better algorithm for covering all state transitions

Author: alexcjohnson

test/jasmine/assets/transitions.js

@@ -0,0 +1,35 @@
+'use strict';
+
+/**
+ * Given n states (denoted by their indices 0..n-1) this routine produces
+ * a sequence of indices such that you efficiently execute each transition
+ * from any state to any other state.
+ */
+module.exports = function transitions(n) {
+    var out = [0];
+    var nextStates = [];
+    var i;
+    for(i = 0; i < n; i++) nextStates[i] = (i + 1) % n;
+    var finishedStates = 0;
+    var thisState = 0;
+    var nextState;
+    while(finishedStates < n) {
+        nextState = nextStates[thisState];
+        if(nextState === thisState) {
+            // I don't actually know how to prove that this algorithm works,
+            // but I've never seen it fail for n>1
+            // For prime n it's the same sequence as the one I started with
+            // (n transitions of +1 index, then n transitions +2 etc...)
+            // but this one works for non-prime n as well.
+            throw new Error('your transitions algo failed.');
+        }
+        nextStates[thisState] = (nextStates[thisState] + 1) % n;
+        if(nextStates[thisState] === thisState) finishedStates++;
+        out.push(nextState);
+        thisState = nextState;
+    }
+    if(out.length !== n * (n - 1) + 1) {
+        throw new Error('your transitions algo failed.');
+    }
+    return out;
+};

test/jasmine/tests/scatter_test.js

@@ -9,6 +9,7 @@ var createGraphDiv = require('../assets/create_graph_div');
 var destroyGraphDiv = require('../assets/destroy_graph_div');
 var customAssertions = require('../assets/custom_assertions');
 var failTest = require('../assets/fail_test');
+var transitions = require('../assets/transitions');
 
 var assertClip = customAssertions.assertClip;
 var assertNodeDisplay = customAssertions.assertNodeDisplay;
@@ -655,14 +656,7 @@ describe('end-to-end scatter tests', function() {
 
         // visit each case N times, in an order that covers each *transition*
         // from any case to any other case.
-        var indices = [];
-        var curIndex = 0;
-        for(i = 1; i < cases.length; i++) {
-            for(j = 0; j < cases.length; j++) {
-                indices.push(curIndex);
-                curIndex = (curIndex + i) % cases.length;
-            }
-        }
+        var indices = transitions(cases.length);
 
         var p = Plotly.plot(gd, [
             {y: [1, 2], text: 'a'},