oj.uz

Submission #1013407

# Submission time Handle Problem Language Result Execution time Memory
1013407 2024-07-03T14:00:30 Z boris_mihov Sky Walking (IOI19_walk) C++17
10 / 100
 716 ms 195924 KB 
#include "walk.h"
#include <algorithm>
#include <iostream>
#include <numeric>
#include <cassert>
#include <vector>
#include <queue>
#include <stack>
#include <map>
 
typedef long long llong;
const int MAXN = 100000 + 10;
const int INTERSECTIONS = 10 + 5;
const llong INF = 1e18;
const int INTINF = 1e9;
const int MAXLOG = 17;
 
namespace
{
    int cnt;
    int n, m;
    int s, t;
    int h[MAXN];
    int x[MAXN];
    int left[MAXN];
    int right[MAXN];
    int y[MAXN];
    std::map <int,int> map[MAXN];
    bool vis[MAXN * INTERSECTIONS];
    llong dist[MAXN * INTERSECTIONS];
    std::vector <std::pair <int,int>> g[MAXN * INTERSECTIONS]; 
    int cntNodes;
}
 
struct Sparse
{
    int sparse[MAXLOG][MAXN];
    int getLOG[MAXN];
 
    void build(int a[])
    {
        for (int i = 1 ; i <= n ; ++i)
        {
            sparse[0][i] = a[i];
        }
 
        for (int lg = 1 ; (1 << lg) <= n ; ++lg)
        {
            for (int i = 1 ; i + (1 << lg) - 1 <= n ; ++i)
            {
                sparse[lg][i] = std::max(sparse[lg - 1][i], sparse[lg - 1][i + (1 << lg - 1)]);
            }
        }
 
        for (int i = 1 ; i <= n ; ++i)
        {
            getLOG[i] = getLOG[i - 1];
            if ((1 << getLOG[i] + 1) < i) getLOG[i]++;
        }
    }
 
    int findMAX(int l, int r)
    {
        int lg = getLOG[r - l + 1];
        return std::max(sparse[lg][l], sparse[lg][r - (1 << lg) + 1]);
    }
};
 
Sparse sparse;
llong solve()
{
    for (int i = 1 ; i <= n ; ++i)
    {
        map[i][0] = ++cnt;
    }
 
    sparse.build(h);
    for (int i = 1 ; i <= m ; ++i)
    {
        int prev = left[i];
        if (map[left[i]][y[i]] == 0)
        {
            map[left[i]][y[i]] = ++cnt;
        }
 
        while (prev < right[i])
        {
            int l = prev, r = right[i] + 1, mid;
            while (l < r - 1)
            {
                mid = l + r >> 1;
                if (sparse.findMAX(prev + 1, mid) < y[i]) l = mid;
                else r = mid;
            }
 
            if (map[r][y[i]] == 0)
            {
                map[r][y[i]] = ++cnt;
            }
 
            // std::cout << "here: " << prev << ' ' << r << ' ' << y[i] << '\n';
            g[map[prev][y[i]]].push_back({map[r][y[i]], x[r] - x[prev]});
            g[map[r][y[i]]].push_back({map[prev][y[i]], x[r] - x[prev]});
            prev = r;
        }
    }
 
    for (int i = 1 ; i <= n ; ++i)
    {
        auto prev = map[i].begin();
        for (auto curr = std::next(map[i].begin()) ; curr != map[i].end() ; ++curr)
        {
            // std::cout << "edge ver: " << x[i] << ' ' << prev->first << ' ' << x[i] << ' ' << curr->first << '\n';
            g[prev->second].push_back({curr->second, curr->first - prev->first});
            g[curr->second].push_back({prev->second, curr->first - prev->first});
            prev = curr;
        }
    }
 
    std::priority_queue <std::pair <llong,int>> pq;
    std::fill(dist + 1, dist + 1 + cnt, INF);
    pq.push({0, map[s][0]});
    dist[map[s][0]] = 0;
 
    while (pq.size())
    {
        auto [d, node] = pq.top();
        pq.pop();
 
        if (vis[node])
        {
            continue;
        }
 
        vis[node] = true;
        for (const auto &[u, ed] : g[node])
        {
            if (dist[u] > dist[node] + ed)
            {
                dist[u] = dist[node] + ed;
                pq.push({-dist[u], u});
            }
        }
    }
 
