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SAN solver 2.html
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<!DOCTYPE html>
<html>
<body>
<textarea id="input">s(3,3{1``3}3)</textarea>
<button onclick="solve()">Solve</button><button onclick="plugFinalResult()">Plug in result and solve</button>
<p id="message">This is a calculator that can be used to solve SAN arrays up to DAN. You input any SAN array you want and click "Solve" and it will evaluate one step for you. You can use [] in place of {}, and it works fine. It recognizes whether to use exAN, mEAN, pDAN, sDAN, or DAN. Use {2^`} and {2^,,} if you want {2<sup>`</sup>} and {2<sup>,,</sup>} respectively. Supported: s(), any m-ple comma (,,,...,,,), curly braces, and multiple grave accents (```...```). Note that this solver may fail to solve an array in a reasonable amount of time if you give it too complex of an expression.<br><b>Update November 7, 2020:</b> `,, and ,,` are now supported. (```...```,, and ,,```...``` too, but not `,,`)</p>
<script>
var SANmode = 0; // 1 - DAN, 2 - sDAN (,,`), 3 - pDAN or sDAN (`,,), 4 - mEAN
var SANmessage;
var finalResult;
var startTime;
var elapsedTime;
function getSANmode(SANArray) {
if (SANArray.includes(",,,")) {
SANmode = 1;
} else if (SANArray.includes(",,`")) {
SANmode = 2;
} else if (SANArray.includes(",,") || SANArray.includes("^,,}") || SANArray.includes("\"") || SANArray.includes("”")) {
SANmode = 3;
} else {
SANmode = 4;
}
return SANmode;
}
function maxCommas(separator) { // Maximum number of commas in ,,,...,,,
var numCommas = 2;
while (separator.indexOf(",".repeat(numCommas)) >= 0) {
numCommas++;
}
return numCommas-1;
}
function convertToMaxCommas(separator) {
// convert all expressions of double,triple,etc.-comma into expressions of m-ple comma
var highestCommas = maxCommas(separator);
var currentCommas = highestCommas;
var mpleComma;
currentCommas--;
separator = separator.replace(/(\d)/g, " " + '$1' + " ");
while (currentCommas >= 2) {
mpleComma = RegExp("\\s" + ",".repeat(currentCommas) + "\\s","g");
separator = separator.replace(mpleComma, "{1".repeat(highestCommas-currentCommas) +
",".repeat(highestCommas) + "2}".repeat(highestCommas-currentCommas));
currentCommas--;
}
return separator.replace(/\s/g,"");
}
function simplify(separator) {
// convert {1,,,...,,,2} (i commas) into ,,...,,, (i-1 commas) and {1} into comma.
var currentCommas = maxCommas(separator);
var mpleComma;
while (currentCommas > 2) {
mpleComma = RegExp("\\{1" + ",".repeat(currentCommas) + "2\\}","g");
separator = separator.replace(mpleComma, ",".repeat(currentCommas-1));
currentCommas--;
}
separator = separator.replace(/\{1\}/g, ","); // convert all {1}'s into commas.
return separator;
}
function parseSeparatorLeft(separator) { /* finds the leftmost separator,
either a separator in braces or an m-ple comma */
separator += "{,";
if (separator.indexOf(",") < separator.indexOf("{")) {
var commas = 1;
while (separator.indexOf(",".repeat(commas+1)) == separator.indexOf(",")) {
commas++;
}
return ",".repeat(commas);
}
if (separator.indexOf("{") == -1) {
return "";
} else {
var currentPosition = 0;
var lbraceStack = 0;
var lbracePosition = 0;
var rbracePosition = 0;
var initialPosition = separator.indexOf("{");
currentPosition = separator.indexOf("{");
lbraceStack++;
while (lbraceStack > 0) {
lbracePosition = separator.indexOf("{", currentPosition+1);
rbracePosition = separator.indexOf("}", currentPosition+1);
if (lbracePosition < rbracePosition) {
lbraceStack++;
currentPosition = lbracePosition;
} else {
lbraceStack--;
currentPosition = rbracePosition;
}
}
return separator.slice(initialPosition,currentPosition+1);
}
}
function parseSeparatorRight(separator) { /* finds the rightmost separator,
either a separator in braces or an m-ple comma */
if (separator.lastIndexOf(",") > separator.lastIndexOf("}")) {
var commas = 1;
while (separator.lastIndexOf(",".repeat(commas+1)) + commas == separator.lastIndexOf(",")) {
commas++;
}
return ",".repeat(commas);
}
if (separator.indexOf("}") == -1) {
return "";
} else {
var currentPosition = separator.length-1;
var rbraceStack = 0;
var lbracePosition = separator.length-1;
var rbracePosition = separator.length-1;
var initialPosition = separator.lastIndexOf("}");
currentPosition = separator.lastIndexOf("}");
rbraceStack++;
while (rbraceStack > 0) {
lbracePosition = separator.lastIndexOf("{", currentPosition-1);
rbracePosition = separator.lastIndexOf("}", currentPosition-1);
if (lbracePosition == -1) {
return "";
} else {
if (lbracePosition < rbracePosition) {
rbraceStack++;
currentPosition = rbracePosition;
} else {
rbraceStack--;
currentPosition = lbracePosition;
}
}
}
return separator.slice(currentPosition,initialPosition+1);
}
}
function getAllSeparatorsInSeparator(separator) {
var leftmostSeparator = parseSeparatorLeft(separator);
var separatorList = []; // array listing all separators in base layer of separator
if (leftmostSeparator.startsWith(",")) { // comma or m-ple comma, there are no separators in it.
