HackerEarth Vertices and edges problem solution

YASH PAL, 31 July 202411 February 2026

In this HackerEarth Vertices and edges problem solution, You are given an undirected weighted graph with n vertices and m edges.

Consider all shortest paths between vertices 1 and n, for any vertex such as v(1 <= v <= n), says that, if v is in either all shortest paths or some of them or none of them.

HackerEarth Vertices and edges problem solution

HackerEarth Vertices and edges problem solution.

#include<bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<ll, int> ii;

const int N = 2e5+100, M = 3e5+10;
const ll INF = 1e18;

ll dis[N];
int T, stt[N], who[N], cnt[N];
vector<ii> g[N], d_es;
vector<int> d[N], r[N];
bool ok[N], mark[N], all[N];

struct ed{
  int v, u, w;
  ed():
    v(-1), u(-1), w(-1) {}
  ed(int v, int u, int w):
    v(v), u(u), w(w) {}
} e[M];

void dfs(int v){
  ok[v] = true;
  for(auto u : r[v])
    if(!ok[u])
      dfs(u);
}

void dfs_top(int v){
  mark[v] = true;
  for(auto u : d[v])
    if(!mark[u] && ok[u])
      dfs_top(u);
  stt[v] = T++;
  who[ stt[v] ] = v;
}

signed main(){
  ios_base::sync_with_stdio(false);cin.tie(NULL);
  int n, m;cin >> n >> m;
  for(int i=0 ; i<m ; i++){
    int v, u, w;cin >> v >> u >> w;v --;u --;
    e[i] = ed(v, u, w);
    g[v].push_back(ii(u, w));
    g[u].push_back(ii(v, w));
  }
  for(int i=0 ; i<n ; i++)
    dis[i] = INF;
  set<ii> st;
  st.insert(ii(0, 0));
  dis[0] = 0;
  while(!st.empty()){
    int v = st.begin()->second;
    st.erase(st.begin());
    for(auto U : g[v]){
      int u = U.first, w = U.second;
      if(dis[u] > dis[v] + w){
        st.erase(ii(dis[u], u));
        dis[u] = dis[v] + w;
        st.insert(ii(dis[u], u));
      }
    }
  }
  for(int i=0 ; i<m ; i++){
    int v = e[i].v, u = e[i].u, w = e[i].w;
    if(dis[v] > dis[u])
      swap(v, u);
    if(dis[v] + w == dis[u]){
      d[v].push_back(u);
      r[u].push_back(v);
      d_es.push_back(ii(u, v));
    }
  }
  dfs(n-1);
  dfs_top(0);
  for(auto e : d_es){
    int v = e.first, u = e.second;
    if(!ok[v] || !ok[u])
      continue;
    cnt[ stt[v]+1 ] ++;
    cnt[ stt[u] ] --;
  }
  int sum=0;
  for(int i=0 ; i<T ; i++){
    sum += cnt[i];
    if(!sum)
      all[ who[i] ] = true;
  }
  int cnt1=0, cnt2=0;
  for(int i=0 ; i<n ; i++){
    if(!ok[i]){
      cout << "nonen";
      continue;
    }
    if(all[i]){
      cnt2 ++;
      cout << "alln";
    }else{
      cnt1 ++;
      cout << "somen";
    }
  }
  // assert(cnt1<100);
  // assert(cnt2<100   );
}

Second solution

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxn = 2e5 + 14;
const ll inf = 1e18;
vector<pair<int, int> > g[maxn];
set<pair<ll, int> > pq;
bool need[maxn];
int n, m;
ll d[2][maxn];

void dij(int source, ll d[]) {
    fill(d, d + n, inf);
    d[source] = 0;
    pq.insert({0, source});
    while (pq.size()) {
        int v = pq.begin()->second;
        pq.erase(pq.begin());
        for (auto e : g[v])
            if (d[e.first] > d[v] + e.second) {
                pq.erase({d[e.first], e.first});
                pq.insert({d[e.first] = d[v] + e.second, e.first});
            }
    }
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    cin >> n >> m;
    for (int i = 0; i < m; ++i) {
        int v, u, w;
        cin >> v >> u >> w;
        v--, u--;
        g[v].emplace_back(u, w);
        g[u].emplace_back(v, w);
    }
    dij(0, d[0]);
    dij(n - 1, d[1]);
    pq.insert({0, 0});
    while (!pq.empty()) {
        int v = pq.begin()->second;
        pq.erase(pq.begin());
        need[v] = pq.empty();
        for (auto e : g[v])
            if (d[0][v] + e.second + d[1][e.first] == d[0][n - 1]) {
                pq.insert({d[0][e.first], e.first});
            }
    }
    for (int i = 0; i < n; ++i) {
        cout << (need[i] ? "all" : d[0][i] + d[1][i] == d[0][n - 1] ? "some" : "none") << 'n';
    }
}

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