Code mẫu

#include <bits/stdc++.h>
using namespace std;

const int N = 500'000;

int n, m, k, dist0[N], dist1[N], cntDist0[N], cntDist1[N];
vector<int> adj[N];

void bfs(int u, int dist[]) {
    for (int i = 0; i < n; ++i) {
        dist[i] = -1;
    }
    queue<int> qu;
    dist[u] = 0;
    qu.push(u);

    while (!qu.empty()) {
        int u = qu.front();
        qu.pop();

        for (int v : adj[u]) {
            if (dist[v] != -1) {
                continue;
            }

            dist[v] = dist[u] + 1;
            qu.push(v);
        }
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    cin >> n >> m >> k;
    for (int i = 1; i <= m; ++i) {
        int u, v;
        cin >> u >> v;
        --u;
        --v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    bfs(0, dist0);
    bfs(n - 1, dist1);

    if (k > dist0[n - 1]) {
        cout << 0 << '\n';
        return 0;
    }

    for (int i = 0; i < n; ++i) {
        assert(dist0[i] != -1 && dist1[i] != -1);
        ++cntDist0[dist0[i]];
        ++cntDist1[dist1[i]];
    }

    long long res = 0;
    if (k < dist0[n - 1]) {
        for (int i = 0; i < k; ++i) {
            res += 1ll * cntDist0[i] * cntDist1[(k - 1) - i];
        }
    } else {
        res = 1ll * n * (n - 1) / 2 - m;
        for (int i = 1; i < n; ++i) {
            cntDist1[i] += cntDist1[i - 1];
        }
        for (int i = 0; i <= k - 2; ++i) {
            res -= 1ll * cntDist0[i] * cntDist1[(k - 2) - i];
        }
    }

    cout << res << '\n';

    return 0;
}