return []; // nothing
}
// separator is of the form {___}
leftmostSeparator = leftmostSeparator.slice(1); // remove first lbrace, then parse the next separator
while (leftmostSeparator.indexOf("{") != -1 || leftmostSeparator.indexOf(",") != -1) {
// repeat until no lbrace or comma is remaining
separatorAddToList = parseSeparatorLeft(leftmostSeparator); // find leftmost separator
separatorList.push(separatorAddToList); // add separator to list
leftmostSeparator = leftmostSeparator.slice(separatorAddToList.length +
leftmostSeparator.indexOf(separatorAddToList)); // remove separator and repeat
}
return separatorList;
// lists all separators in separator, {1,2{1,,2}2,,2} returns "," "{1,,2}" and ",,"
}
function getAllSeparatorsInBaseLayer(SANArray) {
separator = SANArray.replace("s(","{").replace(")","}");
return getAllSeparatorsInSeparator(separator);
}
function convertMEANtoPDAN(separator) {
var numGraves = 1;
var mpleGrave = 0;
while (separator.indexOf("`".repeat(numGraves)) >= 0) {
numGraves++;
}
var currentGraves = numGraves;
var currentGraves2 = numGraves;
while (currentGraves > 0) {
mpleGrave = RegExp("\\^"+"\\`".repeat(currentGraves) + "\\}","g");
separator = separator.replace(mpleGrave, ",," + (currentGraves+1) + "}");
currentGraves--;
}
while (currentGraves2 > 0) {
mpleGrave = RegExp("\\`".repeat(currentGraves2),"g");
separator = separator.replace(mpleGrave, "{1,," + (currentGraves2+1) + "}");
currentGraves2--;
}
return separator;
}
function convertPDANtoDAN(separator) {
if (separator.includes(",,`")) {
graves = 1;
while (separator.includes(",," + "`".repeat(graves))) {
graves++;
}
while (graves >= 1) {
separator = separator.replace(RegExp("\\^,," + "\\`".repeat(graves) + "\\}","g"), ",,," + (graves+2) + "}");
separator = separator.replace(RegExp(",," + "\\`".repeat(graves),"g"), "{1,,," + (graves+2) + "}");
graves--;
}
}
if (separator.includes("`,,")) {
graves = 1;
while (separator.includes("`".repeat(graves) + ",,")) {
graves++;
}
while (graves >= 1) {
separator = separator.replace(RegExp("\\^" + "\\`".repeat(graves) + ",,\\}","g"), "{1,,,3}" + (graves+1) + ",,,2}");
separator = separator.replace(RegExp("\\`".repeat(graves) + ",,","g"), "{1{1,,,3}" + (graves+1) + ",,,2}");
graves--;
}
}
if (separator.includes("\"")) {
separator = separator.replace(/"/g, ",,,2");
}
if (separator.includes("”")) {
separator = separator.replace(/”/g, ",,,2");
}
if (separator.includes("^,,}")) {
separator = separator.replace(/\^,,\}/g, ",,,2}");
}
return separator;
}
function rule3(separator) {
var partialSeparator;
var separatorToRemove;
var oldSeparator;
while (oldSeparator != separator) {
oldSeparator = separator
while (separator.includes(",1}")) {
separator = separator.replace(/,1\}/g, "}");
}
while (separator.includes(",}")) {
separator = separator.replace(/,\}/g, "}");
}
while (separator.includes("}1}")) {
partialSeparator = separator.slice(0, separator.lastIndexOf("}1}")+2);
separatorToRemove = parseSeparatorRight(partialSeparator);
separator = separator.replace(separatorToRemove + "1}", "}");
}
}
return separator;
}
function rule3atBaseLayer(separator) {
var partialSeparator;
var separatorToRemove;
var oldSeparator;
while (oldSeparator != separator) {
oldSeparator = separator
while (separator.includes(",1)")) {
separator = separator.replace(/,1\)/g, ")");
}
while (separator.includes(",)")) {
separator = separator.replace(/,\)/g, ")");
}
while (separator.includes("}1)")) {
partialSeparator = separator.slice(0, separator.lastIndexOf("}1)")+2);
separatorToRemove = parseSeparatorRight(partialSeparator);
separator = separator.replace(separatorToRemove + "1)", ")");
}
}
return separator;
}
function getAllEntriesInSeparator(separator) {
//separator = simplify(separator); // prevent problems like {1}'s
if (separator.startsWith(",")) {
return [];
}
var leftmostSeparator = parseSeparatorLeft(separator); // take only the leftmost separator
entryList = [];
leftmostSeparator = leftmostSeparator.slice(1);
while (leftmostSeparator.includes("{") || leftmostSeparator.includes(",")) {
var separatorPosition = leftmostSeparator.indexOf(parseSeparatorLeft(leftmostSeparator));
var separatorLength = parseSeparatorLeft(leftmostSeparator).length
entryList.push(parseFloat(leftmostSeparator));
leftmostSeparator = leftmostSeparator.slice(separatorLength + separatorPosition);
}
entryList.push(parseFloat(leftmostSeparator));
return entryList;
}
function getAllEntriesInBaseLayer(SANArray) {
separator = SANArray.replace("s(","{").replace(")","}");
return getAllEntriesInSeparator(separator);
}
function higherSeparator(separator1, separator2) {
if (separator1.startsWith("s(")) {
return separator2;
} else if (separator2.startsWith("s(")) {
return separator1;
} // all arrays have the lowest level
//setup
var DANseparator1 = rule3(simplify(convertPDANtoDAN(convertMEANtoPDAN(separator1))));
var DANseparator2 = rule3(simplify(convertPDANtoDAN(convertMEANtoPDAN(separator2))));
var highestCommas = maxCommas(DANseparator1 + "&" + DANseparator2);
var combinedSeparators = convertToMaxCommas(" " + DANseparator1 + " & " + DANseparator2 + " ");
DANseparator1 = combinedSeparators.slice(0, combinedSeparators.indexOf("&"));
DANseparator2 = combinedSeparators.slice(combinedSeparators.indexOf("&")+1);
// convert to DAN and make m-ple comma the only basic separator.
