[Codeforces] E. We Need More Bosses

Author            : Dipu Kumar Mohanto 
                    CSE, Batch - 6
                    BRUR.
Problem Statement : E. We Need More Bosses
Source            : Codeforces
Category          : Graph Theory
Algorithm         : Bridge Tree, Tree Diameter
Verdict           : Accepted

 
#include "bits/stdc++.h"
 
using namespace std;
 
#define FI              freopen("in.txt", "r", stdin)
#define FO              freopen("out.txt", "w", stdout)
#define FAST            ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL)
 
#define FOR(i, n)       for (int i = 1; i <= n; i++)
#define For(i, n)       for (int i = 0; i < n; i++)
#define ROF(i, n)       for (int i = n; i >= 1; i--)
#define Rof(i, n)       for (int i = n-1; i >= 0; i--)
#define FORI(i, n)      for (auto i : n)
#define eb              emplace_back
#define pb              push_back
#define ll              long long
#define ull             unsigned long long
#define vi              vector <int>
#define vl              vector <ll>
#define All(a)          a.begin(), a.end()
#define endl            '\n'
#define sz(a)           a.size()
#define lb              lower_bound
#define mod             1000000007
 
inline int setbit(int mask, int pos)      { return mask |= (1 << pos); }
inline int resetbit(int mask, int pos)    { return mask &= ~(1 << pos); }
inline int togglebit(int mask, int pos)   { return mask ^= (1 << pos); }
inline bool checkbit(int mask, int pos)   { return (bool)(mask & (1 << pos)); }
 
static const int maxn = 3e5 + 5;
static const int logn = 18;
 
struct node
{
      int v, e;
      node(int v = 0, int e = 0) : v(v), e(e) {}
};
 
vector <node> graph[maxn];
bool isBridge[maxn], vis[maxn];
int timer, dis[maxn], low[maxn];
 
inline void findBridge(int u = 1, int p = -1)
{
      vis[u] = 1;
      dis[u] = low[u] = ++timer;
      for (node it : graph[u])
      {
            int v = it.v;
            int e = it.e;
            if (v == p) continue;
            if (!vis[v])
            {
                  findBridge(v, u);
                  low[u] = min(low[u], low[v]);
                  if (dis[u] < low[v]) isBridge[e] = 1;
            }
            else
            {
                  low[u] = min(low[u], dis[v]);
            }
      }
}
 
int compo, compo_num[maxn];
bool used[maxn];
vector <int> tree[maxn];
 
inline void makeTree(int src)
{
      used[src] = 1;
      int cur_compo = compo;
      compo_num[src] = cur_compo;
      queue <int> PQ;
      PQ.emplace(src);
      while (!PQ.empty())
      {
            int u = PQ.front(); PQ.pop();
            for (node it : graph[u])
            {
                  int v = it.v;
                  int e = it.e;
                  if (used[v]) continue;
                  if (isBridge[e])
                  {
                        compo++;
                        tree[cur_compo].eb(compo);
                        tree[compo].eb(cur_compo);
                        makeTree(v);
                  }
                  else
                  {
                        PQ.emplace(v);
                        used[v] = 1;
                        compo_num[v] = cur_compo;
                  }
            }
      }
}
 
int maxDis, maxDisNode;
 
inline void dfs(int u, int p = -1, int level = 0)
{
      if (level > maxDis) maxDis = level, maxDisNode = u;
      for (int v : tree[u])
      {
            if (v == p) continue;
            dfs(v, u, level+1);
      }
}
 
int main()
{
      int tnode, tedge;
      cin >> tnode >> tedge;
      FOR(e, tedge)
      {
            int u, v;
            cin >> u >> v;
            graph[u].eb(v, e);
            graph[v].eb(u, e);
      }
      compo = 1;
      findBridge(1);
      makeTree(1);
      maxDis = -1, maxDisNode = -1;
      dfs(1);
      maxDis = -1;
      dfs(maxDisNode);
      cout << maxDis;
}

[Gym] H. Capital City

Author            : Dipu Kumar Mohanto 
                    CSE, Batch - 6
                    BRUR.
Problem Statement : H. Capital City
                    2015 ACM Arabella Collegiate Programming Contest
Source            : Gym
Category          : Graph Theory, Dynamic Programing
Algorithm         : Bridge Tree, DP on Tree
Verdict           : Accepted

