#include <bits/stdc++.h> using namespace std; const int inf = 1000 * 1000 * 1000 + 7; using Graph = vector<vector<int>>; vector<int> getLongestPath(const Graph& g, const set<int>& d) { int n = (int) g.size(); vector<int> f(n, 1), nxt(n, -1); int s = -1; for (int v = n - 1; v >= 0; --v) { if (d.count(v)) { f[v] = -inf; continue; } for (int to: g[v]) { if (f[v] < f[to] + 1) { f[v] = f[to] + 1; nxt[v] = to; } } if (s == -1 || f[v] > f[s]) { s = v; } } vector<int> path; while (s != -1) { path.push_back(s); s = nxt[s]; } return path; } int solve(const Graph& g, set<int> d, int k) { auto path = getLongestPath(g, d); if (k == 0) { return (int) path.size(); } int result = inf; for (int v: path) { d.insert(v); result = min(result, solve(g, d, k - 1)); d.erase(v); } return result; } int solve(Graph g, int k) { return solve(g, set<int>(), k); } int solveInput() { int n, m, k; cin >> n >> m >> k; Graph g(n); for (int i = 0; i < m; ++i) { int x, y; cin >> x >> y; g[x - 1].push_back(y - 1); } return solve(g, k); } int brute(Graph g, set<int> d, int k) { int n = (int) g.size(); auto path = getLongestPath(g, d); if (k == 0) { return (int) path.size(); } int result = inf; for (int v = 0; v < n; ++v) { if (d.count(v)) { continue; } d.insert(v); result = min(result, brute(g, d, k - 1)); d.erase(v); } return result; } int brute(Graph g, int k) { return brute(g, set<int>(), k); } Graph genRandomGraph(int n, int m) { Graph g(n); set<pair<int, int>> s; for (int i = 0; i < m; ++i) { int x = rand() % n; int y = rand() % n; if (x > y) { swap(x, y); } if (x == y || s.count({x, y})) { --i; continue; } g[x].push_back(y); s.insert({x, y}); } return g; } void stress() { for (int len = 1; len <= 6; ++len) { cerr << "All: " << len << endl; vector<pair<int, int>> edges; for (int i = 0; i < len; ++i) for (int j = 0; j < i; ++j) edges.emplace_back(j, i); int m = (int) edges.size(); for (int i = 0; i < (1 << m); ++i) { Graph g(len); for (int j = 0; j < m; ++j) { if (i & (1 << j)) { g[edges[j].first].push_back(edges[j].second); } } for (int k = 0; k <= min(4, len); ++k) { assert(brute(g, k) == solve(g, k)); } } } cerr << "Correct on small!" << endl; for (int i = 0; i < 100; ++i) { Graph g = genRandomGraph(300, 400); int k = rand() % 3; assert(brute(g, k) == solve(g, k)); cerr << i << endl; } cerr << "Correct on random with small k" << endl; for (int i = 0; i < 100; ++i) { auto start = clock(); Graph g = genRandomGraph(300, 400); int k = rand() % 5; int r = solve(g, k); auto end = clock(); cerr << i << ", time:" << (end - start + .0) / CLOCKS_PER_SEC << " : " << r << endl; } cout << "Fast? :)" << endl; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << solveInput() << '\n'; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 | #include <bits/stdc++.h> using namespace std; const int inf = 1000 * 1000 * 1000 + 7; using Graph = vector<vector<int>>; vector<int> getLongestPath(const Graph& g, const set<int>& d) { int n = (int) g.size(); vector<int> f(n, 1), nxt(n, -1); int s = -1; for (int v = n - 1; v >= 0; --v) { if (d.count(v)) { f[v] = -inf; continue; } for (int to: g[v]) { if (f[v] < f[to] + 1) { f[v] = f[to] + 1; nxt[v] = to; } } if (s == -1 || f[v] > f[s]) { s = v; } } vector<int> path; while (s != -1) { path.push_back(s); s = nxt[s]; } return path; } int solve(const Graph& g, set<int> d, int k) { auto path = getLongestPath(g, d); if (k == 0) { return (int) path.size(); } int result = inf; for (int v: path) { d.insert(v); result = min(result, solve(g, d, k - 1)); d.erase(v); } return result; } int solve(Graph g, int k) { return solve(g, set<int>(), k); } int solveInput() { int n, m, k; cin >> n >> m >> k; Graph g(n); for (int i = 0; i < m; ++i) { int x, y; cin >> x >> y; g[x - 1].push_back(y - 1); } return solve(g, k); } int brute(Graph g, set<int> d, int k) { int n = (int) g.size(); auto path = getLongestPath(g, d); if (k == 0) { return (int) path.size(); } int result = inf; for (int v = 0; v < n; ++v) { if (d.count(v)) { continue; } d.insert(v); result = min(result, brute(g, d, k - 1)); d.erase(v); } return result; } int brute(Graph g, int k) { return brute(g, set<int>(), k); } Graph genRandomGraph(int n, int m) { Graph g(n); set<pair<int, int>> s; for (int i = 0; i < m; ++i) { int x = rand() % n; int y = rand() % n; if (x > y) { swap(x, y); } if (x == y || s.count({x, y})) { --i; continue; } g[x].push_back(y); s.insert({x, y}); } return g; } void stress() { for (int len = 1; len <= 6; ++len) { cerr << "All: " << len << endl; vector<pair<int, int>> edges; for (int i = 0; i < len; ++i) for (int j = 0; j < i; ++j) edges.emplace_back(j, i); int m = (int) edges.size(); for (int i = 0; i < (1 << m); ++i) { Graph g(len); for (int j = 0; j < m; ++j) { if (i & (1 << j)) { g[edges[j].first].push_back(edges[j].second); } } for (int k = 0; k <= min(4, len); ++k) { assert(brute(g, k) == solve(g, k)); } } } cerr << "Correct on small!" << endl; for (int i = 0; i < 100; ++i) { Graph g = genRandomGraph(300, 400); int k = rand() % 3; assert(brute(g, k) == solve(g, k)); cerr << i << endl; } cerr << "Correct on random with small k" << endl; for (int i = 0; i < 100; ++i) { auto start = clock(); Graph g = genRandomGraph(300, 400); int k = rand() % 5; int r = solve(g, k); auto end = clock(); cerr << i << ", time:" << (end - start + .0) / CLOCKS_PER_SEC << " : " << r << endl; } cout << "Fast? :)" << endl; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << solveInput() << '\n'; } |