DANseparator1 = DANseparator1.replace(/(\d),(\d)/g, '$1' + "{1}" + '$2');
DANseparator2 = DANseparator2.replace(/(\d),(\d)/g, '$1' + "{1}" + '$2');
if (DANseparator1 == ",") { DANseparator1 = "{1}"; }
if (DANseparator2 == ",") { DANseparator2 = "{1}"; }
// convert all single commas into {1}'s
if (DANseparator1 == DANseparator2) {
return separator1;
} // The two separators are equal
if (DANseparator1.startsWith(",,")) {
return separator1;
} else if (DANseparator2.startsWith(",,")) {
return separator2;
} // return m-ple comma if one of the separators is m-ple comma.
if (getAllEntriesInSeparator(DANseparator1).length == 1 &&
getAllEntriesInSeparator(DANseparator2).length == 1) {
var entry1 = getAllEntriesInSeparator(DANseparator1)[0];
var entry2 = getAllEntriesInSeparator(DANseparator2)[0];
return "{" + Math.max(entry1, entry2) + "}"; // both separators have only one entry
} else if (getAllEntriesInSeparator(DANseparator1).length == 1) {
return separator2;
} else if (getAllEntriesInSeparator(DANseparator2).length == 1) {
return separator1;
} // step 4 complete
// Now find maximum separator in the list of separators in the separator.
var separatorList1 = getAllSeparatorsInSeparator(DANseparator1);
var separatorList2 = getAllSeparatorsInSeparator(DANseparator2);
var maxSeparator1 = separatorList1[0];
var maxSeparator2 = separatorList2[0];
var k = 0;
while (k < separatorList1.length) {
maxSeparator1 = higherSeparator(maxSeparator1, separatorList1[k]);
k++;
}
var l = 0;
while (l < separatorList2.length) {
maxSeparator2 = higherSeparator(maxSeparator2, separatorList2[l]);
l++;
} // found maximum separator in separator.
if (higherSeparator(maxSeparator1, maxSeparator2) == maxSeparator1 && maxSeparator1 != maxSeparator2) {
return separator1;
}
if (higherSeparator(maxSeparator1, maxSeparator2) == maxSeparator2 && maxSeparator1 != maxSeparator2) {
return separator2;
} // return separator based on highest leveled separator in the separator (rule 3 already applied)
// Now compare the stuff to the right of the highest leveled separator.
//insert code here {1{1,,,2}2,,,2} didnt parse correctly
var partialString1 = DANseparator1.slice(1);
while (parseSeparatorLeft(partialString1) != maxSeparator1) {
partialString1 = partialString1.slice(parseSeparatorLeft(partialString1).length + 1);
}
var partialString2 = DANseparator2.slice(1);
while (parseSeparatorLeft(partialString2) != maxSeparator2) {
partialString2 = partialString2.slice(parseSeparatorLeft(partialString2).length + 1);
}
var startPosition1 = DANseparator1.length - partialString1.length;
var startPosition2 = DANseparator2.length - partialString2.length;
// end stuff
var leftSeparator1 = DANseparator1.slice(0, DANseparator1.indexOf(maxSeparator1, startPosition1)) + "}";
var rightSeparator1 = "{" + DANseparator1.slice(DANseparator1.indexOf(maxSeparator1, startPosition1) + maxSeparator1.length);
var leftSeparator2 = DANseparator2.slice(0, DANseparator2.indexOf(maxSeparator2, startPosition2)) + "}";
var rightSeparator2 = "{" + DANseparator2.slice(DANseparator2.indexOf(maxSeparator2, startPosition2) + maxSeparator2.length);
leftseparator1 = rule3(leftSeparator1);
leftseparator2 = rule3(leftSeparator2);
rightseparator1 = rule3(rightSeparator1);
rightseparator2 = rule3(rightSeparator2);
if (higherSeparator(rightSeparator1, rightSeparator2) == rightSeparator1 && rightSeparator1 != rightSeparator2) {
return separator1;
}
if (higherSeparator(rightSeparator1, rightSeparator2) == rightSeparator2 && rightSeparator1 != rightSeparator2) {
return separator2;
}
if (higherSeparator(leftSeparator1, leftSeparator2) == leftSeparator1 && leftSeparator1 != leftSeparator2) {
return separator1;
}
if (higherSeparator(leftSeparator1, leftSeparator2) == leftSeparator2 && leftSeparator1 != leftSeparator2) {
return separator2;
}
}
function areEqualSeparators(separator1, separator2) {
if (separator1.startsWith("s(") && separator2.startsWith("s(")) {
return true;
} else if (separator1.startsWith("s(") || separator2.startsWith("s(")) {
return false;
} // all arrays have the lowest level
//setup
var DANseparator1 = rule3(simplify(convertPDANtoDAN(convertMEANtoPDAN(separator1))));
var DANseparator2 = rule3(simplify(convertPDANtoDAN(convertMEANtoPDAN(separator2))));
var highestCommas = maxCommas(DANseparator1 + "&" + DANseparator2);
var combinedSeparators = convertToMaxCommas(" " + DANseparator1 + " & " + DANseparator2 + " ");
DANseparator1 = combinedSeparators.slice(0, combinedSeparators.indexOf("&"));
DANseparator2 = combinedSeparators.slice(combinedSeparators.indexOf("&")+1);
// convert to DAN and make m-ple comma the only basic separator.
