// JOIOC 2017-2018 - Xylophone
// Leonardo Paes
//
// To solve it, let's find the position of the number 1 and the number n. To do it, let's use binary search. To find 1 we fix the end
// and guess the start, with the inequality query(mid, end) >= (n-1). To find n we fix the start to be to position of number 1 and guess
// the end point, with the same inequality. After knowing it, we find their neighbors using 1 query for each one. Then, we solve to the
// left of the 1 position and to the left of the n position and to the right of the n position. To discover the number i knowning i+1 and
// i+2 we can just use the differences: query(i, i+1) and query(i, i+2), using the inequality:
// query(i, i+1) + abs(ans[i+1] - ans[i+2]) == query(i, i+2). Knowning this, one can determine the answer of ith position.
// We have to save queries when possible, because using this solution naively costs:
// 2log2(n) + 1 (1 and n are neighbors and one of them doesn't have another neighbor) + 2*(n-3) queries in worst case,
// which is ~ 10019.
#include <bits/stdc++.h>
#include "xylophone.h"
using namespace std;
const int maxn = 5e3+10;
int n, res[maxn], pos[maxn];
inline void find_1(){
int ini=1, fim=n, meio, ans=-1;
while(ini<=fim){
meio = (ini+fim) >> 1;
if(query(meio, n)>=(n-1)){
ans = meio;
ini = meio+1;
}
else{
fim = meio-1;
}
}
pos[1] = ans;
res[ans] = 1;
}
inline void find_n(){
int ini=pos[1]+1, fim=n, meio, ans=-1;
while(ini<=fim){
meio = (ini+fim) >> 1;
if(query(pos[1], meio)>=(n-1)){
ans = meio;
fim = meio-1;
}
else{
ini = meio+1;
}
}
pos[n] = ans;
res[ans] = n;
}
inline void solve_left(int j, int k){
if(j<=1 or res[j-1]!=0) return;
int i = j-1;
int diff1 = query(i, j);
if((res[j] + diff1) > n or pos[res[j] + diff1]!=0){
res[i] = res[j] - diff1;
pos[res[i]] = i;
}
else if((res[j] - diff1) < 1 or pos[res[j] - diff1]!=0){
res[i] = res[j] + diff1;
pos[res[i]] = i;
}
else{
int diff2 = query(i, k);
if(diff1 + abs(res[j]-res[k]) == diff2){
if(res[k]<res[j]){
res[i] = res[j] + diff1;
pos[res[i]] = i;
}
else{
res[i] = res[j] - diff1;
pos[res[i]] = i;
}
}
else{
if(res[k]<res[j]){
res[i] = res[j] - diff1;
pos[res[i]] = i;
}
else{
res[i] = res[j] + diff1;
pos[res[i]] = i;
}
}
}
solve_left(i, j);
}
inline void solve_right(int j, int k){
if(k>=n or res[k+1]!=0) return;
int l = k+1;
int diff1 = query(k, l);
if((res[k] + diff1) > n or pos[res[k] + diff1]!=0){
res[l] = res[k] - diff1;
pos[res[l]] = l;
}
else if((res[k] - diff1) < 1 or pos[res[k] - diff1]!=0){
res[l] = res[k] + diff1;
pos[res[l]] = l;
}
else{
int diff2 = query(j, l);
if(diff1 + abs(res[j]-res[k]) == diff2){
if(res[k]>res[j]){
res[l] = res[k] + diff1;
pos[res[l]] = l;
}
else{
res[l] = res[k] - diff1;
pos[res[l]] = l;
}
}
else{
if(res[k]>res[j]){
res[l] = res[k] - diff1;
pos[res[l]] = l;
}
else{
res[l] = res[k] + diff1;
pos[res[l]] = l;
}
}
}
solve_right(k, l);
}
void solve(int N){
n = N;
find_1();
find_n();
int diff;
if(pos[1]+1 <= n and res[pos[1]+1] == 0){
diff = query(pos[1], pos[1]+1);
res[pos[1]+1] = 1 + diff;
