답안 #602521

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
602521	2022-07-23T07:30:13 Z	jophyyjh	Job Scheduling (IOI19_job)	C++14	100 / 100	243 ms	18748 KB

/**
 * What an interesting pratice contest problem! I could only solve the first 3
 * subtasks. (they're really trivial...) After that I searched online for an answer.
 * 
 * The idea is like "Chain Reactions" (Google Code Jam 2022 Qual.). Since a node can
 * only be chosen when its parent has been, we try to carefully merge leaf nodes into
 * their parent through a greedy approach. Previously, I tried too hard on
 * identifying the first / last selected node, which can be quite difficult when our
 * search base is the whole tree.
 * 
 * Each time, we try to find a node v with the smallest d[]/u[]. (This node need not
 * be a leaf.) We try to merge v into its parent p, i.e. u[p] += u[v], d[p] += d[v],
 * adjust the cost and let children of v have p as their direct parent. Why is
 * this greedy correct?
 * Although it could be difficult to determine which leaf is the last / which node
 * is the first, if v has the smallest d[]/u[], there exists a optimal schedule in
 * which v is built immediately after p is built. Simple argument of "exchange" can
 * prove this. In such case, we can just consider the time diff. (and add the
 * additional cost). Note that all children of v now have p as their direct parent
 * because once v and p are built, all children of v can start.
 * Learnt lots of stuff from this problem!
 * 
 * PS1  The solution above is inspired by Tutis (from Codeforces) in
 *      https://codeforces.com/blog/entry/68632.
 * PS2  When we apply our greedy strategy, the tree may be splited, forming a
 *      forest. We can add a pseudo root (the original -1 in parents[]) to simplify
 *      our code.
 * 
 * Time Complexity: O(n * log(n))
 * Implementation 2     (full solution, inspired by Tutis from Codeforces)
*/

#include <bits/stdc++.h>
#include "job.h"

typedef long long   ll;
typedef std::vector<int>    vec;

// DSU that can assign a value to each set
struct DSU {
    vec parents, rank, values;
    DSU(int n) {
        parents.resize(n);
        rank.resize(n);
        values.resize(n);
        for (int i = 0; i < n; i++)
            parents[i] = i, rank[i] = 1;
    }
    inline int find(int k) {
        if (parents[k] == k)
            return k;
        return parents[k] = find(parents[k]);
    }
    inline int& get_val(int k) {
        k = find(k);
        return values[k];
    }
    bool merge(int a, int b) {      // merge b into a
        a = find(a), b = find(b);
        if (a == b)
            return false;
        int val = values[a];
        if (rank[b] > rank[a])
            std::swap(a, b);
        rank[a] += rank[b], parents[b] = a, values[a] = val;
        return true;
    }
};


struct r_t {
    int node;
    double r;
};

inline bool operator<(const r_t& r1, const r_t& r2)     { return r1.r > r2.r; }

ll scheduling_cost(std::vector<int> _p, std::vector<int> _u, std::vector<int> _d) {
    int n = _p.size();
    std::vector<int> parents(n + 1), u(n + 1), d(n + 1);
    for (int i = 0; i < n; i++)
        parents[i + 1] = _p[i] + 1, u[i + 1] = _u[i], d[i + 1] = _d[i];
    parents[0] = -1, u[0] = d[0] = 0;       // pseudo node

    // Use dsu to maintain merged nodes
    DSU dsu(n + 1);
    dsu.get_val(0) = 0;
    std::vector<double> r(n + 1);
    std::priority_queue<r_t> pq;
    for (int i = 1; i <= n; i++) {
        dsu.get_val(i) = i, r[i] = double(d[i]) / u[i];
        pq.push(r_t{i, r[i]});
    }
    ll cost = 0;
    while (!pq.empty()) {
        r_t rt = pq.top();
        pq.pop();
        if (dsu.get_val(rt.node) != rt.node || r[rt.node] != rt.r)
            continue;
        int v = rt.node, p = dsu.get_val(parents[v]);
        // std::cerr << "(p,v): (" << p << ',' << v << "),\tpairs of (u,d) (" << u[p]
        //           << ',' << d[p] << ") (" << u[v] << ',' << d[v] << ")" << std::endl;
        cost -= ll(d[v]) * ll(u[p]);
        d[p] += d[v], u[p] += u[v], r[p] = double(d[p]) / u[p];
        dsu.merge(p, v);
        if (p > 0)
            pq.push(r_t{p, r[p]});
    }
    cost += ll(u[0]) * ll(d[0]);
    return cost;
}