DANseparator1 = DANseparator1.replace(/(\d),(\d)/g, '$1' + "{1}" + '$2');
DANseparator2 = DANseparator2.replace(/(\d),(\d)/g, '$1' + "{1}" + '$2');
if (DANseparator1 == ",") { DANseparator1 = "{1}"; }
if (DANseparator2 == ",") { DANseparator2 = "{1}"; }
// convert all single commas into {1}'s
if (DANseparator1 == DANseparator2) {
return true;
} // The two separators are equal
if (DANseparator1.startsWith(",,")) {
return false;
} else if (DANseparator2.startsWith(",,")) {
return false;
} // return m-ple comma if one of the separators is m-ple comma.
if (getAllEntriesInSeparator(DANseparator1).length == 1 &&
getAllEntriesInSeparator(DANseparator2).length == 1) {
var entry1 = getAllEntriesInSeparator(DANseparator1)[0];
var entry2 = getAllEntriesInSeparator(DANseparator2)[0];
if (entry1 == entry2) {
return true;
} else {
return false;
}
} else if (getAllEntriesInSeparator(DANseparator1).length == 1) {
return false;
} else if (getAllEntriesInSeparator(DANseparator2).length == 1) {
return false;
} // step 4 complete
// Now find maximum separator in the list of separators in the separator.
var separatorList1 = getAllSeparatorsInSeparator(DANseparator1);
var separatorList2 = getAllSeparatorsInSeparator(DANseparator2);
var maxSeparator1 = separatorList1[0];
var maxSeparator2 = separatorList2[0];
for (i=0; i<separatorList1.length; i++) {
maxSeparator1 = higherSeparator(maxSeparator1, separatorList1[i]);
}
for (i=0; i<separatorList2.length; i++) {
maxSeparator2 = higherSeparator(maxSeparator2, separatorList2[i]);
} // found maximum separator in separator.
if (maxSeparator1 != maxSeparator2) {
return false;
} // return separator based on highest leveled separator in the separator (rule 3 already applied)
// Now compare the stuff to the right of the highest leveled separator.
//insert code here {1{1,,,2}2,,,2} didnt parse correctly
var partialString1 = DANseparator1.slice(1);
while (parseSeparatorLeft(partialString1) != maxSeparator1) {
partialString1 = partialString1.slice(parseSeparatorLeft(partialString1).length + 1);
}
var partialString2 = DANseparator2.slice(1);
while (parseSeparatorLeft(partialString2) != maxSeparator2) {
partialString2 = partialString2.slice(parseSeparatorLeft(partialString2).length + 1);
}
var startPosition1 = DANseparator1.length - partialString1.length;
var startPosition2 = DANseparator2.length - partialString2.length;
// end stuff
var leftSeparator1 = DANseparator1.slice(0, DANseparator1.indexOf(maxSeparator1, startPosition1)) + "}";
var rightSeparator1 = "{" + DANseparator1.slice(DANseparator1.indexOf(maxSeparator1, startPosition1) + maxSeparator1.length);
var leftSeparator2 = DANseparator2.slice(0, DANseparator2.indexOf(maxSeparator2, startPosition2)) + "}";
var rightSeparator2 = "{" + DANseparator2.slice(DANseparator2.indexOf(maxSeparator2, startPosition2) + maxSeparator2.length);
leftseparator1 = rule3(leftSeparator1);
leftseparator2 = rule3(leftSeparator2);
rightseparator1 = rule3(rightSeparator1);
rightseparator2 = rule3(rightSeparator2);
if (rightSeparator1 != rightSeparator2) {
return false;
}
if (leftSeparator1 != leftSeparator2) {
return false;
}
if (higherSeparator(leftSeparator1, leftSeparator2) == leftSeparator1 && leftSeparator1 != leftSeparator2) {
return false;
}
if (higherSeparator(leftSeparator1, leftSeparator2) == leftSeparator2 && leftSeparator1 != leftSeparator2) {
return false;
}
return true;
}
function rule4InBaseLayerOfSeparator(separator) {
if (separator.startsWith("s(")) {
return separator;
}
separator = rule3(separator);
var separators = getAllSeparatorsInSeparator(separator); // {2} {3}
var entries = getAllEntriesInSeparator(separator); // 1 1 2
var i=1;
while (i < entries.length) {
if (entries[i] == 1 && higherSeparator(separators[i-1], separators[i]) == separators[i] &&
!(areEqualSeparators(separators[i-1], separators[i]))) { // {a}1{b} for a<b
separators.splice(i-1, 1);
entries.splice(i, 1);
} else {
i++;
}
}
var completedString = "{";
for (i=0; i<entries.length - 1; i++) {
completedString += entries[i] + separators[i];
}
completedString += entries[entries.length-1] + "}";
return completedString;
}
function getArrayGivenSeparatorsAndEntries(entryList, separatorList, mode) { // entryList and separatorList are arrays
// mode: 0 = s(__), 1 = {__}
var separatorString = ""
for (i=0; i<entryList.length - 1; i++) {
separatorString += entryList[i] + separatorList[i];
}
separatorString += entryList[entryList.length-1];
if (mode == 0) {
return "s(" + separatorString + ")"
} else if (mode == 1) {
return "{" + separatorString + "}"
}
}
function calculate() {
var inputString = document.getElementById("input").value;
inputString = inputString.replace(/\[/g, "{").replace(/\]/g, "}").replace(/\s/g, "");
if (!(inputString.includes("s("))) { // don't evaluate when no s( is found
SANinput = inputString;
SANmessage = "Input: " + SANinput + "<br><br>It's already solved to a number.<br>Result: ";
return inputString;
}
SANinput = rule3atBaseLayer(inputString);
SANinput = simplify(rule3(convertMEANtoPDAN(convertPDANtoDAN(SANinput))));
var SANArray = SANinput.slice(SANinput.lastIndexOf("s("));
SANArray = SANArray.slice(0, SANArray.indexOf(")") + 1); // get innermost SAN array
SANArray = rule3atBaseLayer(SANArray);
SANArray = simplify(rule3(convertMEANtoPDAN(convertPDANtoDAN(SANArray))));
SANArray = convertToMaxCommas(SANArray); // convert to m-ple commas by using ,,...,, (i commas) = {1,,...,,,2} (i+1 commas)
var beforeSANArray = SANinput.slice(0, SANinput.lastIndexOf("s(")); // to remember what was cut off
var afterSANArray = SANinput.slice(SANinput.indexOf(")",SANinput.lastIndexOf("s(")) + 1);
var getMaxCommas = maxCommas(SANArray);
// convert to DAN and apply rule 3 until rule 3 cannot apply anymore.