pos[1+diff] = pos[1]+1;
}
if(pos[1]-1 >= 1 and res[pos[1]-1] == 0){
diff = query(pos[1]-1, pos[1]);
res[pos[1]-1] = 1 + diff;
pos[1+diff] = pos[1]-1;
}
if(pos[n]+1 <=n and res[pos[n]+1] == 0){
diff = query(pos[n], pos[n]+1);
res[pos[n]+1] = n - diff;
pos[n-diff] = pos[n]+1;
}
if(pos[n]-1 >= 1 and res[pos[n]-1] == 0){
diff = query(pos[n]-1, pos[n]);
res[pos[n]-1] = n - diff;
pos[n-diff] = pos[n] - 1;
}
solve_left(pos[1]-1, pos[1]);
solve_left(pos[n]-1, pos[n]);
solve_right(pos[n], pos[n]+1);
for(int i=1; i<=n; i++){
answer(i, res[i]);
}
}
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
248 KB |
Output is correct |
2 |
Correct |
2 ms |
248 KB |
Output is correct |
3 |
Correct |
2 ms |
248 KB |
Output is correct |
4 |
Correct |
3 ms |
312 KB |
Output is correct |
5 |
Correct |
3 ms |
376 KB |
Output is correct |
6 |
Correct |
3 ms |
248 KB |
Output is correct |
7 |
Correct |
3 ms |
376 KB |
Output is correct |
8 |
Correct |
3 ms |
312 KB |
Output is correct |
9 |
Correct |
2 ms |
400 KB |
Output is correct |
10 |
Correct |
3 ms |
376 KB |
Output is correct |
11 |
Correct |
3 ms |
376 KB |
Output is correct |
12 |
Correct |
3 ms |
316 KB |
Output is correct |
13 |
Correct |
3 ms |
248 KB |
Output is correct |
14 |
Correct |
3 ms |
248 KB |
Output is correct |
15 |
Correct |
3 ms |
248 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
248 KB |
Output is correct |
2 |
Correct |
2 ms |
248 KB |
Output is correct |
3 |
Correct |
2 ms |
248 KB |
Output is correct |
4 |
Correct |
3 ms |
312 KB |
Output is correct |
5 |
Correct |
3 ms |
376 KB |
Output is correct |
6 |
Correct |
3 ms |
248 KB |
Output is correct |
7 |
Correct |
3 ms |
376 KB |
Output is correct |
8 |
Correct |
3 ms |
312 KB |
Output is correct |
9 |
Correct |
2 ms |
400 KB |
Output is correct |
10 |
Correct |
3 ms |
376 KB |
Output is correct |
11 |
Correct |
3 ms |
376 KB |
Output is correct |
12 |
Correct |
3 ms |
316 KB |
Output is correct |
13 |
Correct |
3 ms |
248 KB |
Output is correct |
14 |
Correct |
3 ms |
248 KB |
Output is correct |
15 |
Correct |
3 ms |
248 KB |
Output is correct |
16 |
Correct |
7 ms |
376 KB |
Output is correct |
17 |
Correct |
10 ms |
376 KB |
Output is correct |
18 |
Correct |
20 ms |
376 KB |
Output is correct |
19 |
Correct |
13 ms |
248 KB |
Output is correct |
20 |
Correct |
18 ms |
248 KB |
Output is correct |
21 |
Correct |
15 ms |
380 KB |
Output is correct |
22 |
Correct |
9 ms |
404 KB |
Output is correct |
23 |
Correct |
13 ms |
376 KB |
Output is correct |
24 |
Correct |
13 ms |
324 KB |
Output is correct |
25 |
Correct |
13 ms |
248 KB |
Output is correct |
26 |
Correct |
17 ms |
248 KB |
Output is correct |
27 |
Correct |
15 ms |
376 KB |
Output is correct |
28 |
Correct |
16 ms |
248 KB |
Output is correct |
29 |
Correct |
18 ms |
248 KB |
Output is correct |
30 |
Correct |
18 ms |
248 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
2 ms |
248 KB |
Output is correct |
2 |
Correct |
2 ms |
248 KB |
Output is correct |