#include <bits/stdc++.h>
 
using namespace std;
 
typedef long long ll;
 
static const int maxn = 3e5 + 5;
 
struct node
{
    int v, e;
    ll w;
    node() {}
    node(int vv, int ee, ll ww) : v(vv), e(ee), w(ww) {}
};
 
vector <node> G[maxn];
bool isBridge[maxn], vis[maxn];
int timer, dis[maxn], low[maxn];
 
inline void findBridge(int u, int p = -1)
{
    vis[u] = 1;
    dis[u] = low[u] = timer++;
    for (auto &it : G[u])
    {
        int v = it.v;
        int e = it.e;
        if (v == p) continue;
        if (!vis[v])
        {
            findBridge(v, u);
            low[u] = min(low[u], low[v]);
            if (dis[u] < low[v]) isBridge[e] = 1;
        }
        else
        {
            low[u] = min(low[u], dis[v]);
        }
    }
}
 
int compo;
bool used[maxn];
int compo_num[maxn];
set <int> component[maxn];
vector <node> tree[maxn];
 
inline void bridgeTree(int src)
{
    used[src] = 1;
    int cur_compo = compo;
    compo_num[src] = cur_compo;
    component[cur_compo].insert(src);
    queue <int> PQ;
    PQ.push(src);
    while (!PQ.empty())
    {
        int u = PQ.front(); PQ.pop();
        for (auto &it : G[u])
        {
            int v = it.v;
            int e = it.e;
            ll w = it.w;
            if (used[v]) continue;
            if (isBridge[e])
            {
                compo++;
                tree[cur_compo].push_back(node(compo, e, w));
                tree[compo].push_back(node(cur_compo, e, w));
                bridgeTree(v);
            }
            else
            {
                PQ.push(v);
                used[v] = 1;
                compo_num[v] = cur_compo;
                component[cur_compo].insert(v);
            }
        }
    }
}
 
ll in[maxn], out[maxn];
 
inline void dfs(int u, int p)
{
    in[u] = 0;
    for (auto &it : tree[u])
    {
        int v = it.v;
        ll w = it.w;
        if (v == p) continue;
        dfs(v, u);
        in[u] = max(in[u], w + in[v]);
    }
}
 
inline void dfs2(int u, int p)
{
    ll mx1 = -1;
    ll mx2 = -1;
    for (auto &it : tree[u])
    {
        int v = it.v;
        ll w = it.w;
        if (v == p) continue;
        if (in[v]+w >= mx1)
        {
            mx2 = mx1;
            mx1 = w + in[v];
        }
        else if (in[v]+w > mx2)
        {
            mx2 = w + in[v];
        }
    }
    for (auto &it : tree[u])
    {
        int v = it.v;
        ll w = it.w;
        if (v == p) continue;
        ll use = mx1;
        if (in[v]+w == mx1) use = mx2;
        out[v] = max(w+out[u], w+use);
        dfs2(v, u);
    }
}
 
inline void init()
{
    timer = 1;
    compo = 1;
    for (int i = 0; i < maxn; i++)
    {
        dis[i] = 0;
        low[i] = 0;
        isBridge[i] = 0;
        vis[i] = 0;
        used[i] = 0;
        compo_num[i] = -1;
        G[i].clear();
        tree[i].clear();
        in[i] = 0;
        out[i] = 0;
        component[i].clear();
    }
}
 
int main()
{
    //freopen("in.txt", "r", stdin);
 
    int tc;
    scanf("%d", &tc);
    for (int tcase = 1; tcase <= tc; tcase++)
    {
        init();
        int tNode, tEdge;
        scanf("%d %d", &tNode, &tEdge);
        int root = 1;
        for (int e = 1; e <= tEdge; e++)
        {
            int u, v;
            ll w;
            scanf("%d %d %lld", &u, &v, &w);
            assert(u != v);
            root = max(root, max(u, v));
            G[u].push_back(node(v, e, w));
            G[v].push_back(node(u, e, w));
        }
        findBridge(root);
        bridgeTree(root);
        dfs(1, -1);
        dfs2(1, -1);
        ll maxCost = 1e15 + 5;
        int city = tNode + 1;
        for (int i = 1; i <= compo; i++)
        {
            ll cc = max(in[i], out[i]);
            if (cc < maxCost)
            {
                maxCost = cc;
                city = *component[i].begin();
            }
            else if (cc == maxCost)
            {
                city = min(city, *component[i].begin());
            }
        }
        printf("%d %lld\n", city, maxCost);
    }
}
 

[Light OJ] 1300 - Odd Personality

Author            : Dipu Kumar Mohanto 
                    CSE, Batch - 6
                    BRUR.
Problem Statement : 1300 - Odd Personality
Source            : Light Online Judge
Category          : Graph Theory
Algorithm         : Bridge Tree
Verdict           : Accepted
#include <bits/stdc++.h>
 
using namespace std;
 
