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50 digits of π in HQ0-9+-INCOMPUTABLE?

Background

HQ0-9+-INCOMPUTABLE?! is a half-joke programming language introduced in Internet Problem Solving Contest 2011, Problem H.

HQ9+ is an esoteric programming language specialized for certain tasks. For example, printing "Hello, world!" or writing a quine (a program that prints itself) couldn’t be any simpler. Unfortunately, HQ9+ doesn’t do very well in most other situations. This is why we have created our own variant of the language, HQ0-9+-INCOMPUTABLE?!.

A HQ0-9+-INCOMPUTABLE?! program is a sequence of commands, written on one line without any whitespace (except for the trailing newline). The program can store data in two memory areas: the buffer, a string of characters, and the accumulator, an integer variable. Initially, the buffer is empty and the accumulator is set to 0. The value of the buffer after executing all the commands becomes the program’s output.

HQ0-9+-INCOMPUTABLE?! supports the following commands:

command	description
`h`, `H`	appends `helloworld` to the buffer
`q`, `Q`	appends the program source code to the buffer (not including the trailing newline)
`0-9`	replaces the buffer with `n` copies of its old value – for example, `2` doubles the buffer (`aab` would become `aabaab`, etc.)
`+`	increments the accumulator
`-`	decrements the accumulator
`i`, `I`	increments the ASCII value of every character in the buffer
`n`, `N`	applies ROT13 to the letters and numbers in the buffer (for letters ROT13 preserves case; for digits we define `ROT13(d) = (d + 13) mod 10`)
`c`, `C`	swaps the case of every letter in the buffer; doesn’t change other characters
`o`, `O`	removes all characters from the buffer whose index, counted from the end, is a prime or a power of two (or both); the last character has index 1 (which is a power of 2)
`m`, `M`	sets the accumulator to the current buffer length
`p`, `P`	removes all characters from the buffer whose index is a prime or a power of two (or both); the first character has index 1 (which is a power of 2)
`u`, `U`	converts the buffer to uppercase
`t`, `T`	sorts the characters in the buffer by their ASCII values
`a`, `A`	replaces every character in the buffer with its ASCII value in decimal (1–3 digits)
`b`, `B`	replaces every character in the buffer with its ASCII value in binary (exactly eight `0`/`1` characters)
`l`, `L`	converts the buffer to lowercase
`e`, `E`	translates every character in the buffer to l33t using the following table: `ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 0123456789` `48(03=6#\|JXLM~09Q257UVW%Y2 a6<d3f9hijk1m^0p9r57uvw*y2 O!ZEA$G/B9`
`?`	removes 47 characters from the end of the buffer (or everything if it is too short)
`!`	removes 47 characters from the beginning of the buffer (or everything if it is too short)

To prevent code injection vulnerabilities, during the execution of your program the buffer must never contain non-alphanumeric characters, i.e. characters other than A-Z, a-z, and 0-9. Should this happen, the program fails with a runtime error, and your submission will be rejected.

The original problem statement contains limits about the code length and buffer length, but I removed them in this challenge. This is also reflected in the interpreter link below. (If you need even larger buffer, you can change the MAX_BUFFER constant near the top. I doubt using a longer buffer will give reasonably short code though.)

Task

Output the string (which is 50 digits of Pi without leading 3.)

14159265358979323846264338327950288419716939937510

in HQ0-9+-INCOMPUTABLE?!.

An answer is scored as follows:

Each occurrence of Q/q adds 1,000,000 points.
Each occurrence of E/e adds 10,000 points.
Each occurrence of any other valid command adds 1 point.

Lowest score wins.

Bonus: ~~(削除) +500 bounty to the first answer that achieves the score of 9,999 points or lower. I have confirmed that this is possible. (削除ここまで)~~ claimed by dingledooper

C++ interpreter

_{If you're wondering about the role of the accumulator, you're right: it still does nothing useful.}