3 |
Correct |
2 ms |
248 KB |
Output is correct |
4 |
Correct |
3 ms |
312 KB |
Output is correct |
5 |
Correct |
3 ms |
376 KB |
Output is correct |
6 |
Correct |
3 ms |
248 KB |
Output is correct |
7 |
Correct |
3 ms |
376 KB |
Output is correct |
8 |
Correct |
3 ms |
312 KB |
Output is correct |
9 |
Correct |
2 ms |
400 KB |
Output is correct |
10 |
Correct |
3 ms |
376 KB |
Output is correct |
11 |
Correct |
3 ms |
376 KB |
Output is correct |
12 |
Correct |
3 ms |
316 KB |
Output is correct |
13 |
Correct |
3 ms |
248 KB |
Output is correct |
14 |
Correct |
3 ms |
248 KB |
Output is correct |
15 |
Correct |
3 ms |
248 KB |
Output is correct |
16 |
Correct |
7 ms |
376 KB |
Output is correct |
17 |
Correct |
10 ms |
376 KB |
Output is correct |
18 |
Correct |
20 ms |
376 KB |
Output is correct |
19 |
Correct |
13 ms |
248 KB |
Output is correct |
20 |
Correct |
18 ms |
248 KB |
Output is correct |
21 |
Correct |
15 ms |
380 KB |
Output is correct |
22 |
Correct |
9 ms |
404 KB |
Output is correct |
23 |
Correct |
13 ms |
376 KB |
Output is correct |
24 |
Correct |
13 ms |
324 KB |
Output is correct |
25 |
Correct |
13 ms |
248 KB |
Output is correct |
26 |
Correct |
17 ms |
248 KB |
Output is correct |
27 |
Correct |
15 ms |
376 KB |
Output is correct |
28 |
Correct |
16 ms |
248 KB |
Output is correct |
29 |
Correct |
18 ms |
248 KB |
Output is correct |
30 |
Correct |
18 ms |
248 KB |
Output is correct |
31 |
Correct |
25 ms |
248 KB |
Output is correct |
32 |
Correct |
42 ms |
376 KB |
Output is correct |
33 |
Correct |
65 ms |
376 KB |
Output is correct |
34 |
Correct |
54 ms |
312 KB |
Output is correct |
35 |
Correct |
49 ms |
376 KB |
Output is correct |
36 |
Correct |
48 ms |
336 KB |
Output is correct |
37 |
Correct |
56 ms |
248 KB |
Output is correct |
38 |
Correct |
49 ms |
376 KB |
Output is correct |
39 |
Correct |
66 ms |
344 KB |
Output is correct |
40 |
Correct |
69 ms |
376 KB |
Output is correct |
41 |
Correct |
65 ms |
376 KB |
Output is correct |
42 |
Correct |
56 ms |
248 KB |
Output is correct |
43 |
Correct |
60 ms |
528 KB |
Output is correct |
44 |
Correct |
51 ms |
464 KB |
Output is correct |
45 |
Correct |
68 ms |
380 KB |
Output is correct |
46 |
Correct |
73 ms |
380 KB |
Output is correct |
47 |
Correct |
55 ms |
464 KB |
Output is correct |
48 |
Correct |
82 ms |
340 KB |
Output is correct |
49 |
Correct |
67 ms |
384 KB |
Output is correct |
50 |
Correct |
68 ms |
344 KB |
Output is correct |
51 |
Correct |
56 ms |
376 KB |
Output is correct |
52 |
Correct |
50 ms |
344 KB |
Output is correct |
53 |
Correct |
80 ms |
376 KB |
Output is correct |
54 |
Correct |
82 ms |
248 KB |
Output is correct |
55 |
Correct |
73 ms |
356 KB |
Output is correct |
56 |
Correct |
87 ms |
376 KB |
Output is correct |
57 |
Correct |
67 ms |
248 KB |
Output is correct |
58 |
Correct |
72 ms |
348 KB |
Output is correct |
59 |
Correct |
73 ms |
376 KB |
Output is correct |
60 |
Correct |
70 ms |
248 KB |
Output is correct |