Submission #1230649

#	Time	Username	Problem	Language	Result	Execution time	Memory
1230649		jajskao	Colouring a rectangle (eJOI19_colouring)	C++20	60 / 100	201 ms	167936 KiB

colouring

#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>

using namespace std;

// Using a large constant for infinity in the context of flow capacities.
const long long INF = 1e18;

// Defines a directed edge in the flow network.
struct Edge {
    int to;
    long long capacity;
    int rev; // Index of the reverse edge in the adjacency list of 'to'.
};

// Global variables for the graph and flow algorithm.
vector<vector<Edge>> adj;
vector<int> level;
vector<int> iter; // Using int instead of size_t to save memory.
vector<pair<int, int>> seg_tree_children; // Stores children for segment tree nodes.
vector<int> v_nodes; // Stores the graph node indices for one type of diagonal.

// Adds a directed edge and its corresponding residual edge to the graph.
void add_edge(int u, int v, long long cap) {
    adj[u].push_back({v, cap, (int)adj[v].size()});
    adj[v].push_back({u, 0, (int)adj[u].size() - 1});
}

// Performs a Breadth-First Search (BFS) to build the level graph for Dinic's algorithm.
bool bfs(int s, int t) {
    level.assign(adj.size(), -1);
    vector<int> q;
    q.reserve(adj.size()); // Pre-allocates memory to avoid reallocations.
    level[s] = 0;
    q.push_back(s);
    size_t head = 0;
    while (head < q.size()) {
        int u = q[head++];
        for (const auto& edge : adj[u]) {
            if (edge.capacity > 0 && level[edge.to] < 0) {
                level[edge.to] = level[u] + 1;
                q.push_back(edge.to);
            }
        }
    }
    return level[t] != -1;
}

// Performs a Depth-First Search (DFS) to find augmenting paths in the level graph.
long long dfs(int u, int t, long long f) {
    if (u == t) return f;
    for (int& i = iter[u]; i < (int)adj[u].size(); ++i) {
        Edge& e = adj[u][i];
        if (e.capacity > 0 && level[u] < level[e.to]) {
            long long d = dfs(e.to, t, min(f, e.capacity));
            if (d > 0) {
                e.capacity -= d;
                adj[e.to][e.rev].capacity += d;
                return d;
            }
        }
    }
    return 0;
}

// Dinic's max-flow algorithm to compute the maximum flow from source 's' to sink 't'.
long long max_flow(int s, int t) {
    long long flow = 0;
    while (bfs(s, t)) {
        iter.assign(adj.size(), 0);
        long long f;
        while ((f = dfs(s, t, INF)) > 0) {
            flow += f;
        }
    }
    return flow;
}

// Recursively builds a segment tree to represent connections efficiently.
int build_seg_tree(int l, int r, int& node_idx, int seg_base_idx) {
    int curr_node = node_idx++;
    if (l == r) {
        add_edge(curr_node, v_nodes[l], INF);
    } else {
        int mid = l + (r - l) / 2;
        int child1 = build_seg_tree(l, mid, node_idx, seg_base_idx);
        int child2 = build_seg_tree(mid + 1, r, node_idx, seg_base_idx);
        seg_tree_children[curr_node - seg_base_idx] = {child1, child2};
        add_edge(curr_node, child1, INF);
        add_edge(curr_node, child2, INF);
    }
    return curr_node;
}

// Queries the segment tree to add edges from a single u_node to a range of v_nodes.
void query_seg_tree(int node_idx, int seg_base_idx, int l, int r, int ql, int qr, int u_node) {
    if (ql > r || qr < l) return;
    if (ql <= l && r <= qr) {
        add_edge(u_node, node_idx, INF);
        return;
    }
    int mid = l + (r - l) / 2;
    pair<int, int> children = seg_tree_children[node_idx - seg_base_idx];
    if (children.first != -1) {
        query_seg_tree(children.first, seg_base_idx, l, mid, ql, qr, u_node);
    }
    if (children.second != -1) {
        query_seg_tree(children.second, seg_base_idx, mid + 1, r, ql, qr, u_node);
    }
}

