Finding an intermediate value between two variables

Question

I’m developing an algorithm for checkers and I came across a problem, when one piece eats the other, where I need to know the position of the piece that was eaten. According to the image and the code below, knowing the value of a which is the current position of the piece and c the future position, I need to find out the value of b, which is the position of the food piece, taking into account the case pattern a - c = 7, then b is the same or a - 3 or a - 4 or if a - c = 9, then b is the same or a - 4 or a - 5. How can I discover the value of b?

if (a - c == 7){
   if (a - 3 == b){

   } else
   if (a - 4 == b){

   }
} else
if (a - c == 9){
   if (a - 4 == b){

   } else
   if (a - 5 == b){

   }
}

Answer 1

You can use the function calculaB down below:

• This function receives the two numbers a and cand then choose the two values that are in the middle that can be b.

• These values are obtained by averaging a and c, where one of them is the mean rounded down and the other is the mean rounded up.

• If both values match, only one is returned. If they do not match both are returned, the smallest being first.

function calculaB(a, c) {
    var media = (c + a) / 2;
    var b1 = Math.floor(media);
    var b2 = Math.ceil(media);
    return b1 === b2 ? [b1] : [b1, b2];
}

$("#calcular").click(function() {
    var a = parseInt($("#a").val());
    var c = parseInt($("#c").val());
    var bs = calculaB(a, c);
    $("#b").val(bs);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div><label for="a">a:</label><input type="text" id="a" value="" /></div>
<div><label for="c">c:</label><input type="text" id="c" value="" /></div>
<div><button id="calcular">Calcular</button></div>
<div><label for="b">b:</label><input type="text" id="b" value="" readonly="true" /></div>

Click the blue "Run" button to test the above code.

Answer 2

The logic I understand is this::

When a - c = 7, then a and c could have the values:

a   c       b
----------------
9   2 --> a - 3 |
10  3 --> a - 3 | --> qualquer "a" dividido por 4 resulta em par (descartando as decimais)
11  4 --> a - 3 |

13  6 --> a - 4 |
14  7 --> a - 4 | --> qualquer "a" dividido por 4 resulta em ímpar (descartando as decimais)
15  8 --> a - 4 |
...
31  24 --> a - 4

For each group of 3 values of a, the value of b can be a - 3 or a - 4. Note also if I divide each value of a for 4, I will have a logical sequence of each group with result unique or par alternately 3 in 3 numbers.

Soon, b would be:

var b = ~~(a/4)%2 == 0 ? a - 3 : a - 4;

In the case of a - c = 9, the same logic applies to the value of c instead of a of the previous case:

a   c       b
----------------
10  1 --> a - 4 |
11  2 --> a - 4 | --> qualquer "c" dividido por 4 resulta em par (descartando as decimais)
12  3 --> a - 4 |

14  5 --> a - 5 |
15  6 --> a - 5 | --> qualquer "c" dividido por 4 resulta em ímpar (descartando as decimais)
16  7 --> a - 5 |
...
32 23 --> a - 5

Soon:

var b = ~~(c/4)%2 == 0 ? a - 4 : a - 5;

Example:

var a = 13,
    c = 6;

if (a - c == 7){
   
   var b = ~~(a/4)%2 == 0 ? a - 3 : a - 4;
   
   if (a - 3 == b){
      console.log("b igual a-3");
   } else
   if (a - 4 == b){
      console.log("b igual a-4");
   }
} else
if (a - c == 9){

   var b = ~~(c/4)%2 == 0 ? a - 4 : a - 5;

   if (a - 4 == b){
      console.log("b igual a-4");
   } else
   if (a - 5 == b){
      console.log("b igual a-5");
   }
}

console.log("b = "+b);

Answer 3

First, let’s imagine that the board had all 64 squares numbered instead of just the dark 32. For this we need a function that converts its numbering format to a numbering format with 64 squares. Here is this function:

function recalcula32to64(casa) {
    return casa * 2 - (Math.floor((casa - 1) / 4) % 2 === 0 ? 0 : 1);
}

And also a function that does the opposite:

function recalcula64to32(casa) {
    return casa % 2 === 0 ? casa / 2 : (casa + 1) / 2;
}

And then just calculate which is the middle house:

function calculaB(a, c) {
    return recalcula64to32((recalcula32to64(a) + recalcula32to64(c)) / 2);
}

function recalcula32to64(casa) {
    return casa * 2 - (Math.floor((casa - 1) / 4) % 2 === 0 ? 0 : 1);
}

function recalcula64to32(casa) {
    return casa % 2 === 0 ? casa / 2 : (casa + 1) / 2;
}

function calculaB(a, c) {
    return recalcula64to32((recalcula32to64(a) + recalcula32to64(c)) / 2);
}

$("#calcular").click(function() {
    var a = parseInt($("#a").val());
    var c = parseInt($("#c").val());
    var bs = calculaB(a, c);
    $("#b").val(bs);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div><label for="a">a:</label><input type="text" id="a" value="" /></div>
<div><label for="c">c:</label><input type="text" id="c" value="" /></div>
<div><button id="calcular">Calcular</button></div>
<div><label for="b">b:</label><input type="text" id="b" value="" readonly="true" /></div>

Click the blue "Run" button to test the above code.