	return (dist[map[t][0]] == INF ? -1 : dist[map[t][0]]);
}

struct Fenwick
{
    int tree[MAXN];
    void update(int idx, int val)
    {
        assert(idx != 0);
        for (; idx <= n ; idx += idx & (-idx))
        {
            tree[idx] += val;
        }
    }

    int query(int idx)
    {
        int res = 0;
        for (; idx ; idx -= idx & (-idx))
        {
            res += tree[idx];
        }

        return res;
    }

    int kth(int k)
    {
        int idx = 0;
        for (int lg = MAXLOG - 1 ; lg >= 0 ; --lg)
        {
            if (idx + (1 << lg) <= n && tree[idx + (1 << lg)] < k)
            {
                idx += (1 << lg);
                k -= tree[idx];
            }
        }

        return idx + 1;
    }
};

int lastX[MAXN];
int lastNode[MAXN];
int permY[MAXN];
int order[MAXN];
Fenwick fenwick;
std::vector <int> activate[MAXN];
std::vector <int> deactivate[MAXN];
int firstBigger[MAXN];

llong solveSpecial()
{
    map[1][0] = ++cnt; 
    map[n][0] = ++cnt; 
    std::iota(permY + 1, permY + 1 + m, 1);
    std::sort(permY + 1, permY + 1 + m, [&](int a, int b)
    {
        return y[a] < y[b];
    });

    for (int i = 1 ; i <= m ; ++i)
    {
        order[permY[i]] = i;
    }

    firstBigger[permY[m]] = m + 1;
    for (int i = m - 1 ; i >= 1 ; --i)
    {
        firstBigger[permY[i]] = firstBigger[permY[i + 1]];
        while (y[permY[firstBigger[permY[i]] - 1]] > y[permY[i]])
        {
            firstBigger[permY[i]]--;
        }
    }

    for (int i = 1 ; i <= m ; ++i)
    {
        activate[left[i]].push_back(i);
        deactivate[right[i] + 1].push_back(i);
    }
    
    for (int i = 1 ; i <= n ; ++i)
    {
        for (const int &idx : activate[i])
        {
            fenwick.update(order[idx], 1);
        }

        for (const int &idx : deactivate[i])
        {
            fenwick.update(order[idx], -1);
        }

        for (const int &idx : activate[i])
        {
            map[i][y[idx]] = ++cnt;
            lastNode[idx] = cnt;
            lastX[idx] = x[i];
        }

        for (const int &idx : activate[i])
        {
            int below = fenwick.query(order[idx] - 1);
            if (fenwick.query(firstBigger[idx] - 1) > fenwick.query(order[idx]))
            {
                below = fenwick.query(firstBigger[idx] - 1);
            }
            
            if (below)
            {
                int newIdx = permY[fenwick.kth(below)];
                if (lastX[newIdx] != x[i])
                {
                    map[i][y[newIdx]] = ++cnt;
                    g[lastNode[newIdx]].push_back({map[i][y[newIdx]], x[i] - lastX[newIdx]});
                    g[map[i][y[newIdx]]].push_back({lastNode[newIdx], x[i] - lastX[newIdx]});
                    lastX[newIdx] = x[i];
                    lastNode[newIdx] = map[i][y[newIdx]];
                }

                g[map[i][y[newIdx]]].push_back({map[i][y[idx]], y[idx] - y[newIdx]});
                g[map[i][y[idx]]].push_back({map[i][y[newIdx]], y[idx] - y[newIdx]});
            }
        }

        for (const int &idx : deactivate[i + 1])
        {
            if (lastX[idx] != x[i])
            {
                map[i][y[idx]] = ++cnt;
                g[lastNode[idx]].push_back({cnt, x[i] - lastX[idx]});
                g[cnt].push_back({lastNode[idx], x[i] - lastX[idx]});
                lastX[idx] = x[i];
                lastNode[idx] = cnt;
            }

            int below = fenwick.query(order[idx] - 1);
            if (fenwick.query(firstBigger[idx] - 1) > fenwick.query(order[idx]))
            {
                below = fenwick.query(firstBigger[idx] - 1);
            }
            
