Adding problems related to Algorithm Games

Algorithm_Games/GameOfSegments.cpp

@@ -0,0 +1,72 @@
+#include <cstdio>
+#include <cstring>
+#include <cctype>
+#include <cstdlib>
+#include <cmath>
+#include <ctime>
+#include <iostream>
+#include <map>
+#include <set>
+#include <list>
+#include <sstream>
+#include <queue>
+#include <deque>
+#include <stack>
+#include <vector>
+#include <bitset>
+#include <algorithm>
+using namespace std;
+
+template <class T> void checkmax(T &t, T x) { if (x > t) t = x; }
+template <class T> void checkmin(T &t, T x) { if (x < t) t = x; }
+template <class T> void _checkmax(T &t, T x) { if (t == -1 || x > t) t = x; }
+template <class T> void _checkmin(T &t, T x) { if (t == -1 || x < t) t = x; }
+typedef long long ll;
+class GameOfSegments {
+  public:
+  int mem[1010];
+
+  int grundy(int n) {
+    if(n==0 || n == 1) return 0;
+    if(mem[n]!=-1) return mem[n];
+
+    set<int> reachable;
+    for(int i=0;i<=n-2;i++) {
+      int a = grundy(i);
+      int b = grundy(n-i-2);
+      reachable.insert(a^b);
+    }
+    int answer = 0;
+    while(reachable.count(answer)) answer++;
+
+    return mem[n] = answer;
+  }
+
+  int winner(int N)  {
+    memset(mem,-1,sizeof(mem));
+    if(grundy(N)) {
+      return 1;
+    }
+    return 2;
+  }
+
+// BEGIN CUT HERE
+	public:
+	void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); }
+	private:
+	template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
+	void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
+	void test_case_0() { int Arg0 = 3; int Arg1 = 1; verify_case(0, Arg1, winner(Arg0)); }
+	void test_case_1() { int Arg0 = 4; int Arg1 = 1; verify_case(1, Arg1, winner(Arg0)); }
+	void test_case_2() { int Arg0 = 15; int Arg1 = 2; verify_case(2, Arg1, winner(Arg0)); }
+	void test_case_3() { int Arg0 = 191; int Arg1 = 2; verify_case(3, Arg1, winner(Arg0)); }
+
+// END CUT HERE
+
+};
+
+    // BEGIN CUT HERE
+int main() {
+    GameOfSegments ___test;
+    ___test.run_test(-1);
+}

Algorithm_Games/MATGAME.cpp

@@ -0,0 +1,74 @@
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <set>
+#include <string.h>
+
+using namespace std;
+
+int n,m;
+vector<vector<int> > matrix;
+int mem[51][51];
+
+int solve(int row, int index) {
+
+	if(index == m-1) {
+		return matrix[row][index];
+	}
+
+	if(mem[row][index]!=-1) return mem[row][index];
+
+	int temp = solve(row, index+1);
+
+	if(matrix[row][index] <= temp) {
+
+		return  mem[row][index] = matrix[row][index] - 1;
+	} else {
+		return  mem[row][index] = matrix[row][index];
+	}
+}
+
+int compute() {
+	int answer =0;
+	memset(mem,-1,sizeof(mem));
+	for(int i=0;i<n;i++) {
+
+		int temp = solve(i, 0);
+		answer ^= temp;
+
+	} 	
+	return answer;
+}
+int main() {
+	// your code goes here
+	ios_base::sync_with_stdio(false);
+	int test;
+	cin>>test;
+	while(test--) {
+
+		cin>>n>>m;
+		matrix.clear();
+		for(int i=0;i<n;i++) {
+			vector<int> t;
+
+			for(int j=0;j<m;j++) {
+				int temp;
+				cin>>temp;
+
+				t.push_back(temp);
+			}
+			matrix.push_back(t);
+		}
+
+		int val = compute();
+		if(val == 0) {
+			cout<<"SECOND"<<endl;
+		} else {
+			cout<<"FIRST"<<endl;
+		}
+	}
+	return 0;
+}
+
+
+

Algorithm_Games/MMMGAME.cpp

@@ -0,0 +1,47 @@
+#include <iostream>
+#include <string>
+#include <stdio.h>
+#include <algorithm> // binsearch,max(a,b),min(a,b)
+#include <math.h>
+#include <queue>
+
+#include <vector>
+#include <set>
+#include <list>
+#include <map>
+#include <string.h> // memset
+#include <cstdlib> // abs(int),labs(int),llabs(int),min,max
+#include <limits.h> // int_max,int_min,long_long_max,long_long_min
+using namespace std;
+
+int main()
+{
+  int test;
+  cin>>test;
+  while(test--) {
+    int n;
+    cin>>n;
+
+    int ans = 0;
+    bool allOne = true;
+    for(int i=0;i<n;i++) {
+      int temp;
+      cin>>temp;
+      if(temp!=1) allOne = false;
+      ans = ans ^ temp;
+    }
+    string s1,s2;
+    s1 = "John";
+    s2 = "Brother";
+    if(allOne) {
+      if(n%2==0) {
+        cout<<s1<<endl;
+      } else cout<<s2<<endl;
+    } else {
+      if (ans == 0) {
+        cout<<s2<<endl;
+      } else cout<<s1<<endl;
+    }
+  }
+	return 0;
+}