var separatorsInBaseLayer = getAllSeparatorsInBaseLayer(SANArray);
var entriesInBaseLayer = getAllEntriesInBaseLayer(SANArray);
if (separatorsInBaseLayer.length == 0) { // in the form s(a)
SANArray = SANArray.replace(")",",1)"); // change s(a) to s(a,1)
separatorsInBaseLayer = getAllSeparatorsInBaseLayer(SANArray);
entriesInBaseLayer = getAllEntriesInBaseLayer(SANArray);
}
if (separatorsInBaseLayer[0] != ",") { // in the form s(a{b}c #) with b>1
SANArray = SANArray.slice(0, SANArray.indexOf("{")) + ",1" + SANArray.slice(SANArray.indexOf("{"));
separatorsInBaseLayer = getAllSeparatorsInBaseLayer(SANArray);
entriesInBaseLayer = getAllEntriesInBaseLayer(SANArray);
}
if (entriesInBaseLayer.length == 2 && separatorsInBaseLayer[0] == ",") { // in the form s(a,b)
SANmessage = "Input: " + SANinput + "<br><br>Apply rule s(a,b) = a^b.<br>Result: ";
return beforeSANArray + entriesInBaseLayer[0] ** entriesInBaseLayer[1] + afterSANArray; // Evaluate s(a,b) = a^b
}
if (entriesInBaseLayer[1] != 1 && entriesInBaseLayer[2] != 1 && separatorsInBaseLayer[1] == ",") {
// in the form s(a,b,c #) with b,c>1
var innerSANArray = SANArray;
var separatorsInInnerBaseLayer = getAllSeparatorsInBaseLayer(innerSANArray);
var entriesInInnerBaseLayer = getAllEntriesInBaseLayer(innerSANArray);
entriesInInnerBaseLayer[1]--;
entriesInBaseLayer[2]--;
innerSANArray = getArrayGivenSeparatorsAndEntries(entriesInInnerBaseLayer, separatorsInInnerBaseLayer, 0);
entriesInBaseLayer[1] = innerSANArray;
SANmessage = "Input: " + SANinput + "<br><br>Apply recursion rule s(a,b,c #) = s(a,s(a,b-1,c #),c-1 #).<br>Result: ";
return beforeSANArray + getArrayGivenSeparatorsAndEntries(entriesInBaseLayer, separatorsInBaseLayer, 0) + afterSANArray;
} // recursion rule
// prepare for the process
var base = entriesInBaseLayer[0];
var iterator = entriesInBaseLayer[1];
var A_t = [SANArray]; // A_0, A_1, A_2, ...
var B_t = []; // B_0, B_1, B_2, ...
