michi42.github.io/auto.html at master · michi42/michi42.github.io · GitHub

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<!DOCTYPE html>
<html lang="de">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Autonummerngleichungslöser</title>
<style>
:root{
  --paper:#edf2f4;
  --grid:#dbe6ec;
  --grid-strong:#c6d9e2;
  --ink:#16242f;
  --muted:#6e828e;
  --op:#6b2fe0;
  --eq:#0e8f6f;
  --none:#b3453e;
  --mono:ui-monospace,"SF Mono",SFMono-Regular,Menlo,Consolas,"Liberation Mono",monospace;
  --sans:system-ui,-apple-system,"Segoe UI",Roboto,sans-serif;
}
*{box-sizing:border-box}
html,body{margin:0;padding:0}
body{
  background:var(--paper);
  background-image:
    repeating-linear-gradient(to right, var(--grid-strong) 0 1px, transparent 1px 110px),
    repeating-linear-gradient(to bottom, var(--grid-strong) 0 1px, transparent 1px 110px),
    repeating-linear-gradient(to right, var(--grid) 0 1px, transparent 1px 22px),
    repeating-linear-gradient(to bottom, var(--grid) 0 1px, transparent 1px 22px);
  color:var(--ink);
  font-family:var(--sans);
  font-size:16px;
  line-height:1.55;
  padding:clamp(18px,4vw,56px) clamp(14px,4vw,32px) 64px;
}
main{max-width:730px;margin:0 auto}
.eyebrow{
  font-family:var(--mono);font-size:11px;letter-spacing:.18em;text-transform:uppercase;
  color:var(--muted);margin:0 0 10px;
}
h1{
  font-family:var(--mono);font-size:clamp(20px,4.7vw,36px);line-height:1.05;
  letter-spacing:-.02em;margin:0 0 14px;font-weight:700;
}
h1 .sym{color:var(--op)}
.rules{margin:0 0 28px;max-width:56ch;color:#31424e}
.rules code{font-family:var(--mono);background:#fff;border:1px solid var(--grid-strong);
  border-radius:3px;padding:0 4px}

/* ---- input ---- */
.panel{background:#fff;border:1px solid var(--grid-strong);border-radius:2px;
  box-shadow:0 1px 0 rgba(22,36,47,.06);padding:clamp(14px,3vw,22px)}
.row{display:flex;gap:10px;flex-wrap:wrap;align-items:stretch}
input[type=text]{
  flex:1 1 220px;min-width:0;font-family:var(--mono);font-size:clamp(20px,4.4vw,28px);
  letter-spacing:.14em;padding:10px 12px;color:var(--ink);
  background:var(--paper);border:1px solid var(--grid-strong);border-radius:2px;
}
input[type=text]:focus-visible,button:focus-visible,summary:focus-visible{
  outline:2px solid var(--op);outline-offset:2px}
button{
  font-family:var(--sans);font-size:15px;font-weight:600;padding:10px 18px;cursor:pointer;
  border:1px solid var(--ink);border-radius:2px;background:var(--ink);color:#fff;
}
button.ghost{background:transparent;color:var(--ink)}
button:hover{filter:brightness(1.15)}
button:disabled{opacity:.45;cursor:progress}
.opts{display:flex;gap:18px;flex-wrap:wrap;margin-top:14px;
  font-size:13px;color:var(--muted)}
.opts label{display:flex;gap:6px;align-items:center;cursor:pointer}
.chips{margin-top:16px;display:flex;gap:8px;flex-wrap:wrap;align-items:baseline}
.chips b{font-family:var(--mono);font-size:11px;letter-spacing:.14em;text-transform:uppercase;
  color:var(--muted);font-weight:400}
.chip{font-family:var(--mono);font-size:13px;background:var(--paper);color:var(--ink);
  border:1px solid var(--grid-strong);border-radius:2px;padding:3px 8px;cursor:pointer}
.chip:hover{border-color:var(--op);color:var(--op)}