            if (below)
            {
                int newIdx = permY[fenwick.kth(below)];
                if (lastX[newIdx] != x[i])
                {
                    map[i][y[newIdx]] = ++cnt;
                    g[lastNode[newIdx]].push_back({cnt, x[i] - lastX[newIdx]});
                    g[cnt].push_back({lastNode[newIdx], x[i] - lastX[newIdx]});
                    lastX[newIdx] = x[i];
                    lastNode[newIdx] = cnt;
                }

                g[map[i][y[newIdx]]].push_back({map[i][y[idx]], y[idx] - y[newIdx]});
                g[map[i][y[idx]]].push_back({map[i][y[newIdx]], y[idx] - y[newIdx]});
            }
        }
    }
    
    if (map[1].size() > 1)
    {
        auto node = std::next(map[1].begin());
        g[map[1][0]].push_back({node->second, node->first});
        g[node->second].push_back({map[1][0], node->first});
    }

    if (map[n].size() > 1)
    {
        auto node = std::next(map[n].begin());
        g[map[n][0]].push_back({node->second, node->first});
        g[node->second].push_back({map[n][0], node->first});
    }

    std::priority_queue <std::pair <llong,int>> pq;
    std::fill(dist + 1, dist + 1 + cnt, INF);
    pq.push({0, map[s][0]});
    dist[map[s][0]] = 0;
 
    while (pq.size())
    {
        auto [d, node] = pq.top();
        pq.pop();

        if (vis[node])
        {
            continue;
        }

        vis[node] = true;
        for (const auto &[u, ed] : g[node])
        {
            if (dist[u] > dist[node] + ed)
            {
                dist[u] = dist[node] + ed;
                pq.push({-dist[u], u});
            }
        }
    }
 
	return (dist[map[t][0]] == INF ? -1 : dist[map[t][0]]);
}
 
long long min_distance(std::vector<int> x, std::vector<int> h, std::vector<int> l, std::vector<int> r, std::vector<int> y, int s, int t) 
{
    n = x.size();
    m = l.size();
    ::s = s + 1; ::t = t + 1;
 
    for (int i = 0 ; i < n ; ++i)
    {
        ::h[i + 1] = h[i];
        ::x[i + 1] = x[i];
    }
 
    std::vector <int> perm(m);
    std::iota(perm.begin(), perm.end(), 0);
    std::sort(perm.begin(), perm.end(), [&](int x, int y)
    {
        return l[x] < l[y];
    });
 
    for (int i = 0 ; i < m ; ++i)
    {
        ::left[i + 1] = l[perm[i]] + 1;
        ::right[i + 1] = r[perm[i]] + 1;
        ::y[i + 1] = y[perm[i]];
    }
 
    if (::s == 1 && ::t == n) return solveSpecial();
    return solve();
}

Compilation message

walk.cpp: In member function 'void Sparse::build(int*)':
walk.cpp:51:89: warning: suggest parentheses around '-' inside '<<' [-Wparentheses]
   51 |                 sparse[lg][i] = std::max(sparse[lg - 1][i], sparse[lg - 1][i + (1 << lg - 1)]);
      |                                                                                      ~~~^~~
walk.cpp:58:33: warning: suggest parentheses around '+' inside '<<' [-Wparentheses]
   58 |             if ((1 << getLOG[i] + 1) < i) getLOG[i]++;
      |                       ~~~~~~~~~~^~~
walk.cpp: In function 'llong solve()':
walk.cpp:91:25: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   91 |                 mid = l + r >> 1;
      |                       ~~^~~
walk.cpp: At global scope:
walk.cpp:32:9: warning: '{anonymous}::cntNodes' defined but not used [-Wunused-variable]
   32 |     int cntNodes;
      |         ^~~~~~~~

Subtask #1
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 48220 KB Output is correct
2 Correct 8 ms 48096 KB Output is correct
3 Correct 8 ms 48116 KB Output is correct
4 Correct 8 ms 49500 KB Output is correct
5 Correct 8 ms 49500 KB Output is correct
6 Correct 8 ms 48220 KB Output is correct
7 Correct 9 ms 48220 KB Output is correct
8 Correct 8 ms 48220 KB Output is correct
9 Correct 8 ms 48220 KB Output is correct
10 Correct 9 ms 48220 KB Output is correct
11 Correct 8 ms 48220 KB Output is correct
12 Correct 8 ms 48104 KB Output is correct
13 Correct 8 ms 48220 KB Output is correct
14 Correct 11 ms 48220 KB Output is correct
15 Correct 8 ms 48216 KB Output is correct
16 Correct 8 ms 48216 KB Output is correct
17 Correct 8 ms 49500 KB Output is correct

