feat: Added expected and maximum number of comparisons

.gitignore

@@ -3,6 +3,9 @@
 # personal notes
 Notes.md
 
+# hacky upload script
+lib/pushToMongoManually.js
+
 # convenience old folder
 pages/.old/*
 pages/.old

lib/comparisonView.js

@@ -11,6 +11,7 @@ import { DisplayAsMarkdown } from './displayAsMarkdown'
 import { CreateTableWithDistances } from './findPaths'
 import { TextAreaForJson } from "./textAreaForJson"
 import { pushToMongo } from "./pushToMongo.js"
+import { maxMergeSortSteps, expectedNumMergeSortSteps } from "./utils.js"
 
 /* Helpers */
 let increasingList = (n) => Array.from(Array(n).keys())
@@ -40,10 +41,6 @@ export default function ComparisonView({ listOfElementsForView }) {
   // State
   let initialListOfElements = listOfElementsForView.map((element, i) => ({ ...element, id: i }))
   let initialPosList = increasingList(listOfElementsForView.length) // [0,1,2,3,4]
-  //let listOfElements = listOfElementsForView.map((element, i) => ({...element, id: i}))
-  //let list = increasingList(listOfElementsForView.length) // [0,1,2,3,4]
-
-  //let initialComparePair = [list[list.length-2], list[list.length-1]]
   let initialComparePair = [initialPosList[initialPosList.length - 2], initialPosList[initialPosList.length - 1]]
   let initialSliderValue = 1
   let initialReasoning = ''
@@ -54,6 +51,13 @@ export default function ComparisonView({ listOfElementsForView }) {
   let initialShowAdvancedOptions = false
   let initialShowComparisons = false
   let initialShowChangeDataSet = false
+  let initialNumSteps = 0;
+  let maxSteps = maxMergeSortSteps(listOfElementsForView.length)
+  let expectedSteps = expectedNumMergeSortSteps(listOfElementsForView.length)
+
+  //let listOfElements = listOfElementsForView.map((element, i) => ({...element, id: i}))
+  //let list = increasingList(listOfElementsForView.length) // [0,1,2,3,4]
+  //let initialComparePair = [list[list.length-2], list[list.length-1]]
 
   const [listOfElements, setListOfElements] = useState(initialListOfElements)
   const [posList, setPosList] = useState(initialPosList)
@@ -72,6 +76,8 @@ export default function ComparisonView({ listOfElementsForView }) {
   let [showAdvancedOptions, changeShowAdvanceOptions] = useState(initialShowAdvancedOptions);
   let [showComparisons, changeShowComparisons] = useState(initialShowComparisons);
   let [showChangeDataSet, changeshowChangeDataSet] = useState(initialShowChangeDataSet);
+  let [numSteps, increaseNumSteps] = useState(initialNumSteps);
+
 
   let restart = (posList) => {
     setToComparePair([posList[posList.length - 2], posList[posList.length - 1]])
@@ -195,6 +201,7 @@ export default function ComparisonView({ listOfElementsForView }) {
 
     setSliderValue(1)
     setReasoning('')
+    increaseNumSteps(numSteps+1)
     if (successStatus) {
       let jsObject = nicelyFormatLinks(quantitativeComparisons, listOfElements)
       pushToMongo(jsObject)
@@ -216,6 +223,7 @@ export default function ComparisonView({ listOfElementsForView }) {
         <h1 className="text-6xl font-bold">
           Utility Function Extractor
         </h1>
+        <p>{`${numSteps} out of ~${expectedSteps} (max ${maxSteps}) comparisons`}</p>
 
         <div className={`${isListOrdered ? "hidden" : ""}`}>
           <div className="flex flex-wrap items-center max-w-4xl sm:w-full mt-10">

lib/utils.js

@@ -42,3 +42,29 @@ export function formatLargeOrSmall (num) {
 
     }
 }
+const firstFewMaxMergeSortSequence = [0, 0, 1, 3, 5, 8, 11, 14, 17, 21, 25, 29, 33, 37, 41, 45, 49, 54, 59, 64, 69, 74, 79, 84, 89, 94, 99, 104, 109, 114, 119, 124, 129, 135, 141, 147, 153, 159, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219, 225, 231, 237, 243, 249, 255, 261, 267, 273, 279, 285]
+
+export function maxMergeSortSteps(n) {
+    if (n < firstFewMaxMergeSortSequence.length) {
+        return firstFewMaxMergeSortSequence[n]
+    } else {
+        return maxMergeSortSteps(Math.floor(n / 2)) + maxMergeSortSteps(Math.ceil(n / 2)) + n - 1
+    }
+}
+
+export function expectedNumMergeSortSteps(n) {
+    // https://cs.stackexchange.com/questions/82862/expected-number-of-comparisons-in-a-merge-step
+    // n-2 for each step, so (n-2) + (n-2)/2 + (n-2)/4 + ...
+    // ~ 2*(n-2) -1 = 2*n - 3
+    if (n == 0) {
+        return 0
+    } else if (n == 1) {
+        return 0
+    } else if (n == 2) {
+        return 1
+    } else if (n == 3) {
+        return 2
+    } else {
+        return Math.ceil((n ** 2) / (n + 2)) + expectedNumMergeSortSteps(Math.ceil(n / 2))
+    }
+}