답안 #1000789

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1000789	2024-06-18T08:49:20 Z	saayan007	경주 (Race) (IOI11_race)	C++17	100 / 100	261 ms	32080 KB

race

/*

This problem can be found at https://content-available-to-author-only.uz/problem/view/IOI11_race.

SOLUTION

Consider the problem of finding a path of length K containing minimum edges THAT GOES A FIXED NODE x.
This can be done in O(Size of Tree) time. Once this is done, we can remove the node x and edges connected to it. Then we can solve the problem for the remaining connected components.

The best choice of x is the centroid of the tree.

*/ 

#include "race.h"
#include "bits/stdc++.h"
using namespace std;
 
const int mxN = 2e5L + 10;
const int mxK = 1e6L + 10;
int n, k;
vector<pair<int, int>> adj[mxN];
int ans = mxN;
int sz[mxN];
bool proc[mxN] = {};
int dp[mxK];
 
int get_sz(int x, int p) {
    sz[x] = 1;
    for(auto [y, w] : adj[x]) {
        if(proc[y] || y == p) continue;
        sz[x] += get_sz(y, x);
    }
    return sz[x];
}
 
int get_cen(int x, int p, int tot) {
    for(auto [y, w] : adj[x]) {
        if(proc[y] || y == p || sz[y] * 2 <= tot) continue;
        return get_cen(y, x, tot);
    }
    return x;
}
 
void dfs(int x, int p, int dep, int dis, int flag) {
    if(dis > k) return;
    if(flag == 0) {
        if(dp[k - dis] != mxN) ans = min(ans, dep + dp[k - dis]);
    }
    else if(flag == 1) {
        dp[dis] = min(dp[dis], dep);
    }
    else if(flag == 2) {
        dp[dis] = mxN;
    }
 
    for(auto [y, w] : adj[x]) {
        if(proc[y] || y == p) continue;
        dfs(y, x, dep + 1, dis + w, flag);
    }
}
 
void solve(int x = 1, int p = -1) {
    int c = get_cen(x, p, get_sz(x, p));
    dp[0] = 0;
    for(auto [d, w] : adj[c]) {
        if(proc[d]) continue;
        dfs(d, c, 1, w, 0);
        dfs(d, c, 1, w, 1);
    }
    for(auto [d, w] : adj[c]) {
        if(proc[d]) continue;
        dfs(d, c, 1, w, 2);
    }
    dp[0] = mxN;
    proc[c] = 1;
    for(auto [d, w] : adj[c]) {
        if(proc[d]) continue;
        solve(d, c);
    }
}
 
int best_path(int N, int K, int H[][2], int L[])
{
    for(int i = 0; i < mxK; ++i) dp[i] = mxN;
    n = N; k = K;
    for(int i = 0; i < n - 1; ++i) {
        adj[H[i][0] + 1].emplace_back(H[i][1] + 1, L[i]);
        adj[H[i][1] + 1].emplace_back(H[i][0] + 1, L[i]);
    }
 
    solve();
    return (ans > n - 1 ? -1 : ans);
}

Subtask #1
9.0 / 9.0

#	결과	실행 시간	메모리	Grader output
1	Correct	3 ms	9308 KB	Output is correct
2	Correct	3 ms	9308 KB	Output is correct
3	Correct	3 ms	10844 KB	Output is correct
4	Correct	3 ms	9308 KB	Output is correct
5	Correct	5 ms	9560 KB	Output is correct
6	Correct	3 ms	9308 KB	Output is correct
7	Correct	3 ms	9308 KB	Output is correct
8	Correct	3 ms	10936 KB	Output is correct
9	Correct	3 ms	9308 KB	Output is correct
10	Correct	3 ms	9308 KB	Output is correct
11	Correct	2 ms	9308 KB	Output is correct
12	Correct	3 ms	9308 KB	Output is correct
13	Correct	3 ms	9308 KB	Output is correct
14	Correct	3 ms	10844 KB	Output is correct
15	Correct	3 ms	9308 KB	Output is correct
16	Correct	3 ms	9308 KB	Output is correct
17	Correct	3 ms	9304 KB	Output is correct
18	Correct	3 ms	9308 KB	Output is correct

