From e0d1fdf833c382a0d13e40285f96acad6d7d460d Mon Sep 17 00:00:00 2001
From: Ignacio Chiazzo <ignaciochiazzo@gmail.com>
Date: Sat, 27 Oct 2018 13:03:20 -0400
Subject: [PATCH] Added n queens problem

---
 Main.js    |  4 ++-
 NQueens.js | 92 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 95 insertions(+), 1 deletion(-)
 create mode 100644 NQueens.js

diff --git a/Main.js b/Main.js
index b9011fd..50f9633 100644
--- a/Main.js
+++ b/Main.js
@@ -2,9 +2,11 @@
 var permutationWithoutDuplicates = require("./PermutationsWithoutDuplicates.js");
 var permutationWithDuplicates = require("./PermutationsWithDuplicates.js");
 var subsets = require("./Subsets.js");
+var nQueens = require("./NQueens.js");
 
 // Invocation
 
 // permutationWithoutDuplicates.main();
 // permutationWithDuplicates.main();
-// subsets.main();
\ No newline at end of file
+// subsets.main();
+// nQueens.main();
diff --git a/NQueens.js b/NQueens.js
new file mode 100644
index 0000000..e94c906
--- /dev/null
+++ b/NQueens.js
@@ -0,0 +1,92 @@
+/* https://leetcode.com/problems/n-queens/description/
+
+Example:
+
+Input: 4
+Output: [
+ [".Q..",  // Solution 1
+  "...Q",
+  "Q...",
+  "..Q."],
+
+ ["..Q.",  // Solution 2
+  "Q...",
+  "...Q",
+  ".Q.."]
+]
+Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.
+*/
+
+/**
+ * @param {number} n
+ * @return {string[][]}
+ */
+var solveNQueens = function(n) {
+  var sol = [];
+  solveNQueensAux(n, 0, new Set(), new Set(), new Set(), [], sol);
+  return parseSolutions(sol, n);
+};
+
+var solveNQueensAux = function(n, row, diagonalDiffs, diagonalSums, cols, currentSol, sol) {
+  if(row == n) { 
+    sol.push(currentSol);  
+    return; 
+  }
+  
+  for(var i = 0; i < n; i++) {
+    const diagonalDiff = i - row;
+    const diagonalSum = i + row;
+    if(!diagonalDiffs.has(diagonalDiff) && !cols.has(i) && !diagonalSums.has(diagonalSum)) {
+      diagonalDiffs.add(diagonalDiff);
+      diagonalSums.add(diagonalSum);
+      cols.add(i);
+      solveNQueensAux(n, row + 1, diagonalDiffs, diagonalSums, cols, [...currentSol, ...[[row, i]]], sol);
+      cols.delete(i);
+      diagonalDiffs.delete(diagonalDiff);
+      diagonalSums.delete(diagonalSum);
+    }
+  }
+  return;
+}
+
+var parseSolutions = function(sols, n) {
+  var matrixes = [];
+  for(var i = 0; i < sols.length; i++) {
+    var sol = sols[i];
+    var matrix = [];
+    for(var row = 0; row < n; row++) {
+      matrix[row] = []
+      const queenPos = sol[row];
+      for(var col = 0; col < n; col++) {
+        matrix[row] += (queenPos[1] == col) ? "Q" : ".";
+      }
+    }
+
+    matrixes.push(matrix);
+  }
+
+  return matrixes;
+}
+
+var printMatrixes = function(matrixes, n) {
+  console.log("Start solution of n: " + n);
+  for(var i = 0; i < matrixes.length; i++) {
+    printMatrix(matrixes[i]);
+  }
+  console.log("End solution of n: " + n);
+}
+
+var printMatrix = function(matrix) {
+  console.log("------------");
+  for(var i = 0; i < matrix.length; i++) {
+    console.log(matrix[i]);
+  }
+  console.log("------------");
+}
+
+var main = function(n) {
+  printMatrixes(solveNQueens(4), 4);
+  printMatrixes(solveNQueens(5), 5);
+  printMatrixes(solveNQueens(6), 6);
+}
+main();
\ No newline at end of file