/* ---- result ---- */
#result{margin-top:22px}
.eqline{
  font-family:var(--mono);font-weight:600;
  font-size:clamp(19px,4.6vw,31px);letter-spacing:.02em;
  word-break:break-word;margin:0;
}
.eqline .d{color:var(--ink)}
.eqline .ins{color:var(--op)}
.eqline .par{color:#a58cf0}
.eqline .eqs{color:var(--eq);padding:0 .18em}
.anim .ins,.anim .par,.anim .eqs{animation:drop .34s cubic-bezier(.2,.9,.3,1.2) both}
@keyframes drop{from{opacity:0;transform:translateY(-.42em) scale(.7)}to{opacity:1;transform:none}}
@media (prefers-reduced-motion:reduce){.anim .ins,.anim .par,.anim .eqs{animation:none}}
.meta{font-family:var(--mono);font-size:12px;letter-spacing:.06em;color:var(--muted);
  margin:12px 0 0;text-transform:uppercase}
.nores{color:var(--none);font-weight:600}
.nores small{display:block;font-weight:400;color:var(--muted);font-size:13px;
  text-transform:none;letter-spacing:0;margin-top:6px;font-family:var(--sans)}
ol.splits{list-style:none;margin:16px 0 0;padding:0;border-top:1px solid var(--grid-strong)}
ol.splits li{display:flex;gap:14px;align-items:baseline;padding:9px 0;
  border-bottom:1px solid var(--grid-strong);font-family:var(--mono);font-size:14px}
ol.splits .pos{color:var(--muted);font-size:11px;letter-spacing:.1em;flex:0 0 4.4em}
ol.splits .miss{color:var(--none)}

/* ---- facts ---- */
details{margin-top:30px}
summary{font-family:var(--mono);font-size:11px;letter-spacing:.18em;text-transform:uppercase;
  color:var(--muted);cursor:pointer}
table{border-collapse:collapse;margin-top:14px;font-family:var(--mono);font-size:13px}
th,td{text-align:right;padding:4px 16px 4px 0;border-bottom:1px solid var(--grid-strong)}
th{color:var(--muted);font-weight:400;font-size:11px;letter-spacing:.1em;text-transform:uppercase}
td:first-child,th:first-child{text-align:left}
tr.zero td{color:var(--eq);font-weight:600}
details code{font-family:var(--mono)}
details p{font-size:13px;color:var(--muted);max-width:60ch}
</style>
</head>
<body>
<main>
  <h1>Autonummerngleichungslöser</h1>
  <p class="rules">
    Zwischen die Ziffern kommen <code>+</code> <code>−</code> <code>∗</code> <code>:</code>,
    Klammern und genau ein <code>=</code>. Die Ziffern bleiben in ihrer Reihenfolge stehen;
    benachbarte Ziffern dürfen zu mehrstelligen Zahlen zusammenwachsen.
    Beispiel: <code>392451</code> → <code>(3∗9)+24=51</code>.
  </p>

  <div class="panel">
    <div class="row">
      <input id="num" type="text" inputmode="numeric" autocomplete="off" spellcheck="false"
             value="392451" aria-label="Zahl">
      <button id="go">Gleichung suchen</button>
      <button id="rnd" class="ghost">Zufallszahl</button>
    </div>
    <div class="opts">
      <label><input type="checkbox" id="intOnly"> nur ganzzahlige Zwischenergebnisse</label>
      <label><input type="checkbox" id="noLead"> keine führenden Nullen in Blöcken</label>
      <label><input type="checkbox" id="allSplits"> alle Positionen des <code>=</code></label>
    </div>
    <div class="chips">
      <b>Proben</b>
      <button class="chip" data-n="14720">14720</button>
      <button class="chip" data-n="1098959">1098959</button>
      <button class="chip" data-n="121987">121987</button>
      <button class="chip" data-n="58980898">58980898</button>
      <button class="chip" data-n="80098959">80098959</button>
    </div>
  </div>