Subtask #2
12.0 / 12.0

#	결과	실행 시간	메모리	Grader output
1	Correct	3 ms	9308 KB	Output is correct
2	Correct	3 ms	9308 KB	Output is correct
3	Correct	3 ms	10844 KB	Output is correct
4	Correct	3 ms	9308 KB	Output is correct
5	Correct	5 ms	9560 KB	Output is correct
6	Correct	3 ms	9308 KB	Output is correct
7	Correct	3 ms	9308 KB	Output is correct
8	Correct	3 ms	10936 KB	Output is correct
9	Correct	3 ms	9308 KB	Output is correct
10	Correct	3 ms	9308 KB	Output is correct
11	Correct	2 ms	9308 KB	Output is correct
12	Correct	3 ms	9308 KB	Output is correct
13	Correct	3 ms	9308 KB	Output is correct
14	Correct	3 ms	10844 KB	Output is correct
15	Correct	3 ms	9308 KB	Output is correct
16	Correct	3 ms	9308 KB	Output is correct
17	Correct	3 ms	9304 KB	Output is correct
18	Correct	3 ms	9308 KB	Output is correct
19	Correct	3 ms	9304 KB	Output is correct
20	Correct	4 ms	9308 KB	Output is correct
21	Correct	3 ms	9308 KB	Output is correct
22	Correct	3 ms	9304 KB	Output is correct
23	Correct	3 ms	9308 KB	Output is correct
24	Correct	3 ms	9308 KB	Output is correct
25	Correct	3 ms	9308 KB	Output is correct
26	Correct	3 ms	9308 KB	Output is correct
27	Correct	3 ms	9400 KB	Output is correct
28	Correct	3 ms	9308 KB	Output is correct
29	Correct	4 ms	9308 KB	Output is correct
30	Correct	3 ms	9308 KB	Output is correct
31	Correct	3 ms	9308 KB	Output is correct
32	Correct	4 ms	9308 KB	Output is correct
33	Correct	3 ms	9308 KB	Output is correct
34	Correct	4 ms	9308 KB	Output is correct
35	Correct	3 ms	9308 KB	Output is correct
36	Correct	3 ms	9320 KB	Output is correct
37	Correct	3 ms	9308 KB	Output is correct
38	Correct	4 ms	9308 KB	Output is correct

Subtask #3
22.0 / 22.0

#	결과	실행 시간	메모리	Grader output
1	Correct	3 ms	9308 KB	Output is correct
2	Correct	3 ms	9308 KB	Output is correct
3	Correct	3 ms	10844 KB	Output is correct
4	Correct	3 ms	9308 KB	Output is correct
5	Correct	5 ms	9560 KB	Output is correct
6	Correct	3 ms	9308 KB	Output is correct
7	Correct	3 ms	9308 KB	Output is correct
8	Correct	3 ms	10936 KB	Output is correct
9	Correct	3 ms	9308 KB	Output is correct
10	Correct	3 ms	9308 KB	Output is correct
11	Correct	2 ms	9308 KB	Output is correct
12	Correct	3 ms	9308 KB	Output is correct
13	Correct	3 ms	9308 KB	Output is correct
14	Correct	3 ms	10844 KB	Output is correct
15	Correct	3 ms	9308 KB	Output is correct
16	Correct	3 ms	9308 KB	Output is correct
17	Correct	3 ms	9304 KB	Output is correct
18	Correct	3 ms	9308 KB	Output is correct
19	Correct	81 ms	14608 KB	Output is correct
20	Correct	77 ms	14672 KB	Output is correct
21	Correct	86 ms	14684 KB	Output is correct
22	Correct	77 ms	14680 KB	Output is correct
23	Correct	43 ms	14940 KB	Output is correct
24	Correct	34 ms	14812 KB	Output is correct
25	Correct	79 ms	17376 KB	Output is correct
26	Correct	66 ms	20304 KB	Output is correct
27	Correct	90 ms	21480 KB	Output is correct
28	Correct	140 ms	31060 KB	Output is correct
29	Correct	131 ms	30032 KB	Output is correct
30	Correct	89 ms	21328 KB	Output is correct
31	Correct	94 ms	19912 KB	Output is correct
32	Correct	98 ms	19792 KB	Output is correct
33	Correct	150 ms	20128 KB	Output is correct
34	Correct	100 ms	18512 KB	Output is correct

