sessions up to Mar 14; misc. practice

Author: fireofearth

2020/jan18/20102011-acmicpc-neerc-northern-subregional-contest-en.pdf

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+##
+
+Contest:  
+<https://codeforces.com/group/L0zlhp0AHw/contest/100610>
+
+Problem C:
+We solve it using commuting functions.
+The cycle in the commuting functions must have lengths sharing factors.
+

2020/jan18/README.md

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+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long int lld;
+lld MAX = numeric_limits<lld>::max();
+
+/*
+g++ -std=c++11 a-alien.cpp -o k
+*/
+int main() {
+    freopen("acm.in", "r", stdin);
+    freopen("acm.out", "w", stdout);
+
+    int n, m, i, j;
+    cin >> n >> m;
+    int a[n]; int b[m];
+    for(i = 0; i < n; i++)
+        cin >> a[i];
+    for(i = 0; i < m; i++)
+        cin >> b[i];
+
+    //cout << "DEBUG" << endl;
+    string o = "";
+    for(i = 0; i < n; i++) {
+        o += "(10 ";
+        for(j = 0; j < a[i]; j++) {
+            o += " - 1";
+            if(j == a[i] - 1) o += ")";
+            else o += " ";
+        }
+        if(i == n - 1) o += " = 0";
+        else o += " * ";
+    }
+    cout << o << endl;
+
+    return 0;
+}

2020/jan18/a-alien.cpp

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+2 2
+2 4
+3 5

2020/jan18/acm.in

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+1

2020/jan18/acm.out

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+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long int lld;
+lld MAX = numeric_limits<int>::max();
+
+void debug() { cout << "DEBUG" << endl; }
+
+template<class T>
+void print(T msg) { cout << msg << endl; }
+
+typedef pair<int, int> P;
+
+struct by_first {
+    bool operator() (const vector<int> &a,
+            const vector<int> &b) {
+        return a[0] < b[0];
+    }
+};
+
+/*
+g++ -std=c++11 c-commuting.cpp -o k
+
+1 -> 6
+2 -> 3
+3 -> 2
+4 -> 5
+5 -> 4
+6 -> 7
+7 -> 8
+8 -> 1
+
+8
+6 3 2 5 4 7 8 1
+
+1 -> 7
+2 -> 3
+3 -> 5
+4 -> 2
+5 -> 4
+6 -> 1
+7 -> 8
+8 -> 6
+
+8
+7 3 5 2 4 1 8 6
+*/
+int main() {
+    freopen("commuting.in", "r", stdin);
+    freopen("commuting.out", "w", stdout);
+
+    int n, i, j, k;
+    cin >> n;
+    int f[n+1];
+    int g[n+1];
+    bool seen[n+1];
+    vector<int> cycle;
+    vector<int> *pcycle;
+    vector<int>::iterator vit;
+    vector<vector<vector<int>>> cycles(n+1);
+    vector<vector<int>>::iterator sit;
+    set<int> s;
+    set<int> t;
+    for(i = 1; i < n+1; i++) {
+        cin >> f[i];
+        g[i] = 0;
+        seen[i] = false;
+    }
+
+    // make cycles
+    for(i = 1; i < n+1; i++) {
+        if(seen[i] == false) {
+            cycle = vector<int>();
+            j = i;
+            do {
+                seen[j] = true;
+                cycle.push_back(j);
+                j = f[j];
+            } while(i != j);
+            k = cycle.size();
+            cycles[k].push_back(cycle);
+            s.insert(k);
+            t.insert(k);
+        }
+    }
+
+    /*
+    // list the cycles
+    for(const vector<vector<int>> &cs : cycles) {
+        for(const vector<int> &c : cs) {
+            for(int p : c) {
+                cout << p << " ";
+            }
+            cout << endl;
+        }
+    }
+    */
+
+    for(int i : s) {
+        pcycle = NULL;
+        for(int j : t) {
+            if(i % j == 0) {
+                if(j >= i) break;
+                if(!pcycle || pcycle->at(0) > cycles[j][0][0]) {
+                    pcycle = &cycles[j][0];
+                }
+            }
+        }
+
+        if(pcycle && pcycle->at(0) < cycles[i][0][0]) {
+            // use pcycle representing cycle with order dividing i
+            for(const vector<int> &c : cycles[i]) {
+                vit = pcycle->begin();
+                for(int p : c) {
+                    g[p] = *vit;
+                    vit++;
+                    if(vit == pcycle->end()) vit = pcycle->begin();
+                }
+            }
+            t.erase(i);
+        } else {
+            // use first cycle of order i
+            pcycle = &cycles[i][0];
+            for(sit = cycles[i].begin(); sit != cycles[i].end(); sit++) {
+                for(j = 0; j < pcycle->size(); j++)
+                    g[sit->at(j)] = pcycle->at(j);
+            }
+        }
+    }
+    
+    for(i = 1; i < n+1; i++) {
+        cout << g[i];
+        if(i == n) cout << endl;
+        else cout << " ";
+    }
+    
+    /*
+    // test f, g commute
+    for(i = 1; i < n+1; i++) {
+        cout << f[g[i]];
+        if(i == n) cout << endl;
+        else cout << " ";
+    }
+    for(i = 1; i < n+1; i++) {
+        cout << g[f[i]];
+        if(i == n) cout << endl;
+        else cout << " ";
+    }
+    */
+
+    return 0;
+}
+
+
+
+
+
+
+
+
+
+
+