Answer*

# HQ0-9+-INCOMPUTABLE?!, <s>7884</s> <s>5134</s> <s>4122</s> 806 points

*Thanks to @JonathanAllan for suggesting using `n` in the pool code*

*Thanks to @Neil for suggesting being looser with the pool and using strings instead of char code arrays*

```
hahaha!!4?????3?????????h?2!!????2!!!h?2!!!2!!!!!hh2????2???2hhhhh?hhh2!!!!!!!!h?2!!?????!6!!!!!!!!!!!!hhh?hhhhh?hhhh?2!!?????!!2hhhhh?3!!!!!!hhhh?2??2!hh2????2???h?2!???!2hhhh?2!!!h3??????hh?2!??!2!h?3!!!2?2!hhhh?hhh2!!!h?2!!h2??h2??h?2?!6!!!!!!!h?2!!2!?4!!!!h?2?h?2??2?!2!3!!!!!3!!!!h?5????2?h?2?2hhhhh?2!!!h2!!2??2?2!hhh?hhh2!!!hh?hhhh2????2??!2h2!!!hhhh?hhhh?2??!2!3!!!2!!3???2??2?6????????2!???!2!hhh2!!!h?3!!!!!3????h3??????2?!2h?2!!!2!!!!hh2!!!hh?2!??2hh3!!!!!!!!hh?h2??2???h?2??!2hhhh?2!??2!hh2!!!!h?hhhh?2??!2!2!!hhhh?2?4???h2???2???2!??2hh?2!!!!2!!!!!hhhh2?????2!???!2!4!!!!!2!!!3???h?2?2!!hh?2!!2??2?!2h?hhh2!!!!3??????h?2!??2hhhh?2!!!hh2!!!!2???h2???2??!2!h2!hh2!!!!2??2???2?4!!!!h2!!!h2???2????2??!2!hhhh?hhhh?2??!6!!!!!2!!h2??2?2!hh2!!!!h?2??3????2?2!2!!!!!2????2????h?2!???!3!!hhh2!!!h3?????
```

[Verify it online!](https://tio.run/##vVdtU9tGEP7uX3GCEksxdvQCpmCDx1BI6YSSl5KmIa5HSGdLxpY0klw3CfSv071XncDGZsrUjLHudp/dZ/f27lZektSHnnd3tx5G3njqY9T2stwP44OKMuPlXxOszmR5GkZDdcYdD@M0zINJSQ30sAtT0wzUUeROcJa4HkbgolWprPt4EEYYnXU/9Y/OfzpGCFkm@5RkhxcnJ8fvpcysVJh/5MU@bonB1XQwwGmrchXHY3SNcXJZYGtbOz3F4cANx3qj0TCQngA2H@j9/sduv/v@9Yd@39hE@O8w1y3DqFRAiNI4txydPHkG@l5BKBzoHjrYR1W3il68QB5qw/O3qoFSnE/TiM7XkK57dXgy4NFyjA272VKhXQX6WYF2JbS7CGoq0F0FakqoKaGWSaBcw2tVbllI2cxNPDfDT4nKQ3UeGVBbJRYKoPEAbD6NIJ6pFCQQrDq2NGrZTdSBxz1U7VQlOI8tx9lR4V4cZTAI3PQl8sNhmKN9tHaufT7u/vD61eHuWuuezjie4ZTouM227wx2g3B0bU3@NJPddHtn@tfs5Vf7AWaaJAyz9aNuOvvN9ZtfPr05@8fcfWdv71x8/H3jD4ZZtlqU3yVdq15rhexTrpe0onqrJJ/yvKRl1Jub@4kbRjrLG90sZg@islpiaMnhIE5pkkOYsFvw00bqxiJTtZoBipSURtFhj00U6BGgw1rYgocH@BGqgVAgOIHRXALWfALoJXBjBrh/0IXSJ4ki9UHMzIJwjGF7gGSIc7KaumEgbR8dn5/QFMJh0sjCbxiy0pZnEpwczC4VJ9Ms6F@53rXuGXIVmAmDnSprb9N4mLoTKM8YFi0afonWjMK96uQAmcQvnbtUBHWSe1jNL1EV3dygheK0aijUUkzFJUXJseRVhPY4YyXxiUezSX7baprIDCw9rSGe6IkPqnlMq48Flng9SoMpTKPAjfwxJmoDd5xhJspmIayIDnBhDaKC8wlVf67uybpgJ3zDBeORr68FeAy7Ik7H/hr3QJXgxrmm9Asj7xYaIRSXgH9VwGopmqwUuT2REbkXVG@sHtk9ImeWuO0qbr8rFtltxy5WlGUtRfRkdmAtQ@02XBoAM@YxExGAxSxrgFddEd4@GsDhowGgCM/Ejf2fIlAPmB1ylhxQ6KheL@uhwqOyjYvlQLATrXZ7BGdCB1WtKrlt4B6dm4o53B/Pxemz1FCt9njJXDxXpYoNvGqtvnk@x/SeW9nx0XM5lg3Rqp7PpWc2fvv/VHs4QDo9ZPeJS6hUdt3V4E7YY88lC/XiIn5sFyzZ@U8u987D85ZfTyV2ZKtu7UAQZc4wtYfMJfnXHrrAKVlAcxPNd0LNlkRLXBw/X1XTTnXV0vpN8ZvFaS6SdoWHpGWT8ZH7a1kMtXtlWr83PlPTWMLDq5I7HeeFWL2683SKHzgu6gJajkKbtFZQsUovDCPRDYutsmibzMk7wEnXzDKulDO/0dlIpmVxES9oRR5GIPqki@g6imfQQ8eTCUjQhof07oej01O04RvQNG2y9xnSxGwSlqLtGdyveqV9FbYPGU2iAW@fHsY@8NrwqVVFm1l8UjGSnjzM3HE0nSgVWJQq838EfRA0aCPs5WEMIQbYu6Yi7ItNQ16DcnhpyBYFXljfROVav61UnsQ6mbL@vGxFzJLG2FDeaUz6TnN3F7jkT9O2OuTjdMQn6NiaRh7gR6MDjXzhObDpNPkG5NOBLxMJTWpAa2rKh@vx/4WSxm04Ui0gpm3VDVEnuraAagHnGTARMGMWbAosKFFtYoh@wZgkRSWA3eKDDnNLTDEqDhNsMxJEyplSuwRM5m1N9caCE7yBry1CEnFx8zDvMCW70xQZ50FqkjsnQgPlAROCymJIvwQL/Jwi3TRknj0ldzy1LDiFlS1zTwqBxmBzTjYPWq4/D1ESpjmkUof7szkpzRaURY04RXXx@mEJZVJb8U0yYSsCNs3Wi60B5yiUS3luCk6BXCdbLDWrcjLJIpKFJivN0eQqMML/Ag)

