Merge pull request kennyledet#402 from aaronabf/master

Added Javascript implemented for 4 problems

100_Doors_Problem/Javascript/aaronabf/100_Doors.js

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+// Author: Aaron Friedlander 2014
+
+// Problem: You have 100 doors in a row that are all initially closed. You make
+// 100 passes by the doors. The first time through, you visit every door and
+// toggle the door (if the door is closed, you open it; if it is open, you
+// close it). The second time you only visit every 2nd door (door #2, #4, #6,
+// ...). The third time, every 3rd door (door #3, #6, #9, ...), etc, until you
+// only visit the 100th door.
+
+// Question: What state are the doors in after the last pass? Which are open,
+// which are closed?
+
+// Implemented in two ways:
+// 1) Loop through array of "doors" opening respective doors in each iteration
+// 2) The only doors that remain open are whose numbers are perfect squares.
+// Using this knowledge, only doors with indices of a perfect square + 1 are
+// opened.
+
+function run(numberOfDoors) {
+  // Array to represent the doors: false represents closed, true represents open
+  var doors = Array.apply(null, new Array(numberOfDoors)).map(Boolean.prototype.valueOf,false);
+
+  // Run algorithms
+  var doorOutcome1 = iterateDoors(doors);
+  var doorOutcome2 = perfectSquareDoors(doors);
+
+  // Print out results
+  if (doorOutcome1 === doorOutcome2) {
+    for (var i = 0; i < numberOfDoors; i++) {
+      var doorNum = i + 1;
+      var doorVal = doorOutcome1[i] ? 'Open' : 'Closed';
+      console.log('Door #' + doorNum + ' is ' + doorVal);
+    }
+  } else {
+    console.log('There was a issue in the algorithm');
+  }
+}
+
+function iterateDoors(doors) {
+  for (var pass = 0; pass < doors.length; pass++) {
+    for (var i = pass; i < doors.length; i += (pass + 1)) {
+      doors[i] = !doors[i];
+    }
+  }
+
+  return doors;
+}
+
+function isPerfectSquare(num) {
+  // Javascript trick for determining if a number is a perfect square
+  var sqrt = Math.sqrt(num);
+  return (sqrt === (sqrt | 0));
+}
+
+function perfectSquareDoors(doors) {
+  for (var i = 0; i < doors.length; i++) {
+    if (isPerfectSquare(i+1)) {
+      doors[i] = true;
+    }
+  }
+
+  return doors;
+}

Memoization/Javascript/aaronabf/memoize.js

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+// Author: Aaron Friedlander 2014
+
+// A function that memoizes a function
+// Adapted from my code here https://github.com/aaronabf/memoization/blob/master/memoizer.js
+
+// Stores cached results
+var dict = {};
+
+// Memoizes a function
+function memoizer(f) {
+  function newFunction(n) {
+    if (dict[n]) {
+      return dict[n];
+    }
+
+    var newVal = f(newFunction, n);
+    dict[n] = newVal;
+    return newVal;
+  }
+
+  return newFunction;
+}
+
+// Test on fibonnaci
+function fibMemo(g, n) {
+  if (n === 0) {
+    return 0;
+  } else if (n === 1) {
+    return 1;
+  } else {
+    return g(n-2) + g(n-1);
+  }
+}
+var fib = memoizer(fibMemo);

N_Queens/Javascript/aaronabf/n-queens.js

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+// Author: Aaron Friedlander 2014
+
+// A function that memoizes a function
+// Adapted from my code here https://github.com/aaronabf/n-queens/blob/master/n_queen.js
+
+// To test on 8 queens:
+// console.log(attemp(8));
+
+// Main function, abstracted helper function
+function attemp(n) {
+  return try1(point(1,1), n, []);
+}
+
+// Converts two numbers into a "point" object
+function point(x,y) {
+  return { i : x, j : y };
+}
+
+// Tests that the point does not conflict with any other points on the board
+function conflict(p1, board) {
+  return board.some(function(p2) {
+    return ((p1.i === p2.i) ||
+            (p1.j === p2.j) ||
+            (p1.i - p1.j === p2.i - p2.j) ||
+            (p1.i + p1.j === p2.i + p2.j));
+  });
+}
+
+// First mutual recursive function, helps construct array of points
+function try1(p, n, board) {
+  var results = try2(p, n, board);
+
+  if (results) {
+    return results;
+  } else if (p.j === n) {
+    return false;
+  } else {
+    return try1(point(p.i, p.j+1), n, board);
+  }
+}
+
+// Second mutual recursive function, helps construct array of points
+function try2(p, n, board) {
+  if (conflict(p, board)) {
+    return false;
+  } else if (p.i === n) {
+    board.unshift(p);
+    return board;
+  } else {
+    var boardCopy = board.slice(0);
+    boardCopy.unshift(p);
+    return try1(point(p.i+1, 1), n, boardCopy);
+  }
+}

Roman_Numerals/Javascript/aaronabf/roman.js

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+// ALL CREDIT GOES TO Steven Levithan @ http://blog.stevenlevithan.com/archives/javascript-roman-numeral-converter
+
+function romanize (num) {
+  if (!+num)
+    return false;
+  var digits = String(+num).split(""),
+    key = ["","C","CC","CCC","CD","D","DC","DCC","DCCC","CM",
+           "","X","XX","XXX","XL","L","LX","LXX","LXXX","XC",
+           "","I","II","III","IV","V","VI","VII","VIII","IX"],
+    roman = "",
+    i = 3;
+  while (i--)
+    roman = (key[+digits.pop() + (i * 10)] || "") + roman;
+  return Array(+digits.join("") + 1).join("M") + roman;
+}
+
+function deromanize (str) {
+  var str = str.toUpperCase(),
+    validator = /^M*(?:D?C{0,3}|C[MD])(?:L?X{0,3}|X[CL])(?:V?I{0,3}|I[XV])$/,
+    token = /[MDLV]|C[MD]?|X[CL]?|I[XV]?/g,
+    key = {M:1000,CM:900,D:500,CD:400,C:100,XC:90,L:50,XL:40,X:10,IX:9,V:5,IV:4,I:1},
+    num = 0, m;
+  if (!(str && validator.test(str)))
+    return false;
+  while (m = token.exec(str))
+    num += key[m[0]];
+  return num;
+}