[New Problem] Max-Cut (192) and Reduced Max-2-SAT (193) (#73)

* Fix: Support unbounded ratio in scoring formula for p36, p119, p120

* Fix: Support unbounded ratio in scoring formula for p125

* Add Problem 174, 175

* Fix: problem 174, 175 larger public dataset

* Fix: Problem 175 Data Range

* Add Problem 176, 177

* Add Problem 178, 179

* Add Problem 180, 181

* Revert "Add Problem 180, 181"

This reverts commit 94de9f3.

* Add Problem 180, 181

* Add Problem 192, 193

Author: hfhongzy

algorithmic/problems/192/chk.cc

@@ -0,0 +1,40 @@
+#include "testlib.h"
+#include <bits/stdc++.h>
+using namespace std;
+
+int main(int argc, char* argv[]) {
+  registerTestlibCmd(argc, argv);
+
+  int n = inf.readInt(1, 1000);
+  int m = inf.readInt(0, 20000);
+
+  vector<pair<int,int>> edges(m);
+  for (int i = 0; i < m; i++) {
+    int u = inf.readInt(1, n);
+    int v = inf.readInt(1, n);
+    if (u == v) {
+      quitf(_wa, "self-loop on node %d", u);
+    }
+    edges[i] = {u - 1, v - 1};
+  }
+
+  vector<int> side(n);
+  for (int i = 0; i < n; i++) {
+    side[i] = ouf.readInt(0, 1);
+  }
+
+  int cut = 0;
+  for (auto &[u, v] : edges) {
+    if (side[u] != side[v]) cut++;
+  }
+
+  double ratio;
+  if (m == 0) {
+    ratio = 1.0;
+  } else {
+    ratio = (double)cut / (double)m;
+  }
+
+  ratio = max(0.0, min(1.0, ratio));
+  quitp(ratio, "Ratio: %.6f", ratio);
+}

algorithmic/problems/192/config.yaml

@@ -0,0 +1,9 @@
+type: default
+time: 1s
+memory: 1024m
+subtasks:
+  - score: 100
+    n_cases: 3
+checker: chk.cc
+checker_type: testlib
+filename: std.cc

algorithmic/problems/192/statement.txt

@@ -0,0 +1,36 @@
+# Max-Cut
+
+## Problem
+
+You are given an undirected graph with n vertices and m edges.
+Your task is to partition the vertices into two sets to maximize the number of edges crossing the partition.
+
+An edge is a cut edge if its two endpoints are in different sets.
+
+## Input Format
+
+- Line 1: two integers n and m (1 ≤ n ≤ 1000, 0 ≤ m ≤ 20000)
+- Next m lines: two integers u v (1 ≤ u, v ≤ n, u ≠ v)
+
+The graph may be disconnected.
+There are no multiple edges or self-loops.
+
+## Output Format
+
+- Output exactly one line:
+  - n integers s₁ s₂ … sₙ
+  - each sᵢ ∈ {0, 1}
+  - sᵢ = 0 means vertex i is in set S
+  - sᵢ = 1 means vertex i is in set T
+
+## Scoring
+
+Let:
+- m be the number of edges
+- c be the number of cut edges
+
+Score is defined as:
+- If m > 0:  score = c / m
+- If m = 0:  score = 1
+
+The score is clamped to [0, 1].

algorithmic/problems/192/testdata/1.ans

@@ -0,0 +1,2 @@
+10 1
+4 10

algorithmic/problems/192/testdata/1.in

@@ -0,0 +1,10 @@
+50 9
+5 23
+6 12
+9 28
+10 17
+15 49
+18 32
+19 46
+24 29
+32 40

algorithmic/problems/192/testdata/2.ans

@@ -0,0 +1,136 @@
+200 135
+1 135
+2 46
+2 135
+4 38
+4 141
+4 200
+5 121
+5 197
+6 22
+6 100
+8 55
+8 120
+9 135
+10 75
+12 16
+14 84
+14 186
+15 84
+15 169
+15 180
+16 134
+18 194
+19 40
+20 42
+20 139
+20 186
+21 118
+22 148
+23 69
+23 193
+25 70
+26 165
+27 157
+28 156
+29 128
+32 145
+34 65
+35 114
+35 198
+36 56
+36 93
+36 121
+36 170
+37 41
+37 158
+38 117
+39 123
+41 63
+41 75
+41 78
+41 151
+41 189
+43 121
+44 60
+44 112
+47 129
+47 196
+49 106
+51 114
+51 156
+51 177
+52 189
+59 101
+60 91
+60 135
+61 104
+61 114
+61 118
+61 133
+63 140
+63 144
+64 70
+66 95
+67 194
+70 107
+70 175
+71 158
+78 148
+79 169
+82 95
+87 194
+89 122
+89 137
+90 158
+92 145
+92 168
+92 177
+94 154
+95 102
+95 143
+96 171
+101 167
+102 123
+102 187
+108 131
+108 169
+108 195
+110 137
+110 168
+111 152
+112 118
+112 142
+112 168
+112 175
+113 135
+113 194
+115 152
+116 134
+118 137
+119 140
+119 159
+120 122
+120 146
+120 169
+123 174
+124 132
+124 189
+126 181
+132 135
+135 189
+137 157
+137 173
+145 151
+153 169
+154 189
+156 165
+158 193
+164 191
+166 186
+167 180
+168 196
+180 199
+183 198
+189 190
+192 194

algorithmic/problems/192/testdata/2.in

@@ -0,0 +1,46 @@
+#include "testlib.h"
+#include <bits/stdc++.h>
+using namespace std;
+
+int main(int argc, char* argv[]) {
+  registerTestlibCmd(argc, argv);
+
+  int n = inf.readInt(1, 1000);
+  int m = inf.readInt(0, 40000);
+
+  vector<array<int,2>> clauses(m);
+  for (int i = 0; i < m; i++) {
+    int a = inf.readInt(-n, n);
+    int b = inf.readInt(-n, n);
+    if (a == 0 || b == 0) {
+      quitf(_wa, "literal cannot be zero");
+    }
+    clauses[i] = {a, b};
+  }
+
+  vector<int> val(n + 1);
+  for (int i = 1; i <= n; i++) {
+    val[i] = ouf.readInt(0, 1);
+  }
+
+  int sat = 0;
+  for (auto &cl : clauses) {
+    bool ok = false;
+    for (int k = 0; k < 2; k++) {
+      int x = cl[k];
+      int v = abs(x);
+      bool lit = (x > 0 ? val[v] == 1 : val[v] == 0);
+      if (lit) {
+        ok = true;
+        break;
+      }
+    }
+    if (ok) sat++;
+  }
+
+  double score = 1.0;
+  if (m > 0) score = (double)sat / m;
+  score = max(0.0, min(1.0, score));
+
+  quitp(score, "Ratio: %.6f", score);
+}