var leftRemovedB_t = [];
var rightRemovedB_t = [];
var entryIndex = 2; // start from the 3rd entry
while (entriesInBaseLayer[entryIndex] == 1) {
entryIndex++;
} // find first non-1 entry in base layer
if (separatorsInBaseLayer[entryIndex-1] == ",") { // comma is immediately before non-1 entry in base layer
entriesInBaseLayer[entryIndex]--;
entriesInBaseLayer[entryIndex-1] = iterator;
entryIndex -= 2;
while (entryIndex>0) {
entriesInBaseLayer[entryIndex] = base;
entryIndex--;
}
SANmessage = "Input: " + SANinput + "<br><br>Change the \"1,n\" to \"b,n-1\" where b is the iterator and change all values at base layer before them into the base.<br>Result: ";
return simplify(rule3atBaseLayer(beforeSANArray +
getArrayGivenSeparatorsAndEntries(entriesInBaseLayer, separatorsInBaseLayer, 0) + afterSANArray));
} // case B1 at base layer
if (separatorsInBaseLayer[entryIndex-1].startsWith(",,")) { // m-ple comma is before you in base layer
separatorsInBaseLayer.splice(entryIndex-1, 0, "{1" + separatorsInBaseLayer[entryIndex-1] + "2}");
entriesInBaseLayer.splice(entryIndex, 0, 2);
entriesInBaseLayer[entryIndex+1]--;
SANmessage = "Input: " + SANinput + "<br><br>There is an m-ple comma at base layer. Add a layer of \"{1\" and \"2}\" underneath it.<br>Result: ";
return rule3atBaseLayer(beforeSANArray +
getArrayGivenSeparatorsAndEntries(entriesInBaseLayer, separatorsInBaseLayer, 0) + afterSANArray);
}
var SANseparator = "";
if (separatorsInBaseLayer[entryIndex-1].startsWith("{")) {
// a separator not comma or m-ple comma is before you in base layer
separatorsInBaseLayer.splice(entryIndex-1, 0, separatorsInBaseLayer[entryIndex-1]);
entriesInBaseLayer.splice(entryIndex, 0, 2);
entriesInBaseLayer[entryIndex+1]--;
A_t.push(separatorsInBaseLayer[entryIndex-1]);
var leftPartialArray = "s(";
j = 0;
while (j < entryIndex-1) {
leftPartialArray += entriesInBaseLayer[j] + separatorsInBaseLayer[j];
j++;
}
leftPartialArray += entriesInBaseLayer[j];
leftRemovedB_t.push(leftPartialArray);
var rightPartialArray = "";
j = entryIndex;
while (j < separatorsInBaseLayer.length) {
rightPartialArray += entriesInBaseLayer[j] + separatorsInBaseLayer[j];
j++;
}
rightPartialArray += entriesInBaseLayer[j];
rightPartialArray += ")";
rightRemovedB_t.push(rightPartialArray);
SANseparator = rule4InBaseLayerOfSeparator(separatorsInBaseLayer[entryIndex-1]); // work on this separator now
}
var layer = 1;
/* Now work inside the separator.*/
while (true) {
var separatorsInSeparator = getAllSeparatorsInSeparator(SANseparator);
var entriesInSeparator = getAllEntriesInSeparator(SANseparator);
entryIndex = 0; // restart entryindex in new layer
if (entriesInSeparator[0] != 1) { // non-1 entry immediately after lbrace
leftPartialArray = "";
rightPartialArray = "";
for (j=0; j<leftRemovedB_t.length; j++) {
leftPartialArray += leftRemovedB_t[j];
}
for (j=0; j<rightRemovedB_t.length; j++) {
rightPartialArray = rightRemovedB_t[j] + rightPartialArray;
}
entriesInSeparator[0]--;
var copySeparator = getArrayGivenSeparatorsAndEntries(entriesInSeparator, separatorsInSeparator, 1);
SANmessage = "Input: " + SANinput + "<br><br>Apply the exAN rule: Expand {n #} into b copies of {n-1 #} with ones between them.<br>Result: ";
return simplify(rule3atBaseLayer(beforeSANArray + leftPartialArray +
(copySeparator + "1").repeat(iterator-1) + copySeparator + rightPartialArray + afterSANArray));
}
while (entriesInSeparator[entryIndex] == 1) {
entryIndex++;
} // find first non-1 entry in separator
if (separatorsInSeparator[entryIndex-1] == ",") {
entriesInSeparator[entryIndex]--;
entriesInSeparator[entryIndex-1] = iterator;
SANseparator = rule4InBaseLayerOfSeparator(getArrayGivenSeparatorsAndEntries(entriesInSeparator, separatorsInSeparator, 1));
// change all entries at base layer before them into the base.
var arrayToLeftOfSeparator = leftRemovedB_t[0] + ")";
var entriesToChange = getAllEntriesInBaseLayer(arrayToLeftOfSeparator);
var separatorsToUnchange = getAllSeparatorsInBaseLayer(arrayToLeftOfSeparator);
for (i=0; i<entriesToChange.length; i++) {
entriesToChange[i] = base;
}
arrayToLeftOfSeparator = getArrayGivenSeparatorsAndEntries(entriesToChange, separatorsToUnchange, 0).replace(")","");
for (i=1; i<leftRemovedB_t.length; i++) {
arrayToLeftOfSeparator += leftRemovedB_t[i];
}
SANmessage = "Input: " + SANinput + "<br><br>Change the \"1,n\" to \"b,n-1\" where b is the iterator and change all values at base layer before them into the base.<br>Result: ";
return simplify(rule3atBaseLayer(rule3(beforeSANArray + arrayToLeftOfSeparator + SANseparator + rightPartialArray + afterSANArray)));
} // comma is immediately before you in separator
if (separatorsInSeparator[entryIndex-1] == ",".repeat(getMaxCommas)) { // m-ple comma is immediately before you in separator