// Solves the problem for diagonals of a single parity.
long long solve_for_parity(int m, int n, const vector<long long>& c1, const vector<long long>& c2, int parity) {
    vector<long long> costs1, costs2;
    vector<int> i_orig, j_orig;

    for (int i = 1 - n; i <= m - 1; ++i) {
        if (abs(i % 2) == parity) {
            i_orig.push_back(i);
            costs1.push_back(c1[i + n - 1]);
        }
    }
    for (int j = 0; j <= m + n - 2; ++j) {
        if (j % 2 == parity) {
            j_orig.push_back(j);
            costs2.push_back(c2[j]);
        }
    }
    if (costs1.empty() || costs2.empty()) return 0;

    int num_u = costs1.size();
    int num_v = costs2.size();

    // Tighter estimation for memory allocation.
    // A segment tree on num_v leaves has at most 2*num_v nodes.
    int num_seg_nodes_est = (num_v > 0) ? 2 * num_v : 0;
    int total_nodes_est = 2 + num_u + num_v + num_seg_nodes_est;
    adj.assign(total_nodes_est, vector<Edge>());

    int S = 0, T = 1;
    vector<int> u_nodes(num_u);
    v_nodes.assign(num_v, 0);

    int node_idx = 2;
    for (int i = 0; i < num_u; ++i) u_nodes[i] = node_idx++;
    for (int i = 0; i < num_v; ++i) v_nodes[i] = node_idx++;

    for (int i = 0; i < num_u; ++i) add_edge(S, u_nodes[i], costs1[i]);
    for (int i = 0; i < num_v; ++i) add_edge(v_nodes[i], T, costs2[i]);

    int seg_base_idx = node_idx;
    int seg_root = -1;
    if (num_v > 0) {
        seg_tree_children.assign(num_seg_nodes_est, {-1, -1});
        seg_root = build_seg_tree(0, num_v - 1, node_idx, seg_base_idx);
    }

    for (int u_idx = 0; u_idx < num_u; ++u_idx) {
        int i_val = i_orig[u_idx];
        // Corrected calculation for the range of intersecting diagonals.
        long long j_start_val = abs((long long)i_val);
        long long j_end_val = min((long long)2 * m - 2 - i_val, (long long)2 * n - 2 + i_val);

        if (j_start_val > j_end_val) continue;

        auto it_start = lower_bound(j_orig.begin(), j_orig.end(), j_start_val);
        if (it_start == j_orig.end() || *it_start > j_end_val) continue;
        
        auto it_end = upper_bound(j_orig.begin(), j_orig.end(), j_end_val);
        --it_end;

        int v_idx_start = distance(j_orig.begin(), it_start);
        int v_idx_end = distance(j_orig.begin(), it_end);
        
        if (v_idx_start <= v_idx_end && seg_root != -1) {
            query_seg_tree(seg_root, seg_base_idx, 0, num_v - 1, v_idx_start, v_idx_end, u_nodes[u_idx]);
        }
    }
    
    adj.resize(node_idx); // Trim unused pre-allocated memory.
    return max_flow(S, T);
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int m, n;
    cin >> m >> n;
    vector<long long> c1(m + n - 1), c2(m + n - 1);
    for (int i = 0; i < m + n - 1; ++i) cin >> c1[i];
    for (int i = 0; i < m + n - 1; ++i) cin >> c2[i];

    long long total_cost = 0;
    total_cost += solve_for_parity(m, n, c1, c2, 0); // Even parity
    total_cost += solve_for_parity(m, n, c1, c2, 1); // Odd parity
    
    cout << total_cost << endl;

    return 0;
}

• Subtask 1: 10 / 10
• Subtask 2: 10 / 10
• Subtask 3: 10 / 10
• Subtask 4: 20 / 20
• Subtask 5: 10 / 10
• Subtask 6: 0 / 20
• Subtask 7: 0 / 20