algorithm

cryptarithms/alphametics 字母算术

https://www.zhihu.com/question/64650060/answer/223222162
https://www.woodpecker.org.cn/diveintopython3/advanced-iterators.html
https://stackoverflow.com/questions/9960908/permutations-in-javascript

function letter2number(_puzzle){
    //1.将字母等式parse成checkfunc
    const firstLetters = [];
    const digitals = new Array(10).fill(undefined).map((none, i) => i);
    let letters = [];
    let puzzle = _puzzle;
    puzzle.toUpperCase().match(/([A-Z]+)/g)
        .forEach(word => puzzle = puzzle.replace(word,
            new Array(word.length).fill(undefined)
                .map((none, i) => (
                    i === 0 && firstLetters.push(word[i]),
                    letters.push(word[i]),
                    `${Math.pow(10, word.length - i - 1)} * ${word[i]}`
                ))
                .join(' + ')
        ));
    letters = [...new Set(letters)];
    if(letters.length > 10) throw new Error('超过10个字母');
    let checkfunc = new Function(letters.join(','),
        `if(${[...new Set(firstLetters)].map(letter => `!${letter}`).join(' || ')}) return false;
        return ${puzzle}`
    );
    //2.枚举全排列
    let used = [];
    let result = (function permute(input){
        let result;
        for (let i = 0; i < input.length; i++) {
            let ch = input.splice(i, 1)[0];
            used.push(ch);
            if (input.length === 0) {
                if(checkfunc(... result = used.slice())) return result;
            }
            if(result = permute(input)) return result;
            input.splice(i, 0, ch);
            used.pop();
        }
    })(digitals);
    //3.输出
    if(result) {
        let digitalPuzzle = _puzzle;
        let letter2digital = {};
        letters.map((letter, i) =>{
            let digital = result[i];
            digitalPuzzle = digitalPuzzle.replace(new RegExp(letter, 'g'), digital);
            letter2digital[letter] = digital;
        })
        return {puzzle: _puzzle, digitalPuzzle, letter2digital}
    }
    throw new Error('无解！');
}
console.time('cal');
console.log(letter2number('HAWAII + IDAHO + IOWA + OHIO == STATES'));
console.timeEnd('cal');