Subtask #1
5.0 / 5.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	308 KB	Output is correct
5	Correct	34 ms	4844 KB	Output is correct
6	Correct	80 ms	9512 KB	Output is correct
7	Correct	164 ms	15024 KB	Output is correct
8	Correct	191 ms	18604 KB	Output is correct
9	Correct	181 ms	18604 KB	Output is correct
10	Correct	243 ms	18620 KB	Output is correct
11	Correct	0 ms	212 KB	Output is correct
12	Correct	189 ms	18600 KB	Output is correct
13	Correct	146 ms	18720 KB	Output is correct
14	Correct	179 ms	18580 KB	Output is correct
15	Correct	120 ms	18580 KB	Output is correct
16	Correct	159 ms	18748 KB	Output is correct
17	Correct	222 ms	18600 KB	Output is correct
18	Correct	182 ms	18616 KB	Output is correct
19	Correct	111 ms	18620 KB	Output is correct
20	Correct	98 ms	18736 KB	Output is correct

Subtask #2
7.0 / 7.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	1 ms	300 KB	Output is correct
3	Correct	1 ms	212 KB	Output is correct
4	Correct	123 ms	17200 KB	Output is correct
5	Correct	105 ms	17172 KB	Output is correct
6	Correct	108 ms	17172 KB	Output is correct
7	Correct	124 ms	17192 KB	Output is correct
8	Correct	116 ms	17204 KB	Output is correct
9	Correct	106 ms	17208 KB	Output is correct
10	Correct	110 ms	17292 KB	Output is correct
11	Correct	134 ms	17212 KB	Output is correct

Subtask #3
12.0 / 12.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	0 ms	212 KB	Output is correct
3	Correct	1 ms	296 KB	Output is correct
4	Correct	1 ms	316 KB	Output is correct
5	Correct	5 ms	1344 KB	Output is correct
6	Correct	114 ms	17820 KB	Output is correct
7	Correct	110 ms	17724 KB	Output is correct
8	Correct	136 ms	17808 KB	Output is correct
9	Correct	125 ms	17828 KB	Output is correct
10	Correct	1 ms	212 KB	Output is correct
11	Correct	1 ms	340 KB	Output is correct
12	Correct	4 ms	1236 KB	Output is correct
13	Correct	5 ms	1340 KB	Output is correct
14	Correct	122 ms	17716 KB	Output is correct
15	Correct	125 ms	17828 KB	Output is correct
16	Correct	121 ms	17844 KB	Output is correct
17	Correct	114 ms	17832 KB	Output is correct
18	Correct	122 ms	17720 KB	Output is correct
19	Correct	114 ms	17724 KB	Output is correct
20	Correct	123 ms	17724 KB	Output is correct
21	Correct	109 ms	17724 KB	Output is correct
22	Correct	107 ms	17756 KB	Output is correct
23	Correct	125 ms	17832 KB	Output is correct
24	Correct	120 ms	17716 KB	Output is correct

Subtask #4
18.0 / 18.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	194 ms	18600 KB	Output is correct
3	Correct	211 ms	18620 KB	Output is correct
4	Correct	190 ms	18724 KB	Output is correct

Subtask #5
21.0 / 21.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	1 ms	300 KB	Output is correct
4	Correct	1 ms	300 KB	Output is correct
5	Correct	1 ms	212 KB	Output is correct
6	Correct	0 ms	300 KB	Output is correct
7	Correct	1 ms	296 KB	Output is correct
8	Correct	1 ms	212 KB	Output is correct
9	Correct	0 ms	212 KB	Output is correct
10	Correct	1 ms	212 KB	Output is correct
11	Correct	1 ms	212 KB	Output is correct
12	Correct	0 ms	300 KB	Output is correct
13	Correct	1 ms	300 KB	Output is correct
14	Correct	0 ms	212 KB	Output is correct
15	Correct	1 ms	212 KB	Output is correct
16	Correct	0 ms	212 KB	Output is correct
17	Correct	1 ms	300 KB	Output is correct

