Author : Dipu Kumar Mohanto
CSE, Batch - 6
BRUR.
Problem Statement : 10462 - Is There A Second Way Left?
Source : UVA Online Judge
Category : Graph Theory
Algorithm : Minimum Spanning Tree, kth mst
Verdict : Accepted
Complexity : O(km), k = kth spanning tree, m = edges
- #include "bits/stdc++.h"
- #include "ext/pb_ds/assoc_container.hpp"
- #include "ext/pb_ds/tree_policy.hpp"
- #include "ext/rope"
-
- using namespace std;
- using namespace __gnu_pbds;
- using namespace __gnu_cxx;
-
- #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 FORAB(i, a, b) for (int i = a; i <= b; i++)
-
- #define ll long long
- #define ull unsigned long long
- #define vi vector <int>
- #define vl vector <ll>
- #define pii pair <int, int>
- #define pll pair <ll, ll>
- #define mk make_pair
- #define ff first
- #define ss second
- #define eb emplace_back
- #define em emplace
- #define pb push_back
- #define ppb pop_back
- #define All(a) a.begin(), a.end()
- #define memo(a, b) memset(a, b, sizeof a)
- #define Sort(a) sort(All(a))
- #define ED(a) Sort(a), a.erase(unique(All(a)), a.end())
- #define rev(a) reverse(All(a))
- #define sz(a) (int)a.size()
- #define max3(a, b, c) max(a, max(b, c))
- #define min3(a, b, c) min(a, min(b, c))
- #define maxAll(a) *max_element(All(a))
- #define minAll(a) *min_element(All(a))
- #define allUpper(a) transform(All(a), a.begin(), :: toupper)
- #define allLower(a) transform(All(a), a.begin(), :: tolower)
- #define endl '\n'
- #define nl puts("")
- #define ub upper_bound
- #define lb lower_bound
- #define Exp exp(1.0)
- #define PIE 2*acos(0.0)
- #define Sin(a) sin(((a)*PIE)/180.0)
- #define EPS 1e-9
-
- template <typename T> using orderset = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
-
-
-
-
-
-
-
-
-
-
- #define here cerr << "Here" << endl;
- #define trace1(x) cerr << #x << ": " << x << endl;
- #define trace2(x, y) cerr << #x << ": " << x << " | " << #y << ": " << y << endl;
- #define trace3(x, y, z) cerr << #x << ": " << x << " | " << #y << ": " << y << " | " << #z << ": " << z << endl;
- #define trace4(a, b, c, d) cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << endl;
- #define trace5(a, b, c, d, e) cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << endl;
- #define trace6(a, b, c, d, e, f) cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << " | " << #f << ": " << f << endl;
-
- 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)); }
-
- #define ones(mask) __builtin_popcount(mask) // count set bit
- #define onesLL(mask) __builtin_popcountll(mask) // for long long
- #define lzeros(mask) __builtin_clz(mask) // no of leading zeros
- #define tzeros(mask) __builtin_ctz(mask) // no of trailing zeros
-
- inline int read() { int a; scanf("%d", &a); return a; }
- inline ll readLL() { ll a; scanf("%lld", &a); return a; }
- inline double readDD() { double a; scanf("%lf", &a); return a; }
-
- template <typename T> string toString(T num) { stringstream ss; ss << num; return ss.str(); }
- int toInt(string s) { int num; istringstream iss(s); iss >> num; return num; }
- ll toLLong(string s) { ll num; istringstream iss(s); iss >> num; return num; }
-
- #define inf 1e8
- #define mod 1000000007
-
- static const int maxn = 100 + 5;
- static const int logn = 18;
-
- struct Edge
- {
- int u, v, w;
- Edge(int u = 0, int v = 0, int w = 0) : u(u), v(v), w(w) {}
-
- friend bool operator < (Edge p, Edge q)
- {
- return p.w < q.w;
- }
- };
-
- struct Partition
- {
- vi choices;
- int mstCost;
- vi mstEdges;
- Partition(vi choices, int mstCost, vi mstEdges)
- {
- this->choices = choices;
- this->mstCost = mstCost;
- this->mstEdges = mstEdges;
- }
- friend bool operator < (Partition p, Partition q)
- {
- return p.mstCost > q.mstCost;
- }
- };
-
- int tnode, tedge;
- vector <Edge> graph;
-
- int par[maxn];
-
- void makeSet()
- {
- FOR(i, tnode) par[i] = i;
- }
-
- int findRep(int r)
- {
- if (r == par[r]) return r;
- return par[r] = findRep(par[r]);
- }
-
- bool Union(int u, int v)
- {
- int p = findRep(u);
- int q = findRep(v);
- if (p == q) return false;
- par[q] = p;
- return true;
- }
-
- Partition createPartition(vi choices)
- {
- makeSet();
- int take = 0;
- int ptr = 0;
- int mstCost = 0;
- vi mstEdges(tedge+1, -1);
- for (int i = 0; i < tedge; i++)
- {
- if (choices[i] == 1)
- {
- Edge e = graph[i];
- Union(e.u, e.v);
- mstCost += e.w;
- mstEdges[ptr++] = i;
- ++take;
- }
- }
- if (take == tnode-1) return Partition(choices, mstCost, mstEdges);
- for (int i = 0; i < tedge; i++)
- {
- if (take == tnode-1) break;
- if (choices[i] == 0)
- {
- Edge e = graph[i];
- if (Union(e.u, e.v))
- {
- mstCost += e.w;
- mstEdges[ptr++] = i;
- ++take;
- }
- }
- }
- sort(mstEdges.begin(), mstEdges.begin()+ptr);
- if (take == tnode-1) return Partition(choices, mstCost, mstEdges);
- return Partition(choices, -1, mstEdges);
- }
-
- int solve(int k)
- {
- priority_queue <Partition> PQ;
- vi choices(tedge+1);
- Partition part = createPartition(choices);
- if (part.mstCost == -1) return -1;
- PQ.emplace(part);
-
- while (PQ.empty() == false)
- {
- Partition p = PQ.top(); PQ.pop();
- --k;
-
- if (k == 0) return p.mstCost;
-
- for (int i = 0; i < tnode-1; i++)
- {
- if (p.choices[ p.mstEdges[i] ] == 0)
- {
- choices = p.choices;
- choices[ p.mstEdges[i] ] = -1;
- for (int j = 0; j < i; j++)
- {
- choices[ p.mstEdges[j] ] = 1;
- }
- Partition nxt = createPartition(choices);
- if (nxt.mstCost != -1) PQ.emplace(nxt);
- }
- }
- }
- return -2;
- }
-
- int main()
- {
-
-
- int tc = read();
- FOR(tcase, tc)
- {
- tnode = read();
- tedge = read();
- For(i, tedge)
- {
- int u = read();
- int v = read();
- int w = read();
- graph.eb(u, v, w);
- }
- Sort(graph);
- int mst = solve(2);
- printf("Case #%d : ", tcase);
- if (mst == -1) puts("No way");
- else if (mst == -2) puts("No second way");
- else printf("%d\n", mst);
- graph.clear();
- }
- }
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