Generate a random math Equation using Random numbers and operators in Javascript

Question

I want to create a program that should printout simplest form of mathematical expression like ( 21 + 13 ) * 56 using Random no. 1 to 100, The program must take a level parameter, the level determines the length of the generated equation, for example :

The game must produce equations with addition + and multiplication * operators like ( 21 + 13 ) * 56.(using Brackets)

----level 2

75 - 54 = 21
62 + 15 = 77
88 / 22 = 4
93 + 22 = 115
90 * 11 = 990

--level 3

( 21 + 13 ) * 56 = 1904
82 - 19 + 16 = 79
51 * ( 68 - 2 ) = 3366

Input would be form : for example

level 3

Output should be:

( 21 + 13 ) * 56 // Simple expression using Random no.s

So far i can create equations without brackets but i need help that would give me reliable solution

This is what i have done so far:

var input = 'level 3'
input = input.split(' ')
var n = Number(input[1])
var x = ['/','*','-','+']
function randomNumberRange(min, max) {
return Math.floor(Math.random() * (max - min) + min);
}
var a = ''    
for(var i=0;i<n;i++){
    if(i !== n-1){
        var n1 = randomNumberRange(1, 100)
        var m = randomNumberRange(0, x.length);
        var str = x[m];
        a += n1
        a +=' '+str+' '
    }else{
        a += n1
    }  
}

Answer 1

I picked up the idea of @plamut to create a binary tree, where each node represents an operator with a left and a right side.

For instance, the equation 2 * (3 + 4) can be seen as

  *
 / \
2   +
   / \
  3   4

You can represent this quite straight forward using objects as follows:

var TreeNode = function(left, right, operator) {
    this.left = left;
    this.right = right;
    this.operator = operator;

    this.toString = function() {
        return '(' + left + ' ' + operator + ' ' + right + ')';
    }
}

Then you can create a recursive function to build such trees, where one sub-tree would have half of the desired total number of nodes (= length of equation):

function buildTree(numNodes) {
    if (numNodes === 1)
        return randomNumberRange(1, 100);

    var numLeft = Math.floor(numNodes / 2);
    var leftSubTree = buildTree(numLeft);
    var numRight = Math.ceil(numNodes / 2);
    var rightSubTree = buildTree(numRight);

    var m = randomNumberRange(0, x.length);
    var str = x[m];
    return new TreeNode(leftSubTree, rightSubTree, str);
}

Here's a JSFiddle with a working example.

Maybe you still want to care about special cases, like avoiding brackets at top level, but that shouldn't be too hard from here.