HackerRank/kingdom_connectivity.cpp at master · fedeoliv/HackerRank · GitHub

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// https://www.hackerrank.com/challenges/kingdom-connectivity

#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

const int MODULO = 1000000000;
const int MAX_N = 10005;
const int MAX_M = 100005;

struct Edge {
    int v, next;
} edge[2 * MAX_M], edge2[2 * MAX_M];

int N, M;
int low[MAX_N], dfn[MAX_N], cnt[MAX_N], id[MAX_N], vis[MAX_N], Stack[MAX_N];
int dp[MAX_N], reach[MAX_N], reach2[MAX_N], topo[MAX_N];
int num, Head[MAX_N], num2, Head2[MAX_N];
int Size, Top, Index, topcnt;

void addEdge(int u, int v) {
    edge[num].v = v;
    edge[num].next = Head[u];
    Head[u] = num++;
}

void addEdge2(int u, int v) {
    edge2[num2].v = v;
    edge2[num2].next = Head2[u];
    Head2[u] = num2++;
}

void Tarjan(int u) {
    low[u] = dfn[u] = ++Index;
    Stack[++Top] = u;
    vis[u] = 1;

    for (int i = Head[u]; i != -1; i = edge[i].next) {
            int v = edge[i].v;

            if (!dfn[v]) {
                Tarjan(v);
                low[u] = min(low[u], low[v]);
            } else if (vis[v])
                low[u] = min(low[u], dfn[v]);
    }

    if (low[u] == dfn[u]) {
            Size++;

            for (; Stack[Top + 1] != u; --Top) {
                    vis[Stack[Top]] = 0;
                    id[Stack[Top]] = Size;
            }
    }
}

void dfs(int u) {
    reach[u] = 1;

    for (int i = Head[u]; i != -1; i = edge[i].next)
        if (!reach[edge[i].v])
            dfs(edge[i].v);
}

void dfs2(int u) {
    reach2[u] = 1;

    for (int i = Head2[u]; i != -1; i = edge2[i].next)
        if (!reach2[edge2[i].v])
            dfs2(edge2[i].v);
}

void topdfs(int u) {
    vis[u] = true;

    for (int i = Head[u]; i != -1; i = edge[i].next)
        if (!vis[edge[i].v]) dfs(edge[i].v);

    topo[topcnt++] = u;
}

int main() {
    num = num2 = Top = Size = Index = 0;
    memset(Head, -1, sizeof(Head));
    memset(Head2, -1, sizeof(Head2));

    cin >> N >> M;

    for (; M--; ) {
        int u, v;
        cin >> u >> v;
        addEdge(u, v);
        addEdge2(v, u);
    }

    for (int i = 1; i <= N; i++)
        if (!dfn[i]) Tarjan(i);

    for (int i = 1; i <= N; i++)
        cnt[id[i]]++;

    dfs(1);
    dfs2(N);

    if (!reach[N]) {
        cout << 0 << endl;
        return 0;
    }

    for (int i = 1; i <= N; i++)
        if (reach[i] && reach2[i] && cnt[id[i]] > 1) {
            cout << "INFINITE PATHS" << endl;
            return 0;
        }

    num2 = 0;
    memset(Head2, -1, sizeof(Head2));

    for (int i = 1; i <= N; i++)
        for (int j = Head[i]; j != -1; j = edge[j].next)
            if (id[i] != id[edge[j].v])
                addEdge2(id[i], id[edge[j].v]);

    memset(vis, 0, sizeof(vis));
    topcnt = 0;

    for (int i = 1; i <= Size; i++)
        if (!vis[i]) topdfs(i);

    reverse(topo, topo + Size);

    memset(dp, 0, sizeof(dp));
    dp[id[1]] = 1;

    for (int u = 0; u < topcnt; u++) {
        int idx = topo[u];
        if (dp[idx]) {
            for (int i = Head2[idx]; i != -1; i = edge2[i].next) {
                dp[edge2[i].v] += dp[idx];
                dp[edge2[i].v] %= MODULO;
            }
        }
    }

    cout << dp[id[N]] << endl;

    return 0;
}