  <div id="result" aria-live="polite"></div>

  <details>
    <summary>Was über diese Aufgabe bekannt ist</summary>
    <table>
      <tr><th>Stellen</th><th>Zahlen</th><th>ohne Lösung</th><th>Anteil</th></tr>
      <tr><td>1</td><td>9</td><td>9</td><td>100 %</td></tr>
      <tr><td>2</td><td>90</td><td>81</td><td>90 %</td></tr>
      <tr><td>3</td><td>900</td><td>725</td><td>81 %</td></tr>
      <tr><td>4</td><td>9 000</td><td>4 718</td><td>52 %</td></tr>
      <tr><td>5</td><td>90 000</td><td>11 853</td><td>13 %</td></tr>
      <tr><td>6</td><td>900 000</td><td>3 526</td><td>0,39 %</td></tr>
      <tr><td>7</td><td>9 000 000</td><td>167</td><td>0,0019 %</td></tr>
      <tr class="zero"><td>8</td><td>90 000 000</td><td>0</td><td>0 %</td></tr>
    </table>
    <p>Aus einer vollständigen Suche über alle Zahlen dieser Längen. Einstellige Zahlen
    haben gar keine Lücke für das <code>=</code>, zweistellige nur die neun Doppelziffern
    <code>1=1</code> … <code>9=9</code>. Ab drei Stellen kippt es schnell: jede weitere
    Ziffer bringt eine zusätzliche Schnittstelle und exponentiell mehr Ausdrücke, während
    die zu treffenden Werte gleich bleiben. Die kleinste siebenstellige Zahl ohne Lösung
    ist 1 098 959; ab acht Stellen tritt keine Ausnahme mehr auf.</p>
    <p>Diese Seite durchsucht zuerst alle klammerfreien Ausdrücke und danach, falls nötig,
    alle Klammerungen. Zähler und Nenner werden dabei auf 10¹² begrenzt.</p>
  </details>
</main>

<script>
"use strict";
/* ---------------- exakte Bruchrechnung (Zähler/Nenner als ganze Zahlen) ---------- */
const CAP = 1e12, SAFE = 9007199254740991;
let INT_ONLY = false, NO_LEAD = false;

function gcd(a,b){ a=a<0?-a:a; b=b<0?-b:b; while(b){ const t=a%b; a=b; b=t; } return a; }
function mk(n,d){
  if(d===0) return null;
  if(d<0){ n=-n; d=-d; }
  const g = gcd(n,d) || 1;
  n/=g; d/=g;
  if(n>CAP||n<-CAP||d>CAP) return null;
  if(INT_ONLY && d!==1) return null;
  return {n,d};
}
function mul(a,b){                       // exaktes Produkt oder NaN
  if(a===0||b===0) return 0;
  const r=a*b;
  return (r>SAFE||r<-SAFE) ? NaN : r;
}
function apply(a,b,k){                   // k: 0=+ 1=- 2=* 3=:
  let n,d;
  const dd = mul(a.d,b.d);
  if(dd!==dd) return null;
  if(k===2){ n = mul(a.n,b.n); d = dd; }
  else if(k===3){
    if(b.n===0) return null;
    n = mul(a.n,b.d); d = mul(a.d,b.n);
  } else {
    const p = mul(a.n,b.d), q = mul(b.n,a.d);
    if(p!==p||q!==q) return null;
    n = k===0 ? p+q : p-q; d = dd;
  }
  if(n!==n||d!==d||n>SAFE||n<-SAFE) return null;
  return mk(n,d);
}
const key = r => r.n+"/"+r.d;
const OPCH = ["+","−","∗",":"];

/* ---------------- Phase 1: klammerfreie Ausdrücke (Punkt vor Strich) ------------- */
/* Für einen Ziffernblock alle Werte, die ohne Klammern erreichbar sind.
   Rückgabe: Map wertschlüssel -> {r, expr, ops}                                     */
let bfCache = new Map();
function bracketFree(s){
  const hit = bfCache.get(s); if(hit) return hit;
  const out = new Map(), gaps = s.length-1, total = Math.pow(5,gaps);
  const nums=[], ops=[];
  for(let mask=0; mask<total; mask++){
    // Muster dekodieren: 0 = zusammenschreiben, 1..4 = Operator
    nums.length=0; ops.length=0;
    let chunk = s[0], m = mask, ok = true, expr = s[0], nops = 0;
    for(let g=0; g<gaps; g++){
      const c = m%5; m = (m/5)|0;
      if(c===0){ chunk += s[g+1]; expr += s[g+1]; }
      else{
        if(NO_LEAD && chunk.length>1 && chunk[0]==="0"){ ok=false; break; }
        nums.push(chunk); ops.push(c-1);
        chunk = s[g+1]; expr += OPCH[c-1] + s[g+1]; nops++;
      }
    }
    if(!ok) continue;
    if(NO_LEAD && chunk.length>1 && chunk[0]==="0") continue;
    nums.push(chunk);
    const r = evalFlat(nums,ops);
    if(!r) continue;
    const k = key(r), prev = out.get(k);
    if(!prev || nops < prev.ops) out.set(k,{r,expr,ops:nops});
  }
  if(bfCache.size>400) bfCache.clear();
  bfCache.set(s,out);
  return out;
}
function evalFlat(nums,ops){
  const val=[], op=[];
  for(let i=0;i<nums.length;i++){
    const v = Number(nums[i]);
    if(v>CAP) return null;
    const cur = {n:v,d:1};
    if(i>0){
      const o = ops[i-1];
      if(o===2||o===3){                     // Punktrechnung sofort
        const left = val.pop();
        const res = apply(left,cur,o);
        if(!res) return null;
        val.push(res); continue;
      }
      op.push(o);
    }
    val.push(cur);
  }
  let acc = val[0];
  for(let i=0;i<op.length;i++){
    acc = apply(acc,val[i+1],op[i]);
    if(!acc) return null;
  }
  return acc;
}