Subtask #6
37.0 / 37.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	1 ms	212 KB	Output is correct
3	Correct	0 ms	212 KB	Output is correct
4	Correct	1 ms	308 KB	Output is correct
5	Correct	34 ms	4844 KB	Output is correct
6	Correct	80 ms	9512 KB	Output is correct
7	Correct	164 ms	15024 KB	Output is correct
8	Correct	191 ms	18604 KB	Output is correct
9	Correct	181 ms	18604 KB	Output is correct
10	Correct	243 ms	18620 KB	Output is correct
11	Correct	0 ms	212 KB	Output is correct
12	Correct	189 ms	18600 KB	Output is correct
13	Correct	146 ms	18720 KB	Output is correct
14	Correct	179 ms	18580 KB	Output is correct
15	Correct	120 ms	18580 KB	Output is correct
16	Correct	159 ms	18748 KB	Output is correct
17	Correct	222 ms	18600 KB	Output is correct
18	Correct	182 ms	18616 KB	Output is correct
19	Correct	111 ms	18620 KB	Output is correct
20	Correct	98 ms	18736 KB	Output is correct
21	Correct	1 ms	212 KB	Output is correct
22	Correct	1 ms	300 KB	Output is correct
23	Correct	1 ms	212 KB	Output is correct
24	Correct	123 ms	17200 KB	Output is correct
25	Correct	105 ms	17172 KB	Output is correct
26	Correct	108 ms	17172 KB	Output is correct
27	Correct	124 ms	17192 KB	Output is correct
28	Correct	116 ms	17204 KB	Output is correct
29	Correct	106 ms	17208 KB	Output is correct
30	Correct	110 ms	17292 KB	Output is correct
31	Correct	134 ms	17212 KB	Output is correct
32	Correct	1 ms	212 KB	Output is correct
33	Correct	0 ms	212 KB	Output is correct
34	Correct	1 ms	296 KB	Output is correct
35	Correct	1 ms	316 KB	Output is correct
36	Correct	5 ms	1344 KB	Output is correct
37	Correct	114 ms	17820 KB	Output is correct
38	Correct	110 ms	17724 KB	Output is correct
39	Correct	136 ms	17808 KB	Output is correct
40	Correct	125 ms	17828 KB	Output is correct
41	Correct	1 ms	212 KB	Output is correct
42	Correct	1 ms	340 KB	Output is correct
43	Correct	4 ms	1236 KB	Output is correct
44	Correct	5 ms	1340 KB	Output is correct
45	Correct	122 ms	17716 KB	Output is correct
46	Correct	125 ms	17828 KB	Output is correct
47	Correct	121 ms	17844 KB	Output is correct
48	Correct	114 ms	17832 KB	Output is correct
49	Correct	122 ms	17720 KB	Output is correct
50	Correct	114 ms	17724 KB	Output is correct
51	Correct	123 ms	17724 KB	Output is correct
52	Correct	109 ms	17724 KB	Output is correct
53	Correct	107 ms	17756 KB	Output is correct
54	Correct	125 ms	17832 KB	Output is correct
55	Correct	120 ms	17716 KB	Output is correct
56	Correct	0 ms	212 KB	Output is correct
57	Correct	194 ms	18600 KB	Output is correct
58	Correct	211 ms	18620 KB	Output is correct
59	Correct	190 ms	18724 KB	Output is correct
60	Correct	1 ms	212 KB	Output is correct
61	Correct	1 ms	212 KB	Output is correct
62	Correct	1 ms	300 KB	Output is correct
63	Correct	1 ms	300 KB	Output is correct
64	Correct	1 ms	212 KB	Output is correct
65	Correct	0 ms	300 KB	Output is correct
66	Correct	1 ms	296 KB	Output is correct
67	Correct	1 ms	212 KB	Output is correct
68	Correct	0 ms	212 KB	Output is correct
69	Correct	1 ms	212 KB	Output is correct
70	Correct	1 ms	212 KB	Output is correct
71	Correct	0 ms	300 KB	Output is correct
72	Correct	1 ms	300 KB	Output is correct
73	Correct	0 ms	212 KB	Output is correct
74	Correct	1 ms	212 KB	Output is correct
75	Correct	0 ms	212 KB	Output is correct
76	Correct	1 ms	300 KB	Output is correct
77	Correct	0 ms	212 KB	Output is correct
78	Correct	1 ms	296 KB	Output is correct
79	Correct	0 ms	212 KB	Output is correct
80	Correct	0 ms	300 KB	Output is correct
81	Correct	0 ms	212 KB	Output is correct
82	Correct	0 ms	212 KB	Output is correct
83	Correct	0 ms	212 KB	Output is correct
84	Correct	1 ms	212 KB	Output is correct
85	Correct	0 ms	300 KB	Output is correct
86	Correct	0 ms	292 KB	Output is correct
87	Correct	0 ms	212 KB	Output is correct
88	Correct	3 ms	852 KB	Output is correct
89	Correct	4 ms	980 KB	Output is correct
90	Correct	8 ms	1376 KB	Output is correct
91	Correct	32 ms	4932 KB	Output is correct
92	Correct	70 ms	9384 KB	Output is correct
93	Correct	167 ms	18588 KB	Output is correct
94	Correct	170 ms	18492 KB	Output is correct
95	Correct	189 ms	18608 KB	Output is correct
96	Correct	180 ms	18488 KB	Output is correct
97	Correct	163 ms	18452 KB	Output is correct
98	Correct	178 ms	18596 KB	Output is correct
99	Correct	167 ms	18468 KB	Output is correct
100	Correct	165 ms	18504 KB	Output is correct
101	Correct	221 ms	18712 KB	Output is correct
102	Correct	127 ms	18492 KB	Output is correct
103	Correct	175 ms	18588 KB	Output is correct
104	Correct	194 ms	18620 KB	Output is correct
105	Correct	133 ms	18600 KB	Output is correct
106	Correct	112 ms	17968 KB	Output is correct

답안 #602521

Compilation message

Subtask #1 5.0 / 5.0

Subtask #2 7.0 / 7.0

Subtask #3 12.0 / 12.0

Subtask #4 18.0 / 18.0

Subtask #5 21.0 / 21.0

Subtask #6 37.0 / 37.0

Subtask #1
5.0 / 5.0

Subtask #2
7.0 / 7.0

Subtask #3
12.0 / 12.0

Subtask #4
18.0 / 18.0

Subtask #5
21.0 / 21.0

Subtask #6
37.0 / 37.0