This uses a much different approach from dingledooper's answer – notably, it only uses `h1-9a?!`. The initial `hahaha` fills the buffer with a pool containing all digits, and then it uses careful duplications and slices to construct the string in a contiguous stretch in the buffer, at which point it chops off the surrounding character pool.

## [Generating Program](https://replit.com/@tjjfvi/hq0-9-INCOMPUTABLE#index.ts)

```lang-typescript
import { BinaryHeap } from "https://deno.land/std@0.164.0/collections/binary_heap.ts";

class State {
 constructor(public answer = "", public buffer = "") {}

 clone() {
 return new State(this.answer, this.buffer.slice());
 }

 set(state: State) {
 this.answer = state.answer;
 this.buffer = state.buffer;
 }

 i() {
 this.answer += "i";
 this.buffer = fromCharCodes(toCharCodes(this.buffer).map((x) => x + 1));
 }

 a() {
 this.answer += "a";
 this.buffer = toCharCodes(this.buffer).join("");
 }

 h() {
 this.answer += "h";
 this.buffer += "helloworld";
 }

 n() {
 this.answer += "n";
 this.buffer = fromCharCodes(
 toCharCodes(this.buffer).map((x) =>
 x >= "0".charCodeAt(0) && x <= "9".charCodeAt(0)
 ? ((x - "0".charCodeAt(0) + 13) % 10) + "0".charCodeAt(0)
 : x >= "a".charCodeAt(0) && x <= "z".charCodeAt(0)
 ? ((x - "a".charCodeAt(0) + 13) % 26) + "a".charCodeAt(0)
 : x >= "A".charCodeAt(0) && x <= "Z".charCodeAt(0)
 ? ((x - "A".charCodeAt(0) + 13) % 26) + "A".charCodeAt(0)
 : -1
 ),
 );
 }

 cutStart47(n = 47): number {
 while (n >= 47) {
 n -= 47;
 this.answer += "!";
 this.buffer = this.buffer.slice(47);
 }
 return n;
 }

 cutEnd47(n = 47): number {
 while (n >= 47) {
 n -= 47;
 this.answer += "?";
 this.buffer = this.buffer.slice(0, -47);
 }
 return n;
 }

 copy(n: 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9) {
 this.answer += n;
 this.buffer = this.buffer.repeat(n);
 }

 cut(start: number, end: number) {
 start = this.cutStart47(start);
 end = this.cutEnd47(end);
 [start, end] = this.search(
 [start, end],
 (_, [start]) => start === 0,
 function* (state, [start, end]) {
 if (state.buffer.length % 47) {
 for (const n of [2, 3, 4, 5, 6, 7, 8, 9] as const) {
 const state2: State = state.clone();
 let start2 = start + state2.buffer.length * (n - 1);
 state2.copy(n);
 start2 = state2.cutStart47(start2);
 yield [state2, [start2, end]];
 }
 }
 state.h();
 end += 10;
 end = state.cutEnd47(end);
 yield [state, [start, end]];
 },
 )!;
 // start = this.cutStart47(start);
 // end = this.cutEnd47(end);
 this.search(
 end,
 (_, end) => end === 0,
 function* (state, end) {
 if (state.buffer.length % 47) {
 for (const n of [2, 3, 4, 5, 6, 7, 8, 9] as const) {
 const state2 = state.clone();
 let end2 = end + state2.buffer.length * (n - 1);
 state2.copy(n);
 end2 = state2.cutEnd47(end2);
 yield [state2, end2];
 }
 }
 state.h();
 end += 10;
 end = state.cutEnd47(end);
 yield [state, end];
 },
 );
 }

 search<T>(
 init: T,
 isDone: (state: State, data: T) => boolean,
 opts: (state: State, data: T) => Iterable<[State, T]>,
 ) {
 const pq = new BinaryHeap<[State, T]>(([a], [b]) =>
 a.answer.length - b.answer.length
 );
 pq.push([this.clone(), init]);
 let cur;
 while ((cur = pq.pop())) {
 if (isDone(...cur)) {
 this.set(cur[0]);
 return cur[1];
 }
 pq.push(...opts(...cur));
 }
 }
}

function toCharCodes(x: string) {
 return [...x].map((x) => x.charCodeAt(0));
}

function fromCharCodes(x: number[]) {
 return x.map((x) => String.fromCharCode(x)).join("");
}

let state = new State();

state.h();
state.a();
state.h();
state.a();
state.h();
state.a();

const goal = "14159265358979323846264338327950288419716939937510";

let nextEnd = 0;
for (let i = 0; i < goal.length;) {
 if (state.buffer.length > i + nextEnd + 47) {
 const state2 = state.clone();
 state2.cutStart47();
 if (
 [..."1234567890"].every((x) =>
 state2.buffer.slice(0, -nextEnd).includes(x)
 )
 ) {
 state = state2;
 continue;
 }
 }
 console.log(state.buffer, i);
 let bestCnt = 0;
 for (let j = 0; j < state.buffer.length; j++) {
 let cnt = 0;
 while (goal[i + cnt] === state.buffer[j + cnt]) cnt++;
 bestCnt = Math.max(cnt, bestCnt);
 }
 if (bestCnt === 0) throw 0;
 let bestLen = Infinity;
 let best: [State, [number, number]] | undefined;
 for (let j = 0; j < state.buffer.length; j++) {
 let cnt = 0;
 while (goal[i + cnt] === state.buffer[j + cnt]) cnt++;
 if (cnt !== bestCnt) continue;
 const inner: State = state.clone();
 const len = inner.buffer.length - nextEnd;
 if (i === 0) {
 const end = inner.cutEnd47(len + nextEnd - j - cnt);
 best = [inner, [i + cnt, end]];
 continue;
 }
 inner.copy(2);
 inner.cut(j, nextEnd);
 inner.copy(2);
 inner.cutStart47(len + nextEnd - j);
 const end = inner.cutEnd47(len * 2 + nextEnd - j - cnt);
 if (i + cnt === goal.length) {
 inner.cut(inner.buffer.length - end - goal.length, end);
 }
 if (inner.answer.length < bestLen) {
 bestLen = inner.answer.length;
 best = [inner, [i + cnt, end]];
 }
 }
 [state, [i, nextEnd]] = best!;
}

state.answer = state.answer.replace(/22/g, "4").replace(/23|32/g, "6");

console.log(state.answer);
console.log(state.answer.length);
console.log(state.buffer);
console.log(goal);
```