entriesInSeparator[entryIndex]--;
separatorsInSeparator[entryIndex-1] += "2" + separatorsInSeparator[entryIndex-1];
modifiedSeparator = getArrayGivenSeparatorsAndEntries(entriesInSeparator, separatorsInSeparator, 1);
simplifiedModifiedSeparator = rule4InBaseLayerOfSeparator(rule3(modifiedSeparator));
entriesInSeparator = getAllEntriesInSeparator(simplifiedModifiedSeparator);
separatorsInSeparator = getAllSeparatorsInSeparator(simplifiedModifiedSeparator);
A_t.push(separatorsInSeparator[entryIndex-1]);
leftRemovedB_t[layer] = "{";
for (i=0; i<entryIndex-1; i++) {
leftRemovedB_t[layer] += entriesInSeparator[i] + separatorsInSeparator[i];
}
leftRemovedB_t[layer] += entriesInSeparator[entryIndex-1];
rightRemovedB_t[layer] = entriesInSeparator[entriesInSeparator.length-1] + "}";
for (i=entriesInSeparator.length-2; i>=entryIndex; i--) {
rightRemovedB_t[layer] = entriesInSeparator[i] + separatorsInSeparator[i] + rightRemovedB_t[layer];
}
B_t[layer+1] = A_t[layer+1];
for (i = layer; i>=0; i--) {
B_t[i] = leftRemovedB_t[i] + B_t[i+1] + rightRemovedB_t[i]
} // set up B_t[0,1,2,...until layer]
// searching out step
u = layer+1; // something
j = getMaxCommas; // j-separator
m = layer;
t = layer;
v = 0;
//repeat
while (j > 1) {
while (higherSeparator(A_t[t], A_t[m]) == A_t[t] || areEqualSeparators(A_t[t], A_t[m])) {
t--;
} // search for the innermost separator
nSeparator = "";
leftnSeparator = "";
rightnSeparator = "";
for (i = m; i < u; i++) {
leftnSeparator += leftRemovedB_t[i];
rightnSeparator = rightRemovedB_t[i] + rightnSeparator;
}
nSeparator = leftnSeparator + A_t[m] + rightnSeparator;
if (higherSeparator(A_t[t], nSeparator) == nSeparator &&
!(areEqualSeparators(A_t[t], nSeparator))) { // has lower level than what it's searching for
v = t+1;
while (higherSeparator(A_t[v], A_t[u]) == A_t[v] || areEqualSeparators(A_t[v], A_t[u])) { // adding rule
v++;
}
leftArray = "";
rightArray = "";
for (i=0; i<v; i++) {
leftArray += leftRemovedB_t[i];
rightArray = rightRemovedB_t[i] + rightArray;
}
var leftAddingSeparator = "";
var rightAddingSeparator = "";
for (z = m; z < u; z++) {
leftAddingSeparator += leftRemovedB_t[z];
rightAddingSeparator = rightRemovedB_t[z] + rightAddingSeparator;
}
SANmessage = "Input: " + SANinput + "<br><br>The innermost separator with lower level than the " + (j-1) + "-separator " + A_t[m] + " has lower level than " + nSeparator + " so we go to the adding rule. Now add \"" + leftnSeparator + "\" and \"" + rightnSeparator + "\" outside A<sub>v</sub>, which is " + A_t[v] + ". Note that all arrays in the form s(#) have lower level than all separators.<br>Result: ";
return rule3(rule3atBaseLayer(beforeSANArray + leftArray + leftAddingSeparator + A_t[v] + rightAddingSeparator + rightArray + afterSANArray));
} // adding rule
u = m;
m = t;
j--;
}
// expanding rule
// u is the layer of the 1-separator, m is the layer of the 0-separator.
var unchangedLeftParts = "";
var unchangedRightParts = "";
for (i=0; i<m; i++) {
unchangedLeftParts += leftRemovedB_t[i];
unchangedRightParts = rightRemovedB_t[i] + unchangedRightParts;
}
var repeatLeftParts = "";
var repeatRightParts = "";
for (i=m; i<u; i++) {
repeatLeftParts += leftRemovedB_t[i];
repeatRightParts = rightRemovedB_t[i] + repeatRightParts;
}
SANmessage = "Input: " + SANinput + "<br><br>The innermost separator with lower level than the " + (j) + "-separator " + A_t[u] + " has equal or higher level than " + nSeparator + " so we go to the expanding rule: Change the 0-separator " + A_t[m] + " to S<sub>b</sub>, where b is iterator, S<sub>1</sub> is comma and S<sub>n</sub> is " + repeatLeftParts + " S<sub>n-1</sub> " + repeatRightParts + " by replacing the 1-separator with S<sub>n-1</sub> in S<sub>n</sub>.<br>Result: ";
return simplify(rule3atBaseLayer(rule3(beforeSANArray + unchangedLeftParts + repeatLeftParts.repeat(iterator-1) + "," +
repeatRightParts.repeat(iterator-1) + unchangedRightParts + afterSANArray)));
//expanding rule
}
if (separatorsInSeparator[entryIndex-1].startsWith("{")) { // a separator not comma or m-ple comma immediately before you in separator
entriesInSeparator[entryIndex]--;
separatorsInSeparator[entryIndex-1] += "2" + separatorsInSeparator[entryIndex-1];
modifiedSeparator = getArrayGivenSeparatorsAndEntries(entriesInSeparator, separatorsInSeparator, 1);
simplifiedModifiedSeparator = rule4InBaseLayerOfSeparator(rule3(modifiedSeparator));
entriesInSeparator = getAllEntriesInSeparator(simplifiedModifiedSeparator);
separatorsInSeparator = getAllSeparatorsInSeparator(simplifiedModifiedSeparator);
A_t.push(separatorsInSeparator[entryIndex-1]);
leftRemovedB_t[layer] = "{";
for (i=0; i<entryIndex-1; i++) {
leftRemovedB_t[layer] += entriesInSeparator[i] + separatorsInSeparator[i];
}