/* ---------------- Phase 2: alle Klammerungen (DP über Teilstrings) --------------- */
let dpS = "", dpMemo = null, dpCount = 0, ABORT = 900000;
function dpSet(i,j){
  const k = i*100+j, hit = dpMemo.get(k); if(hit) return hit;
  const m = new Map();
  if(!(NO_LEAD && j-i>1 && dpS[i]==="0")){
    const v = Number(dpS.slice(i,j));
    if(v<=CAP) m.set(v+"/1",{n:v,d:1,leaf:true});
  }
  for(let t=i+1;t<j;t++){
    const A = dpSet(i,t), B = dpSet(t,j);
    for(const a of A.values()) for(const b of B.values()){
      for(let o=0;o<4;o++){
        const r = apply(a,b,o);
        if(!r) continue;
        const kk = r.n+"/"+r.d;
        if(m.has(kk)) continue;
        m.set(kk,{n:r.n,d:r.d,op:o,t,ka:a.n+"/"+a.d,kb:b.n+"/"+b.d});
      }
    }
  }
  dpCount += m.size;
  if(dpCount>ABORT) throw new Error("zu gross");
  dpMemo.set(k,m);
  return m;
}
function tree(i,j,k){
  const rec = dpSet(i,j).get(k);
  if(rec.leaf) return {txt:dpS.slice(i,j)};
  return {op:rec.op, a:tree(i,rec.t,rec.ka), b:tree(rec.t,j,rec.kb)};
}
function render(node){                        // minimale Klammerung
  if(node.txt) return {s:node.txt, p:9};
  const p = node.op<2 ? 1 : 2;
  const A = render(node.a), B = render(node.b);
  const l = A.p<p ? "("+A.s+")" : A.s;
  const rParen = B.p<p || (B.p===p && (node.op===1||node.op===3));
  const r = rParen ? "("+B.s+")" : B.s;
  return {s: l+OPCH[node.op]+r, p};
}

/* ---------------- Suche ---------------------------------------------------------- */
function solveSplit(s,p){                     // ein Ergebnis für ein festes "="
  const L = bracketFree(s.slice(0,p)), R = bracketFree(s.slice(p));
  let best = null;
  for(const [k,a] of L){
    const b = R.get(k);
    if(b && (!best || a.ops+b.ops < best.cost))
      best = {left:a.expr, right:b.expr, cost:a.ops+b.ops, free:true};
  }
  if(best) return best;
  const A = dpSet(0,p), B = dpSet(p,s.length);
  const small = A.size<=B.size ? A : B, big = small===A ? B : A;
  let cand = null, seen = 0;
  for(const k of small.keys()){
    if(!big.has(k)) continue;
    const l = render(tree(0,p,k)).s, r = render(tree(p,s.length,k)).s;
    const c = (l.match(/\(/g)||[]).length + (r.match(/\(/g)||[]).length;
    if(!cand || c < cand.cost) cand = {left:l, right:r, cost:c, free:false};
    if(++seen>400) break;
  }
  return cand;
}
function solve(s){
  const n = s.length, t0 = performance.now();
  dpS = s; dpMemo = new Map(); dpCount = 0; bfCache.clear();
  const order = [];
  for(let p=1;p<n;p++) order.push(p);
  order.sort((x,y)=> Math.max(x,n-x)-Math.max(y,n-y) || x-y);
  for(const p of order){
    const r = solveSplit(s,p);
    if(r){ r.p = p; r.ms = performance.now()-t0; return r; }
  }
  return {none:true, ms:performance.now()-t0};
}
function solveAll(s){
  const n = s.length, out = [];
  dpS = s; dpMemo = new Map(); dpCount = 0; bfCache.clear();
  for(let p=1;p<n;p++){
    let r = null;
    try{ r = solveSplit(s,p); }catch(e){ r = null; }
    out.push({p, r});
  }
  return out;
}