If this is an answer to a challenge…

…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one. Explanations of your answer make it more interesting to read and are very much encouraged.
…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).

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Edit Summary*

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\$\begingroup\$ @JonathanAllan Testing it on Bubbler's interpreter, it doesn't seem to work – I think the issue is with c%16+13%10+48, as precedence makes it equivalent to (c%16)+51, but I'm not sure what exactly the precedence you intended was \$\endgroup\$

tjjfvi
– tjjfvi

2022年11月15日 00:11:39 +00:00
Commented Nov 15, 2022 at 0:11
\$\begingroup\$ I don't think n in the generated code would help, as it operates on the whole buffer, and the generated code relies on preserving what it's already build. \$\endgroup\$

tjjfvi
– tjjfvi

2022年11月15日 00:15:18 +00:00
Commented Nov 15, 2022 at 0:15
\$\begingroup\$ Ah, in that case it is only 5129, seems you've beaten that now anyway :) \$\endgroup\$

Jonathan Allan
– Jonathan Allan

2022年11月15日 01:23:07 +00:00
Commented Nov 15, 2022 at 1:23
\$\begingroup\$ Score 3063 if you replace both uses of len - ind with len - ind - (len - ind) % 47. (Also, using arrays of character codes is very fiddly; generator code is much simpler if you use strings instead.) \$\endgroup\$

Neil
– Neil

2022年11月15日 10:15:17 +00:00
Commented Nov 15, 2022 at 10:15
\$\begingroup\$ Ah, so you can in fact avoid eagerly trimming the end as well. I guess that makes your explanation slightly out of date. \$\endgroup\$

Neil
– Neil

2022年11月16日 11:34:02 +00:00
Commented Nov 16, 2022 at 11:34

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