JavaScript to achieve the third-order magic square algorithm puzzle solution _javascript Tips

Puzzles

Third-order magic square. Try to fill in a 3x3 table with these 9 different integers, making the sum of the numbers on each row, each column, and each diagonal 1~9.

Strategy

Exhaustive search. Lists all the integer fill schemes, and then filters them.

JavaScript solution

Copy Code code as follows:

/**
* Created by Cshao on 12/28/14.
*/

function Getpermutation (arr) {
if (arr.length = = 1) {
return [arr];
}

  var permutation = [];
  for (var i=0; i<arr.length; i++) {
    var firstele = arr[i];
    var Arrclone = Arr.slice (0);
    Arrclone.splice (i, 1);
    var childpermutation = getpermutation (Arrclone);
    for (var j=0; j<childpermutation.length; J + +) {
      Childpermutation[j].unshift (Firstele);
   }
    permutation = Permutation.concat (childpermutation);
 }
  return permutation;
}

Function Validatecandidate (candidate) {
  var sum = candidate[0] + candidate[1] + candidate[2];
  for (var i=0; i<3; i++) {
    if (!) ( Sumofline (candidate,i) ==sum && sumofcolumn (candidate,i) ==sum)) {
      return False
   }
 }
  if (sumofdiagonal (candidate,true) ==sum && sumofdiagonal (candidate,false) ==sum) {
     return true;
 }
  return false;
}
Function Sumofline (candidate, line) {
  return candidate[line*3] + candidate[line*3+1] + Candidate[lin E*3+2];
}
Function Sumofcolumn (candidate, col) {
  return Candidate[col] + candidate[col+3] + candidate[col+6];< br>}
Function sumofdiagonal (candidate, Isforwardslash) {
  return Isforwardslash? candidate[2]+candidate[ 4]+CANDIDATE[6]: candidate[0]+candidate[4]+candidate[8];
}

var permutation = Getpermutation ([1,2,3,4,5,6,7,8,9]);
var candidate;
for (var i=0; i<permutation.length; i++) {
candidate = Permutation[i];
if (Validatecandidate (candidate)) {
Break
} else {
candidate = null;
}
}
if (candidate) {
Console.log (candidate);
} else {
Console.log (' No valid result found ');
}

Results

Copy Code code as follows:

[2, 7, 6, 9, 5, 1, 4, 3, 8]

Depicted as a magic square is:

Copy Code code as follows:

2 7 6
9 5 1
4 3 8

Analysis

Using this strategy, we can theoretically obtain the solution of any n-order magic square, but in fact we can only get the 3-order magic square, because when n>3, it will be extremely time-consuming to get all the fill schemes.