2020/jan18/c-commuting.cpp

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+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long int lld;
+lld MAX = numeric_limits<int>::max();
+
+/*
+g++ -std=c++11 c-commuting.cpp -o k
+did not work...
+
+10
+2 3 4 5 6 7 8 1 9 10
+
+10
+1 2 3 4 5 6 7 8 9 10
+
+5
+5 2 4 3 1
+out: 1 2 2 2 5
+
+8
+8 3 2 4 6 5 7 1
+out: 1 2 3 4 4 4 4 8
+
+11
+6 8 3 5 4 7 1 9 2 10 11
+out: 1 2 3 3 3 6 7 8 9 3 3
+
+9
+2 1 4 3 5 7 8 9 6
+*/
+int main() {
+    freopen("commuting.in", "r", stdin);
+    freopen("commuting.out", "w", stdout);
+
+    int n, i, j, k;
+    cin >> n;
+    int f[n+1];
+    int g[n+1];
+    for(i = 1; i < n+1; i++) {
+        cin >> f[i];
+        g[i] = 0;
+    }
+
+    // k is the first fixed point in f
+    k = 0;
+    for(i = 1; i < n+1; i++) {
+        if((bool) g[i]) {
+            // identified i as part of a cycle that has elements j < k
+            // do nothing
+        } else if(i == f[i]) {
+            // i is a fixed point
+            if(! (bool) k) {
+                // landed on first fixed point
+                k = i;
+            }
+            g[i] = k;
+        } else {
+            // i is in a cycle
+            if(!k) {
+                // has not reached first fixed point
+                j = f[i];
+                while(j != i) {
+                    g[j] = j;
+                    j = f[j];
+                }
+                g[i] = i;
+            } else {
+                // is past first fixed point
+                g[i] = k;
+            }
+        }
+    }
+
+    //cout <<  "f(g) ";
+    //for(i = 1; i < n+1; i++) {
+    //    cout << f[g[i]];
+    //    if(i == n) cout << endl;
+    //    else cout << " ";
+    //}
+    //cout << "g(f) ";
+    //for(i = 1; i < n+1; i++) {
+    //    cout << g[f[i]];
+    //    if(i == n) cout << endl;
+    //    else cout << " ";
+    //}
+
+    for(i = 1; i < n+1; i++) {
+        cout << g[i];
+        if(i == n) cout << endl;
+        else cout << " ";
+    }
+
+    return 0;
+}