/* Model solution to the task Treasure hunt
* Author: Jakub Radoszewski
* Date: 10.06.2011
* Time complexity: O(#calls * log(#calls)).
* 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;
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];
/* real_depth includes implicit nodes, depth considers only explicit nodes. */
int real_depth[2 * MAX_CALLS], 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. */
int real_node(int a)
{
return expl_anc[a].second;
}
int get_real_depth(node a)
{
return real_depth[a.expl] + a.dist;
}
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. */
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. */
node go_up(int a, int h)
{
/* Finding the highest explicit node located at most h units above a. */
int i = 0;
while (i + 1 < (int)anc[a].size() && anc[a][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. */
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);
}
/* Advances h explicit edges up, starting from the node a. */
int go_up_real(int a, int h)
{
int i = 0;
while ((1 << (i + 1)) <= h)
i++;
while (h)
{
if ((1 << i) <= h)
{
a = anc[a][i].node;
h -= (1 << i);
}
i--;
}
return a;
}
/* O(log(n)) time */
node lca(node a, node b)
{
/* Equalizing depths */
int da = depth[a.expl], db = depth[b.expl];
if (da < db || da == db && a.dist < b.dist)
{
swap(a, b);
swap(da, db);
}
if (a.expl == b.expl)
return b;
a.dist = 0;
if (da > db)
{
a.expl = go_up_real(a.expl, da - db - 1);
if (anc[a.expl][0].node == b.expl)
{
node c = attached[a.expl];
if (c.expl == -1)
c = b;
if (c.dist <= b.dist)
return c;
else
return b;
}
a.expl = anc[a.expl][0].node;
}
b.dist = 0;
/* Finding LCA */
int i = 0;
while (anc[a.expl][i].node != anc[b.expl][i].node)
i++;
i--;
while (i >= 0)
{
a.expl = anc[a.expl][i].node;
b.expl = anc[b.expl][i].node;
while (i >= 0 && anc[a.expl][i].node == anc[b.expl][i].node)
i--;
}
node p = attached[a.expl], q = attached[b.expl];
node res;
if (p.expl == -1 || q.expl == -1)
{
res = p;
if (res.expl == -1)
res = q;
if (res.expl == -1)
{
res.expl = anc[a.expl][0].node;
res.dist = 0;
}
} else
{
res.expl = anc[a.expl][0].node;
res.dist = min(p.dist, q.dist);
}
return res;
}
/*****************************************************************************/
void init()
{
real_depth[0] = depth[0] = -1;
real_depth[1] = 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 l)
{
node v = get_node(a);
int real_start = curr, real_end = curr + l - 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;
depth[start] = depth[v.expl] + 1;
if (start != end)
{
real_depth[end] = real_depth[start] + l - 1;
depth[end] = depth[start] + 1;
}
compute_anc(start, v.expl, v.dist + 1);
if (start != end)
compute_anc(end, start, l - 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;
}
Compilation message
tre.cpp: In function 'node lca(node, node)':
tre.cpp:177:27: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
if (da < db || da == db && a.dist < b.dist)
~~~~~~~~~^~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
21 ms |
19320 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
23 ms |
19448 KB |
Output is correct |
| 2 |
Correct |
24 ms |
19960 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1006 ms |
137284 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
992 ms |
43340 KB |
Output is correct |
| 2 |
Correct |
471 ms |
80760 KB |
Output is correct |
| 3 |
Correct |
433 ms |
80868 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
763 ms |
84608 KB |
Output is correct |
| 2 |
Correct |
414 ms |
30336 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1608 ms |
140516 KB |
Output is correct |
| 2 |
Correct |
924 ms |
138816 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
358 ms |
52340 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
882 ms |
140856 KB |
Output is correct |
| 2 |
Correct |
1636 ms |
253256 KB |
Output is correct |
| 3 |
Correct |
544 ms |
137572 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1139 ms |
145236 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1151 ms |
144968 KB |
Output is correct |
