;
#define MAX_CALLS 400000
#define LOG_2_MAX_CALLS 20
/* This node will be created if a path call appears */
int curr;
/*****************************************************************************/
/* Data structures */
/* An (implicit or explicit) node located dist units below the explicit node
* expl. */
typedef struct
{
int expl, dist;
} node;
inline bool operator==(const node &a, const node &b)
{
return a.expl == b.expl && a.dist == b.dist;
}
/* anc[v][i] = the ancestor of the node v located 2^i edges upwards. */
typedef struct
{
int node, dist;
} ancestor;
/* The ancestors of the nodes (anc[v][i] is the ancestor 2^i edges above)
* and their depths. */
vector<ancestor> anc[2 * MAX_CALLS];
int real_depth[2 * MAX_CALLS];
/* If v is the upper end of an edge, attached[v] is the node to which
* it is directly attached. Otherwise attached[v].node == -1. */
node attached[2 * MAX_CALLS];
/* If expl_anc contains a pair (y, x) then x is the explicit ancestor of
* all the nodes x..y.
* Initially the vector contains sentinel pairs (0, 0) and (1, 1). */
vector<pair<int, int> > expl_anc;
/*****************************************************************************/
/* Simple utility functions */
/* From a renumbered node to the real node value. */
inline int real_node(int a)
{
return expl_anc[a].second;
}
inline int get_real_depth(const node &a)
{
return real_depth[a.expl] + a.dist;
}
inline node get_node(int a)
{
node v;
v.expl = lower_bound(expl_anc.begin(), expl_anc.end(), make_pair(a, -1)) - expl_anc.begin();
v.dist = a - real_node(v.expl);
return v;
}
/*****************************************************************************/
/* Important utility functions */
/* Computes anc[a], starting with anc[a][0] = par. */
inline void compute_anc(int a, int par, int len)
{
ancestor v;
v.node = par;
v.dist = len;
anc[a].push_back(v);
for (int i = 0; i < LOG_2_MAX_CALLS; i++)
{
v.node = anc[anc[a][i].node][i].node;
v.dist = anc[a][i].dist + anc[anc[a][i].node][i].dist;
anc[a].push_back(v);
}
}
/* Auxiliary function, only on explicit nodes. */
inline node go_up(int a, int h)
{
/* Finding the highest explicit node located at most h units above a. */
vector<ancestor> &t = anc[a];
int i = 0;
while (i + 1 < (int)t.size() && t[i + 1].dist <= h)
i++;
while (i >= 0)
{
ancestor &p = anc[a][i];
if (p.dist <= h)
{
h -= p.dist;
a = p.node;
}
i--;
}
/* The final touch: finding the potentially implicit node. */
node b;
if (!h)
{
b.expl = a;
b.dist = 0;
return b;
}
node p = attached[a];
if (p.expl == -1) /* a is the lower end of its edge */
{
b.expl = anc[a][0].node;
b.dist = (real_node(a) - real_node(b.expl)) - h;
} else /* a is the upper end of its edge */
{
h--;
b.expl = p.expl;
b.dist = p.dist - h;
}
return b;
}
/* Advances the distance h up, starting from the node a. */
inline node go_up(node a, int h)
{
if (h <= a.dist)
{
node b = a;
b.dist = a.dist - h;
return b;
}
return go_up(a.expl, h - a.dist);
}
inline node lca(node a, node b)
{
/* Equalizing real_depths */
int da = get_real_depth(a), db = get_real_depth(b);
if (da < db)
{
swap(a, b);
swap(da, db);
}
a = go_up(a, da - db);
if (a == b)
return a;
/* Finding LCA */
int lo = 1, hi = db;
while (lo < hi)
{
int med = (lo + hi) / 2;
if (go_up(a, med) == go_up(b, med))
hi = med;
else
lo = med + 1;
}
return go_up(a, lo);
}
/*****************************************************************************/
void init()
{
real_depth[0] = -1;
real_depth[1] = 0;
ancestor a;
a.node = 1;
a.dist = 0;
for (int i = 0; i < LOG_2_MAX_CALLS; i++)
anc[1].push_back(a); /* sentinel */
expl_anc.push_back(make_pair(0, 0));
expl_anc.push_back(make_pair(1, 1));
curr = 2;
}
/*****************************************************************************/
void path(int a, int s)
{
node v = get_node(a);
int real_start = curr, real_end = curr + s - 1;
int start = int(expl_anc.size()), end = start;
if (real_start != real_end)
end++;
real_depth[start] = real_depth[v.expl] + v.dist + 1;
real_depth[end] = real_depth[start] + s - 1;
compute_anc(start, v.expl, v.dist + 1);
if (start != end)
compute_anc(end, start, s - 1);
attached[start] = v;
if (start != end)
attached[end].expl = -1;
if (start != end)
expl_anc.push_back(make_pair(real_end - 1, real_start));
expl_anc.push_back(make_pair(real_end, real_end));
curr = real_end + 1;
}
/*****************************************************************************/
int dig(int a, int b)
{
node na = get_node(a), nb = get_node(b);
node v = lca(na, nb);
int da = real_depth[na.expl] + na.dist;
int db = real_depth[nb.expl] + nb.dist;
int dv = real_depth[v.expl] + v.dist;
int len = da + db - 2 * dv;
int pos = len / 2;
node res;
if (pos <= da - dv)
res = go_up(na, pos);
else
res = go_up(nb, len - pos);
return real_node(res.expl) + res.dist;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
22 ms |
19192 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
23 ms |
19192 KB |
Output is correct |
| 2 |
Correct |
23 ms |
19832 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
963 ms |
134388 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
824 ms |
39928 KB |
Output is correct |
| 2 |
Correct |
485 ms |
78436 KB |
Output is correct |
| 3 |
Correct |
445 ms |
78376 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
966 ms |
78272 KB |
Output is correct |
| 2 |
Correct |
669 ms |
28584 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1629 ms |
136156 KB |
Output is correct |
| 2 |
Correct |
1630 ms |
137692 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
472 ms |
49144 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
908 ms |
133304 KB |
Output is correct |
| 2 |
Correct |
1628 ms |
248624 KB |
Output is correct |
| 3 |
Correct |
529 ms |
134108 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
4054 ms |
135920 KB |
Time limit exceeded |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
4056 ms |
135524 KB |
Time limit exceeded |
