Add problem Fixed-point theorem from UVA #math

Author: jhonber

uva/13074.cpp

@@ -0,0 +1,51 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+#define D(x) cout << #x << " = " << (x) << endl;
+
+int mcm (int a, int b) {
+  return (a * b) / __gcd(a, b);
+}
+
+int main() {
+  ios_base::sync_with_stdio(0); cin.tie(0);
+  int n;
+  while (cin >> n) {
+    if (!n) break;
+
+    vector<int> v(n);
+    for (auto &i: v) cin >> i;
+
+    vector<set<int>> count(n);
+    vector<int> cur(n), next(n);
+
+    for (int i = 1; i <= n; ++i) cur[i - 1] = i;
+
+    vector<int> cycle(n, 0);
+    bool found = true;
+    while (found) {
+      found = false;
+      for (int i = 0; i < n; ++i) {
+        int t = cur[v[i] - 1];
+        next[i] = t;
+        if (count[i].count(t) == 0) {
+          count[i].insert(t);
+          cycle[i] ++;
+          found = true;
+        }
+      }
+      cur = next;
+    }
+
+    set<int> st(cycle.begin(), cycle.end());
+    int ans = 1;
+    for (auto i: st) {
+      ans = mcm(ans, i);
+    }
+
+    cout << ans << endl;
+  }
+
+  return 0;
+}