/* ---------------- Darstellung ---------------------------------------------------- */
function paint(left,right){                   // Ziffern bleiben, Eingesetztes leuchtet
  const s = left+"="+right;
  let html = "", i = 0;
  for(const ch of s){
    let cls = "ins";
    if(ch>="0"&&ch<="9") cls="d";
    else if(ch==="("||ch===")") cls="par";
    else if(ch==="=") cls="eqs";
    const delay = cls==="d" ? "" : ` style="animation-delay:${(i++*28)}ms"`;
    html += `<span class="${cls}"${delay}>${ch}</span>`;
  }
  return html;
}
const $ = id => document.getElementById(id);
const res = $("result");

function readOpts(){
  INT_ONLY = $("intOnly").checked;
  NO_LEAD  = $("noLead").checked;
}
function run(){
  const raw = $("num").value.replace(/\D/g,"");
  if(raw.length<2){ res.innerHTML = `<p class="meta nores">Mindestens zwei Ziffern eingeben.</p>`; return; }
  if(raw.length>11){ res.innerHTML = `<p class="meta nores">Höchstens elf Ziffern.</p>`; return; }
  $("num").value = raw;
  readOpts();
  const btn = $("go"); btn.disabled = true; btn.textContent = "Rechne …";
  res.innerHTML = `<p class="meta">Suche läuft …</p>`;
  setTimeout(()=>{
    try{ show(raw); }
    catch(e){ res.innerHTML = `<p class="meta nores">Suche abgebrochen — die Zahl ist zu lang für den Browser.</p>`; }
    btn.disabled = false; btn.textContent = "Gleichung suchen";
  },20);
}
function show(s){
  if($("allSplits").checked){
    const all = solveAll(s);
    let html = `<ol class="splits">`;
    for(const {p,r} of all){
      html += `<li><span class="pos">= n. ${p}</span>` +
        (r ? `<span>${paint(r.left,r.right)}</span>`
           : `<span class="miss">keine Lösung an dieser Position</span>`) + `</li>`;
    }
    res.innerHTML = html + `</ol>`;
    return;
  }
  const r = solve(s);
  if(r.none){
    res.innerHTML =
      `<p class="eqline nores">keine Lösung</p>
       <p class="meta nores">Alle ${s.length-1} Positionen des = geprüft
       <small>Vollständig durchsucht: jede Klammerung, jede Zerlegung in mehrstellige Blöcke.
       Diese Zahl gehört zu den seltenen Ausnahmen.</small></p>`;
    return;
  }
  res.innerHTML =
    `<p class="eqline anim">${paint(r.left,r.right)}</p>
     <p class="meta">= nach Stelle ${r.p} · ${r.free?"ohne Klammern":"mit Klammern"} · ${r.ms.toFixed(0)} ms</p>`;
}

$("go").addEventListener("click",run);
$("num").addEventListener("keydown",e=>{ if(e.key==="Enter") run(); });
$("rnd").addEventListener("click",()=>{
  const len = Math.max(4, Math.min(9, ($("num").value.replace(/\D/g,"").length||7)));
  let s = String(1+Math.floor(Math.random()*9));
  for(let i=1;i<len;i++) s += Math.floor(Math.random()*10);
  $("num").value = s; run();
});
document.querySelectorAll(".chip").forEach(c=>
  c.addEventListener("click",()=>{ $("num").value = c.dataset.n; run(); }));
["intOnly","noLead","allSplits"].forEach(id=>$(id).addEventListener("change",run));
run();
</script>
</body>
</html>