leftRemovedB_t[layer] += entriesInSeparator[entryIndex-1];
leftPartialArray += leftRemovedB_t[layer]; // got the left part
rightRemovedB_t[layer] = entriesInSeparator[entriesInSeparator.length-1] + "}";
for (i=entriesInSeparator.length-2; i>=entryIndex; i--) {
rightRemovedB_t[layer] = entriesInSeparator[i] + separatorsInSeparator[i] + rightRemovedB_t[layer];
}
rightPartialArray = rightRemovedB_t[layer] + rightPartialArray; // got the right part
SANseparator = rule4InBaseLayerOfSeparator(separatorsInSeparator[entryIndex-1]);
layer++;
}
}
}
// for s(3,3{1{1,3}3}2), entriesinbaselayer = [3, 3, 2], separators=[",", "{1{1,3}3}"]
// SANArray = s(3,3{1{1,3}3}2), getMaxCommas=1
// A_t = [s(3,3{1{1,3}3}2)], B_t = [], entryIndex=2
// SANseparator = {1{1,3}3}
// entriesInBaseLayer = 3,3,2,1
// leftPartialArray = "s(3,3", rightPartialArray = 2{1{1,3}3}1)
// leftRemovedB_t = "s(3,3", rightRemovedB_t = "2{1{1,3}3}1)"
// separatorsInSeparator = "{1,3}", entriesInSeparator = "1","3", entryIndex=1
// after: separatorsInSeparator[x-1] = "{1,3}","{1,3}", entriesInSeparator = "1","2","2", entryindex=1
// {1{1,3}2{1,3}2}
// beforeSANArray + leftPartialArray + Separator + rightPartialArray + afterSANArray
function solve() {
startTime = new Date().getTime();
getSANmode(document.getElementById("input").value);
finalResult = calculate();
finalResult = simplify(rule3(rule3atBaseLayer(finalResult)));
SANmessage += finalResult;
SANmessage = simplify(SANmessage);
elapsedTime = new Date().getTime() - startTime;
var timeSeconds;
var timeMinutes;
var timeHours;
if (SANmode == 4) {
for (i=99; i>=1; i--) {
replaceString = RegExp("\\{1,," + (i+1) + "\\}", "g")
SANmessage = SANmessage.replace(replaceString, "`".repeat(i));
replaceString2 = RegExp(",," + (i+1) + "\\}", "g")
SANmessage = SANmessage.replace(replaceString2, "<sup>" + "`".repeat(i)+"</sup>}");
}
}
if (SANmode == 2 || SANmode == 3) {
if (SANmode == 3) {
for (i=99; i>=1; i--) { // for sDAN
SANmessage = SANmessage.replace(RegExp("\\{1\\{1,,,3\\}" + (i+1) + ",,,2\\}", "g"), "`".repeat(i) + ",,");
SANmessage = SANmessage.replace(RegExp("\\{1,,,3\\}" + (i+1) + ",,,2\\}", "g"), "<sup>" + "`".repeat(i) + ",,</sup>}");
}
}
for (i=99; i>=1; i--) { // for sDAN
SANmessage = SANmessage.replace(RegExp("\\{1,,," + (i+2) + "\\}", "g"), ",," + "`".repeat(i));
SANmessage = SANmessage.replace(RegExp(",,," + (i+2) + "\\}", "g"), "<sup>,," + "`".repeat(i)+"</sup>}");
}
SANmessage = SANmessage.replace(/,,,2\}/g, "<sup>,,</sup>}");
}
timeSeconds = Math.floor((elapsedTime/1000)%60);
timeMinutes = Math.floor((elapsedTime/60000)%60);
timeHours = Math.floor(elapsedTime/3600000);
SANmessage += "<br><br>Solving time: ";
if (elapsedTime < 60000) {
SANmessage += (elapsedTime/1000).toFixed(3) + " seconds";
} else if (elapsedTime < 3600000) {
SANmessage += timeMinutes + " minute" + (timeMinutes==1 ? ", " : "s, ") +
timeSeconds + " second" + (timeSeconds==1 ? "" : "s");
} else {
SANmessage += timeHours + " hour" + (timeHours==1 ? ", " : "s, ") +
timeMinutes + " minute" + (timeMinutes==1 ? ", " : "s, ") +
timeSeconds + " second" + (timeSeconds==1 ? "" : "s");
}
document.getElementById("message").innerHTML = SANmessage;
//(Math.random() < 0.01) ? window.location =atob("aHR0cHM6Ly93d3cueW91dHViZS5jb20vd2F0Y2g/dj1kUXc0dzlXZ1hjUQ==") : "";
}
function plugFinalResult() {
if (finalResult != undefined) {
startResult = finalResult;
if (SANmode == 2 || SANmode == 3) {
if (SANmode == 3) {
for (i=99; i>=1; i--) { // for sDAN
startResult = startResult.replace(RegExp("\\{1\\{1,,,3\\}" + (i+1) + ",,,2\\}", "g"), "`".repeat(i) + ",,");
startResult = startResult.replace(RegExp("\\{1,,,3\\}" + (i+1) + ",,,2\\}", "g"), "^" + "`".repeat(i) + ",,}");
}
}
for (i=99; i>=1; i--) { // for sDAN
startResult = startResult.replace(RegExp("\\{1,,," + (i+2) + "\\}", "g"), ",," + "`".repeat(i));
startResult = startResult.replace(RegExp(",,," + (i+2) + "\\}", "g"), "^,," + "`".repeat(i)+"}");
}
startResult = startResult.replace(/,,,2\}/g, "^,,}");
} else if (SANmode == 4) {
for (i=99; i>=1; i--) {
replaceString = RegExp("{1,," + (i+1) + "\\}", "g")
startResult = startResult.replace(replaceString, "`".repeat(i));
replaceString2 = RegExp(",," + (i+1) + "\\}", "g")
startResult = startResult.replace(replaceString2, "^" + "`".repeat(i)+"}");
}
}
document.getElementById("input").value = startResult;
}
solve();
}
// function list: maxCommas, convertToMaxCommas, convertMEANtoPDAN, convertPDANtoDAN,
// parseSeparatorLeft, parseSeparatorRight, getAllSeparatorsInSeparator, getAllSeparatorsInBaseLayer,
// getAllEntriesInSeparator, getAllEntriesInBaseLayer, simplify, rule3,
// rule3atBaseLayer, rule4InBaseLayerOfSeparator, higherSeparator, areEqualSeparators,
// getArrayGivenSeparatorsAndEntries (3 arguments)
</script>
</body>
</html>