2016 Update

Task/Heronian-triangles/JavaScript/heronian-triangles-2.js

@@ -1,23 +1,82 @@
-Primitive Heronian triangles with sides up to 200: 517
+(function (n) {
 
-First ten when ordered by increasing area, then perimeter:
-Sides	Perimeter	Area
-3 x 4 x 5	12	6
-5 x 5 x 6	16	12
-5 x 5 x 8	18	12
-4 x 13 x 15	32	24
-5 x 12 x 13	30	30
-9 x 10 x 17	36	36
-3 x 25 x 26	54	36
-7 x 15 x 20	42	42
-10 x 13 x 13	36	60
-8 x 15 x 17	40	60
+  var chain = function (xs, f) {                  // Monadic bind/chain
+      return [].concat.apply([], xs.map(f));
+    },
 
-Area = 210
-Sides	Perimeter	Area
-17 x 25 x 28	70	210
-20 x 21 x 29	70	210
-12 x 35 x 37	84	210
-17 x 28 x 39	84	210
-7 x 65 x 68	140	210
-3 x 148 x 149	300	210
+    hArea = function (x, y, z) {
+      var s = (x + y + z) / 2,
+        a = s * (s - x) * (s - y) * (s - z);
+      return a ? Math.sqrt(a) : 0;
+    },
+
+    gcd = function (m, n) { return n ? gcd(n, m % n) : m; },
+
+    rng = function (m, n) {
+      return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
+        return m + i;
+      });
+    },
+
+    sum = function (a, x) { return a + x; };
+
+  // DEFINING THE SORTED SUB-SET IN TERMS OF A LIST MONAD
+
+  var lstHeron = chain( rng(1, n), function (x) {
+          return chain( rng(x, n), function (y) {
+          return chain( rng(y, n), function (z) {
+
+        return (
+          (x + y > z) &&
+          gcd(gcd(x, y), z) === 1 &&            // Primitive.
+          (function () {                        // Heronian.
+            var a = hArea(x, y, z);
+            return a && (a === parseInt(a, 10))
+          })()
+        ) ? [[x, y, z]] : [];                   // Monadic inject or fail
+
+  })})}).sort(function (a, b) {
+    var dArea = hArea.apply(null, a) - hArea.apply(null, b);
+    if (dArea) return dArea;
+    else {
+      var dPerim = a.reduce(sum, 0) - b.reduce(sum, 0);
+      return dPerim ? dPerim : (a[2] - b[2]);
+    }
+  });
+
+  // OUPUT FORMATTED AS TWO WIKITABLES
+
+  var lstColumns = ['Sides Perimeter Area'.split(' ')],
+    fnData = function (lst) {
+      return [JSON.stringify(lst), lst.reduce(sum, 0), hArea.apply(null, lst)];
+    },
+    wikiTable = function (lstRows, blnHeaderRow, strStyle) {
+      return '{| class="wikitable" ' + (
+        strStyle ? 'style="' + strStyle + '"' : ''
+      ) + lstRows.map(function (lstRow, iRow) {
+        var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|');
+
+        return '\n|-\n' + strDelim + ' ' + lstRow.map(function (v) {
+          return typeof v === 'undefined' ? ' ' : v;
+        }).join(' ' + strDelim + strDelim + ' ');
+      }).join('') + '\n|}';
+    };
+
+  return 'Found: ' + lstHeron.length +
+    ' primitive Heronian triangles with sides up to ' + n + '.\n\n' +
+    '(Showing first 10, sorted by increasing area, ' +
+    'perimeter, and longest side)\n\n' +
+    wikiTable(
+      lstColumns.concat(lstHeron.slice(0, 10).map(fnData)),
+      true
+    ) + '\n\n' +
+    'All primitive Heronian triangles in this range where area = 210\n' +
+    '\n(also in order of increasing perimeter and longest side)\n\n' +
+    wikiTable(
+      lstColumns.concat(lstHeron.filter(function (x) {
+        return 210 === hArea.apply(null, x);
+      }).map(fnData)),
+      true
+    ) + '\n\n';
+
+})(200);