Subtask #2
0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 48116 KB Output is correct
2 Correct 8 ms 48220 KB Output is correct
3 Correct 534 ms 142416 KB Output is correct
4 Correct 356 ms 155732 KB Output is correct
5 Correct 217 ms 141328 KB Output is correct
6 Correct 192 ms 130640 KB Output is correct
7 Correct 215 ms 142672 KB Output is correct
8 Correct 716 ms 170020 KB Output is correct
9 Correct 254 ms 140360 KB Output is correct
10 Correct 582 ms 195924 KB Output is correct
11 Correct 220 ms 101240 KB Output is correct
12 Correct 108 ms 79696 KB Output is correct
13 Correct 198 ms 95828 KB Output is correct
14 Correct 102 ms 86352 KB Output is correct
15 Correct 93 ms 87892 KB Output is correct
16 Correct 115 ms 87888 KB Output is correct
17 Correct 96 ms 87120 KB Output is correct
18 Correct 320 ms 80312 KB Output is correct
19 Correct 12 ms 51036 KB Output is correct
20 Correct 50 ms 66640 KB Output is correct
21 Correct 102 ms 78672 KB Output is correct
22 Correct 101 ms 82776 KB Output is correct
23 Correct 151 ms 87632 KB Output is correct
24 Incorrect 98 ms 82512 KB Output isn't correct
25 Halted 0 ms 0 KB -

Subtask #3
0 / 15.0

# Verdict Execution time Memory Grader output
1 Incorrect 40 ms 59472 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #4
0 / 18.0

# Verdict Execution time Memory Grader output
1 Incorrect 40 ms 59472 KB Output isn't correct
2 Halted 0 ms 0 KB -

Subtask #5
0 / 43.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 48220 KB Output is correct
2 Correct 8 ms 48096 KB Output is correct
3 Correct 8 ms 48116 KB Output is correct
4 Correct 8 ms 49500 KB Output is correct
5 Correct 8 ms 49500 KB Output is correct
6 Correct 8 ms 48220 KB Output is correct
7 Correct 9 ms 48220 KB Output is correct
8 Correct 8 ms 48220 KB Output is correct
9 Correct 8 ms 48220 KB Output is correct
10 Correct 9 ms 48220 KB Output is correct
11 Correct 8 ms 48220 KB Output is correct
12 Correct 8 ms 48104 KB Output is correct
13 Correct 8 ms 48220 KB Output is correct
14 Correct 11 ms 48220 KB Output is correct
15 Correct 8 ms 48216 KB Output is correct
16 Correct 8 ms 48216 KB Output is correct
17 Correct 8 ms 49500 KB Output is correct
18 Correct 9 ms 48116 KB Output is correct
19 Correct 8 ms 48220 KB Output is correct
20 Correct 534 ms 142416 KB Output is correct
21 Correct 356 ms 155732 KB Output is correct
22 Correct 217 ms 141328 KB Output is correct
23 Correct 192 ms 130640 KB Output is correct
24 Correct 215 ms 142672 KB Output is correct
25 Correct 716 ms 170020 KB Output is correct
26 Correct 254 ms 140360 KB Output is correct
27 Correct 582 ms 195924 KB Output is correct
28 Correct 220 ms 101240 KB Output is correct
29 Correct 108 ms 79696 KB Output is correct
30 Correct 198 ms 95828 KB Output is correct
31 Correct 102 ms 86352 KB Output is correct
32 Correct 93 ms 87892 KB Output is correct
33 Correct 115 ms 87888 KB Output is correct
34 Correct 96 ms 87120 KB Output is correct
35 Correct 320 ms 80312 KB Output is correct
36 Correct 12 ms 51036 KB Output is correct
37 Correct 50 ms 66640 KB Output is correct
38 Correct 102 ms 78672 KB Output is correct
39 Correct 101 ms 82776 KB Output is correct
40 Correct 151 ms 87632 KB Output is correct
41 Incorrect 98 ms 82512 KB Output isn't correct
42 Halted 0 ms 0 KB -