Subtask #4
57.0 / 57.0

#	결과	실행 시간	메모리	Grader output
1	Correct	3 ms	9308 KB	Output is correct
2	Correct	3 ms	9308 KB	Output is correct
3	Correct	3 ms	10844 KB	Output is correct
4	Correct	3 ms	9308 KB	Output is correct
5	Correct	5 ms	9560 KB	Output is correct
6	Correct	3 ms	9308 KB	Output is correct
7	Correct	3 ms	9308 KB	Output is correct
8	Correct	3 ms	10936 KB	Output is correct
9	Correct	3 ms	9308 KB	Output is correct
10	Correct	3 ms	9308 KB	Output is correct
11	Correct	2 ms	9308 KB	Output is correct
12	Correct	3 ms	9308 KB	Output is correct
13	Correct	3 ms	9308 KB	Output is correct
14	Correct	3 ms	10844 KB	Output is correct
15	Correct	3 ms	9308 KB	Output is correct
16	Correct	3 ms	9308 KB	Output is correct
17	Correct	3 ms	9304 KB	Output is correct
18	Correct	3 ms	9308 KB	Output is correct
19	Correct	3 ms	9304 KB	Output is correct
20	Correct	4 ms	9308 KB	Output is correct
21	Correct	3 ms	9308 KB	Output is correct
22	Correct	3 ms	9304 KB	Output is correct
23	Correct	3 ms	9308 KB	Output is correct
24	Correct	3 ms	9308 KB	Output is correct
25	Correct	3 ms	9308 KB	Output is correct
26	Correct	3 ms	9308 KB	Output is correct
27	Correct	3 ms	9400 KB	Output is correct
28	Correct	3 ms	9308 KB	Output is correct
29	Correct	4 ms	9308 KB	Output is correct
30	Correct	3 ms	9308 KB	Output is correct
31	Correct	3 ms	9308 KB	Output is correct
32	Correct	4 ms	9308 KB	Output is correct
33	Correct	3 ms	9308 KB	Output is correct
34	Correct	4 ms	9308 KB	Output is correct
35	Correct	3 ms	9308 KB	Output is correct
36	Correct	3 ms	9320 KB	Output is correct
37	Correct	3 ms	9308 KB	Output is correct
38	Correct	4 ms	9308 KB	Output is correct
39	Correct	81 ms	14608 KB	Output is correct
40	Correct	77 ms	14672 KB	Output is correct
41	Correct	86 ms	14684 KB	Output is correct
42	Correct	77 ms	14680 KB	Output is correct
43	Correct	43 ms	14940 KB	Output is correct
44	Correct	34 ms	14812 KB	Output is correct
45	Correct	79 ms	17376 KB	Output is correct
46	Correct	66 ms	20304 KB	Output is correct
47	Correct	90 ms	21480 KB	Output is correct
48	Correct	140 ms	31060 KB	Output is correct
49	Correct	131 ms	30032 KB	Output is correct
50	Correct	89 ms	21328 KB	Output is correct
51	Correct	94 ms	19912 KB	Output is correct
52	Correct	98 ms	19792 KB	Output is correct
53	Correct	150 ms	20128 KB	Output is correct
54	Correct	100 ms	18512 KB	Output is correct
55	Correct	8 ms	9816 KB	Output is correct
56	Correct	11 ms	9820 KB	Output is correct
57	Correct	68 ms	16356 KB	Output is correct
58	Correct	28 ms	14796 KB	Output is correct
59	Correct	67 ms	20308 KB	Output is correct
60	Correct	261 ms	32080 KB	Output is correct
61	Correct	100 ms	21500 KB	Output is correct
62	Correct	113 ms	19704 KB	Output is correct
63	Correct	130 ms	21508 KB	Output is correct
64	Correct	239 ms	19540 KB	Output is correct
65	Correct	96 ms	21344 KB	Output is correct
66	Correct	209 ms	29680 KB	Output is correct
67	Correct	58 ms	20160 KB	Output is correct
68	Correct	124 ms	20052 KB	Output is correct
69	Correct	119 ms	20048 KB	Output is correct
70	Correct	138 ms	21108 KB	Output is correct

답안 #1000789

Compilation message

Subtask #1 9.0 / 9.0

Subtask #2 12.0 / 12.0

Subtask #3 22.0 / 22.0

Subtask #4 57.0 / 57.0

Subtask #1
9.0 / 9.0

Subtask #2
12.0 / 12.0

Subtask #3
22.0 / 22.0

Subtask #4
57.0 / 57.0