nQueen

Miscellaneous/NQueen/nqueen.cpp

@@ -0,0 +1,114 @@
+// Created on 05-10-2019 19:54:30 by necronomicon
+#include <iostream>
+#include <string>
+#include <vector>
+#include <algorithm>
+#include <sstream>
+#include <queue>
+#include <deque>
+#include <bitset>
+#include <iterator>
+#include <list>
+#include <stack>
+#include <map>
+#include <set>
+#include <unordered_map>
+#include <unordered_set>
+#include <functional>
+#include <numeric>
+#include <utility>
+#include <limits>
+#include <iomanip>
+#include <ctime>
+#include <cmath>
+#include <cstdio>
+#include <cstring>
+#include <cstdlib>
+#include <cassert>
+using namespace std;
+
+#define MP make_pair
+#define PB push_back
+#define ARR_MAX (int)1e5 //Max array length
+#define INF (int)1e9 //10^9
+#define EPS 1e-9 //10^-9
+#define MOD 1000000007 //10^9+7
+#define PI 3.1415926535897932384626433832795
+typedef long int int32;
+typedef unsigned long int uint32;
+typedef long long int int64;
+typedef unsigned long long int  uint64;
+typedef pair<int, int> Pii;
+typedef vector<int> Vi;
+typedef vector<string> Vs;
+typedef vector<Pii> VPii;
+typedef vector<Vi> VVi;
+typedef map<int,int> Mii;
+typedef set<int> Si;
+typedef multimap<int,int> MMii;
+typedef multiset<int> MSi;
+typedef unordered_map<int,int> UMii;
+typedef unordered_set<int> USi;
+typedef unordered_multimap<int,int> UMMii;
+typedef unordered_multiset<int> UMSi;
+typedef priority_queue<int> PQi;
+typedef queue<int> Qi;
+typedef deque<int> DQi;
+
+
+/* 
+NQueen: place n queend in n*n board without conflicts.
+
+Most effecient solution
+Data: 3 arrays of bools:
+    col: to checl if col[i] has element
+    diag1: to check if col[i+j] has element (backDiag \)
+    diag2: to check if col[i-j+n-1] has element (FwrdDiag /)
+Function called from y=0 whihc means it places element on row y from 0 to n
+for each call it places queen on every possible col x from 0 to n which is valid.
+*/
+
+int n;
+Vi col, diag1, diag2;
+
+int nQueen(int y=0) {
+    if(y == n) return 1;
+    int r = 0;
+    for (int x = 0; x < n; x++)
+    {
+        if(!(col[x] || diag1[x+y] || diag2[x-y+n-1])) {
+            col[x] = diag1[x+y] = diag2[x-y+n-1] = 1;
+            r += nQueen(y+1);
+            col[x] = diag1[x+y] = diag2[x-y+n-1] = 0;
+        }
+    }
+    return r;
+}
+
+void nQueenSolution(int y=0, string s ="") {
+    if(y == n) {
+        cout << s << endl;
+        return;
+    }
+    int r = 0;
+    for (int x = 0; x < n; x++)
+    {
+        if(!(col[x] || diag1[x+y] || diag2[x-y+n-1])) {
+            col[x] = diag1[x+y] = diag2[x-y+n-1] = 1;
+            string t = "a";
+            t[0] = '0'+x;
+            nQueenSolution(y+1, s+t);
+            col[x] = diag1[x+y] = diag2[x-y+n-1] = 0;
+        }
+    }
+    return;
+}
+
+int main (int argc, char const *argv[]) {
+	n = 8;
+    col= Vi(n, 0);
+    diag1 = diag2 = Vi(2*n, 0);
+    cout << nQueen() << endl << endl;
+    nQueenSolution();
+    return EXIT_SUCCESS;
+}