oj.uz

Submission #160807

# Submission time Handle Problem Language Result Execution time Memory
160807 2019-10-30T02:43:43 Z Leonardo_Paes Xylophone (JOI18_xylophone) C++17
100 / 100
 87 ms 528 KB 
// 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]);
    }
}

Subtask #1
11.0 / 11.0

# 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

Subtask #2
36.0 / 36.0

# 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

Subtask #3
53.0 / 53.0

# 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