What is the algorithm for distributing the paragraphs?

Question

I am reading a specific portion of the Bible per week based on programming published on the website Jw.org.

I made a javascript script that takes the paragraphs and verses of each chapter and shows the sum of the verses.

So I have this entry: (The passages are divided into paragraphs, and the number in parentheses is the number of verses)

1:1     (1)
1:2-6   (5)
1:7-10  (4)
1:11-12 (2)
1:13-17 (5)
2:1-10  (10)
2:11-16 (6)
2:17-18 (2)
3:1-7   (7)
3:8-9   (2)
3:10-13 (4)
3:14    (1)
3:15-17 (3)
4:1     (1)
4:2-5   (4)
4:6     (1)
4:7     (1)
4:8     (1)
4:9-10  (2)
4:11-18 (8)
4:19-22 (4)
5:1-3   (3)
5:4-10  (7)
5:11-14 (4)

As I will read in 7 days I need to not only distribute the 74 verses for 7 days, but find the best stop between paragraphs.

How to decide the best stop between paragraphs? We should take the average of verses a day. For example 14.6. So each day we will try to get as close to 14.6. If in one day the nearest is 13, in the next we will try to get as close to the 15.6. And so consecutively. However... doing this on paper you will realize that sometimes it is necessary to decide between reading less one day and more in another forward to have a more balanced average.

I’m currently doing this manually because I couldn’t devise an algorithm to do this.

But I’ll use python to process the input and I’m thinking about doing a brute force algorithm that will take all the possibilities of distributing the number of paragraphs in 7 sections, for example, (3, 2, 3, 5, 5, 2, 3 ) which is what I found in my hand.

After I had these numbers I could pass a function that would see what the best alternative was. But I don’t know what algorithm to use to do this. Maybe the algorithm of median? To average it is not because it will always give the same number.

I found this site: Purple Math that talks about "Mean, Median, Mode, and Range" (in English). I’m thinking about using all but the average to find the best value.

Does anyone have any tips?

Answer 1

Just accumulate the values and, when you exceed the target (the average times the number of days travelled), check which alternative has the smallest prediction error (i.e. the difference between the found value and the expected value) and follow with it:

document.querySelector("#calcular").onclick = function() {

var entrada = document.querySelector("#entrada").value;
var dias = parseInt(document.querySelector("#dias").value, 10);

/* Interpreta a entrada */
var regex = /^.*\((\d+)\)\n/gm;
var match;

var acc = 0;
var versiculos = [];

while ( match = regex.exec(entrada) ) {
  var no = parseInt(match[1], 10);
  acc += no;
  versiculos.push({ texto:match[0], no:no });
}

/* Calcula o valor esperado (a média) e distribui */
var media = acc / dias;
var erro = 0; // Soma dos quadrados dos erros

acc = 0;
var valorEsperado = 0;
var classe = 0;
for ( var i = 0 ; i < versiculos.length ; ) {
  valorEsperado += media;
  
  // Verifica se acrescentar o próximo versículo terá erro maior que não acrescentar
  while ( i < versiculos.length && valorEsperado - acc > acc + versiculos[i].no - valorEsperado ) {
    versiculos[i].classe = classe ? "a" : "b";
    acc += versiculos[i].no;
    i++;
  }
  
  // Fecha a sequência do dia e calcula o QE
  erro += Math.pow(acc - valorEsperado, 2);
  classe = 1-classe;
}

/* Saída */
document.querySelector("#saida").innerHTML = 
  versiculos.map(function(v) {
      return '<pre class="' + v.classe + '">' + v.texto + "</pre>";
  }).join("") + 
  "<p>Média: " + media + "</p>" +
  "<p>SQE: " + erro + "</p>";
  
};

.a { background-color: white; }
.b { background-color: lightgray; }

#saida, pre { padding: 0; margin: 0; }

<textarea id="entrada">
1:1     (1)
1:2-6   (5)
1:7-10  (4)
1:11-12 (2)
2:1-10  (10)
2:11-16 (6)
3:1-7   (7)
3:8-9   (2)
3:10-13 (4)
3:14    (1)
4:1     (1)
4:2-5   (4)
4:6     (1)
4:7     (1)
4:8     (1)
4:9-10  (2)
4:11    (1)
4:11-18 (8)
5:1-3   (3)
5:4-10  (7)
5:11-14 (4)
-----------------
1:1-5:14
(74 versículos, 21 parágrafos)
</textarea>
<br>
Dias: <input id="dias" value="7">
<button id="calcular">Calcular</button>
<br/>
<div id="saida"></div>

The result was (3, 2, 2, 4, 6, 2, 2), with an EQS (sum of error squares) equal to 9.42:

Grupos: (3,    2,    2,    4,    6,    2,    2)
Totais: (10,   12,   13,   8,    10,    11,   11)
Acc:    (10,   22,   35,   43,   53,    64,   75)
Pred:   (10.7, 21.4, 32.1, 42.8, 53.5, 64.2, 75)
QE:     (0.51, 0.32, 8.16, 0.02, 0.32, 0.08, 0)
SQE: 9.42