Algorithm_Games/TRIOMINO.cpp

@@ -0,0 +1,89 @@
+#include <iostream>
+#include <string>
+#include <stdio.h>
+#include <algorithm> // binsearch,max(a,b),min(a,b)
+#include <math.h>
+#include <queue>
+
+#include <vector>
+#include <set>
+#include <list>
+#include <map>
+#include <string.h> // memset
+#include <cstdlib> // abs(int),labs(int),llabs(int),min,max
+#include <limits.h> // int_max,int_min,long_long_max,long_long_min
+using namespace std;
+
+int mem[810][2][2][2][2];
+int grundy(int n,int leftLower, int leftUpper, int rightLower, int rightUpper) {
+
+  // base cases:
+  //cout << n << " " << leftLower << " " << leftUpper << " " << rightLower << " " << rightUpper << endl;
+  if(n==1 && !leftLower && !leftUpper && !rightUpper && !rightLower) {
+    return 0;
+  }
+  if(n==0) {
+    return 0;
+  }
+
+  if (mem[n][leftLower][leftUpper][rightLower][rightUpper]!=-1) {
+    //cout<<"Already stored"<<endl;
+    return mem[n][leftLower][leftUpper][rightLower][rightUpper];
+  }
+
+  set<int> reachable;
+  if(leftUpper || leftLower) {
+     reachable.insert(grundy(n-1,0,0,rightLower,rightUpper));
+  }
+  if(rightUpper || rightLower) {
+    reachable.insert(grundy(n-1,leftLower,leftUpper,0,0));
+  }
+  if (n >= 2) {
+    reachable.insert(grundy(n-2,0,1,rightLower,rightUpper));
+    reachable.insert(grundy(n-2,1,0,rightLower,rightUpper));
+    reachable.insert(grundy(n-2,leftLower,leftUpper,0,1));
+    reachable.insert(grundy(n-2,leftLower,leftUpper,1,0));
+  }
+
+
+  for(int i=2;i<=n-1;i++) {
+  int a,b,c,d;
+  // right orientations
+  a = grundy(i-1,leftLower,leftUpper,0,0);
+  b = grundy(n-i-1,0,1,rightLower,rightUpper);
+  c = grundy(n-i-1,1,0,rightLower,rightUpper);
+  reachable.insert(a^c);
+  reachable.insert(a^b);
+
+  // left orientations
+  a = grundy(n-i,0,0,rightLower,rightUpper);
+  b = grundy(i-2,leftLower,leftUpper,0,1);
+  c = grundy(i-2,leftLower,leftUpper,1,0);
+  reachable.insert(a^c);
+  reachable.insert(a^b);
+
+  }
+
+
+  // calculating mex of the reachable set
+  int answer = 0;
+  while(reachable.count(answer)) {
+    answer++;
+  }
+  return mem[n][leftLower][leftUpper][rightLower][rightUpper] = answer;
+}
+int main() {
+  int test;
+  memset(mem,-1,sizeof(mem));
+  cin>>test;
+  while(test--) {
+    int n;
+    cin>>n;
+    if(grundy(n,0,0,0,0)) {
+      cout<<"X"<<endl;
+    } else {
+      cout<<"Y"<<endl;
+    }
+  }
+	return 0;
+}

DP/COINS_MAP.cpp

@@ -0,0 +1,30 @@
+#include <iostream>
+#include <string>
+#include <stdio.h>
+#include <algorithm> // binsearch,max(a,b),min(a,b)
+#include <math.h>
+#include <queue>
+
+#include <vector>
+#include <set>
+#include <list>
+#include <map>
+#include <string.h> // memset
+#include <cstdlib> // abs(int),labs(int),llabs(int),min,max
+#include <limits.h> // int_max,int_min,long_long_max,long_long_min
+using namespace std;
+map<long long,long long> m;
+
+long long solve(long long n) {
+  if(m.count(n)) {
+    return m[n];
+  }
+  return m[n] = max(n,solve(n/2) + solve(n/3) + solve(n/4));
+}
+int main() {
+  long long val;
+  while(cin>>val) {
+    cout<<solve(val)<<endl;
+  }
+	return 0;
+}

DP/COINS_NAIVE.c

@@ -0,0 +1,22 @@
+# include<stdio.h>
+long long mem[1000000];
+long long solve(long long a) {
+  if(a==0) return 0;
+  if(a<1000000 && mem[a]!=0) return mem[a];
+  long long ret=solve(a/2) + solve(a/3) + solve(a/4) ;
+  ret= ret > a ? ret:a;
+  if(a<1000000) mem[a]=ret;
+  return ret;
+
+}
+int main()
+{
+long long test;
+while(scanf("%lld",&test)==1) {
+  printf("%lld\n",solve(test));
+}
+return 0;
+}
+
+
+

DP/MCOINS.cpp

@@ -0,0 +1,27 @@
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+
+int main(){
+    int K,L,m;
+    cin >> K >> L >> m;
+    bool play[1000001];   // to calculate wins of 'A'  
+    int coin;            
+
+    for(int i = 1;i <= 1000001;++i){
+        play[i] = !play[i-1];
+        if(i >= K && !play[i-K]) play[i] = true;
+        if(i >= L && !play[i-L]) play[i] = true;
+    }
+
+    for(int i = 0;i < m;++i){
+        cin >> coin;
+        if(play[coin]) cout << 'A';
+        else cout << 'B';
+    }
+
+    cout << "\n";
+
+    return 0;
+}