 
#define WHITE                  1
#define RED                    2
#define BLUE                   3
 
static const int maxn = 1e5 + 5;
 
struct node
{
    int v, e;
    node(int v = 0, int e = 0) : v(v), e(e) {}
};
 
vector <node> graph[maxn];
bool isBridge[maxn], vis[maxn];
int dis[maxn], low[maxn], timer;
 
inline void findBridge(int u, int p)
{
    vis[u] = 1;
    dis[u] = low[u] = timer++;
    vector <node>::iterator E;
    for (E = graph[u].begin(); E != graph[u].end(); E++)
    {
        int v = E->v;
        int e = E->e;
        if (v == p) continue;
        if (!vis[v])
        {
            findBridge(v, u);
            low[u] = min(low[u], low[v]);
            if (dis[u] < low[v])
            {
                isBridge[e] = 1;
            }
        }
        else
        {
            low[u] = min(low[u], dis[v]);
        }
    }
}
 
int compo;
bool used[maxn];
int  node_compo[maxn], edge_compo[maxn], num_node_in_a_compo[maxn], start[maxn];
 
inline void bridgeTree(int src)
{
    int cur_compo = compo;
    used[src] = 1;
    node_compo[src] = cur_compo;
    num_node_in_a_compo[cur_compo]++;
    if (start[cur_compo] == -1) start[cur_compo] = src;
    queue <int> PQ;
    PQ.push(src);
    while (!PQ.empty())
    {
        int u = PQ.front(); PQ.pop();
        vector <node>::iterator E;
        for (E = graph[u].begin(); E != graph[u].end(); E++)
        {
            int v = E->v;
            int e = E->e;
            if (used[v])
            {
                if (isBridge[e] == 0) edge_compo[e] = cur_compo;
                continue;
            }
            if (isBridge[e])
            {
                compo++;
                // make tree
                bridgeTree(v);
            }
            else
            {
                PQ.push(v);
                used[v] = 1;
                node_compo[v] = cur_compo;
                edge_compo[e] = cur_compo;
 
                num_node_in_a_compo[cur_compo]++;
            }
        }
    }
}
 
 
inline int read()           { int a; scanf("%d", &a); return a; }
 
int tNode, tEdge;
int color[maxn];
 
inline bool bicolor(int src, int compo_num)  // if a graph is bipartite graph, the graph must not
{                                            // contain any odd length cycle
    queue <int> PQ;
    PQ.push(src);
    color[src] = RED;
    while (!PQ.empty())
    {
        int u = PQ.front(); PQ.pop();
        vector <node>::iterator E;
        for (E = graph[u].begin(); E != graph[u].end(); E++)
        {
            int v = E->v;
            int e = E->e;
            if (node_compo[v] != compo_num || edge_compo[e] != compo_num) continue;
            if (color[v] == WHITE)
            {
                if (color[u] == RED) color[v] = BLUE;
                else color[v] = RED;
                PQ.push(v);
            }
            else if (color[u] == color[v])
            {
                return true;         // odd length cycle found
            }
        }
    }
    return false;   // Bipartite Graph, even length cycle
}
 
void init()
{
    timer = 1;
    compo = 1;
    for (int i = 0; i < maxn; i++)
    {
        dis[i] = 0;
        low[i] = 0;
        isBridge[i] = 0;
        vis[i] = 0;
        used[i] = 0;
        node_compo[i] = 0;
        edge_compo[i] = 0;
        start[i] = -1;
        color[i] = WHITE;  // ALL WHITE
        num_node_in_a_compo[i] = 0;
        graph[i].clear();
    }
}
 
int main()
{
    int tc = read();
    for (int tcase = 1; tcase <= tc; tcase++)
    {
        init();
        tNode = read();
        tEdge = read();
        for (int e = 1; e <= tEdge; e++)
        {
            int u = read();
            int v = read();
            graph[u].push_back({v, e});
            graph[v].push_back({u, e});
        }
        for (int i = 0; i < tNode; i++)
        {
            if (!vis[i])
            {
                findBridge(i, -1);
            }
        }
        for (int i = 0; i < tNode; i++)
        {
            if (!used[i])
            {
                bridgeTree(i);
                compo++;
            }
        }
        int total = 0;
        for (int c = 1; c <= compo; c++)
        {
            bool odd;
            if (num_node_in_a_compo[c]) ODD = bicolor(start[c], c);
            if (ODD) total += num_node_in_a_compo[c];
        }
        printf("Case %d: %d\n", tcase, total);
    }
}