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// 1489. Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree
#include "leetcode.h"
/*
* given a weighted undirected connected graph with 'n' vertices numbered from 0
* to 'n - 1' and an array 'edges' where 'edges[i] = [ai, bi, weighti]'
* represents a bidrectional and weighted edge between nodes 'ai' and 'bi'. a
* minimum spanning tree (MST) is a subset of the graph's edges that connects
* all vertices withoutcycles and with the minimum possible total edge weight.
* find all critical and pseudo-critical edges in the given graph's MST. an MST
* edge whose deletion from the graph would casue the MST weight to increase is
* called a critical edge. on the other hand, a pseudo-critical edge is that
* which can appear in some MSTs butnot all. note that you can return the
* indices of the edges in any order.
*/
class UnionFind {
vector<int> f, rank;
public:
UnionFind(int n) {
rank = vector<int>(n, 1);
f.resize(n);
for (int i = 0; i < n; ++i)
f[i] = i;
}
int find(int x) {
if (f[x] == x)
return x;
else
return f[x] = find(f[x]);
}
void uinion(int x, int y) {
int fx = find(x), fy = find(y);
if (fx == fy)
return;
if (rank[fx] > rank[fy])
swap(fx, fy);
f[fx] = fy;
if (rank[fx] == rank[fy])
rank[fy]++;
}
};
class Solution {
int get_mst(const int n, const vvd & edges, int block_edge,
int pre_edge = -1) {
UnionFind uf(n);
int weight = 0;
if (pre_edge != -1) {
weight += edges[pre_edge][2];
uf.uinion(edges[pre_edge][0], edges[pre_edge][1]);
}
for (int i = 0; i < edges.size(); ++i) {
if (block_edge == i)
continue;
const auto &e = edges[i];
if (uf.find(e[0]) == uf.find(e[1]))
continue;
uf.uinion(e[0], e[1]);
weight += e[2];
}
for (int i = 0; i < n; ++i)
if (uf.find(i) != uf.find(0))
return 1e9 + 7;
return weight;
}
public:
vvd findCriticalAndPseudoCriticalEdges(int n, vvd & edges) {
for (int i = 0; i < edges.size(); ++i)
edges[i].push_back(i);
sort(
edges.begin(), edges.end(),
[](const vector<int> &a, const vector<int> &b) { return a[2] < b[2]; });
int origin_mst = get_mst(n, edges, -1);
vector<int> critical, non_critical;
for (int i = 0; i < edges.size(); ++i) {
if (origin_mst < get_mst(n, edges, i))
critical.push_back(edges[i][3]);
else if (origin_mst == get_mst(n, edges, -1, i))
non_critical.push_back(edges[i][3]);
}
return {critical, non_critical};
}
};
int main() {
Solution obj;
vvd e1 = {{0, 1, 1}, {1, 2, 1}, {2, 3, 2}, {0, 3, 2},
{0, 4, 3}, {3, 4, 3}, {1, 4, 6}},
e2 = {{0, 1, 1}, {1, 2, 1}, {2, 3, 1}, {0, 3, 1}};
for (auto i : obj.findCriticalAndPseudoCriticalEdges(5, e1))
for (auto j : i)
printf("%d ", j);
printf("\n");
for (auto i : obj.findCriticalAndPseudoCriticalEdges(4, e2))
for (auto j : i)
printf("%d ", j);
printf("\n");
}
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