//Problem 1
function Counter(c=0){
	var count = c ;
	this.inc = function() { count++ ;}
	this.getCount = function(){ return count; }
}

//to make sure that we can call print on an instance of Counter objects we need
// to implement a specific code for the 'toString' method that it inherents from the
// ancestor object 'Object'
Counter.prototype.toString = function(){ return this.getCount(); }

//Problem 2
/* Question 2.1
Matrix.prototype.toString() {
        var line="" ;
        for(var i =0 ; i < this.data.length ; i++) {
                line += this.data[i] + " " ;
                if( (i+1) % this.dim[1] == 0 )  line += "<br>" ; //new line at end of row
        }
        return line ;
}
*/


// The following code contains the answers to questions 2.2, 2.3 and 2.4

//Matrix Library 

/*The matrix constructor

Input: 
	dim :: array of 2 integers
	data:: array of all matrix elements from left->right and top->bottom

"Output": (not really a return value, mind you!)
	Object with properties:
		dim :: an array of 2 integers
		data:: a 1-dimensional array w/ actual elements sorted left->right,top->bottom
*/
function Matrix(dim=[0,0], data=[], name="noname"){
	this.dim = dim ;		
	this.data = data ;
        this.name = name;
	//consistency test	v--- Question 2.3 
        if( this.dim[0]*this.dim[1] != this.data.length){
		var msg="ERROR:"+
		        " matrix "+this.name+" :"+
                        " Incompatible data length ("+this.data.length+")"+
                        " w/ matrix dimensions ("+this.dim[0]+"x"+this.dim[1]+") ";
		console.log(msg);
		alert(msg); //only in browser
	}
}

// Question 2.2
Matrix.prototype.toString = function(){
        var nl = "<br>";
        var om = "[ ";
        var cm = " ]";
	var line=this.name+om ;
        for(var i=0 ; i<this.name.length ; i++){om = "&nbsp;"+om}

	for(var i =0 ; i < this.data.length ; i++) {
		line += this.data[i] + " " ;
		if( (i+1) % this.dim[1] == 0 ) {
			if( (i+1) == this.data.length ) line += cm+nl ; //new after at end of row
			else line += cm+nl+om ;
                }
	}
	return line ;
}

// Question 2.4
Matrix.prototype.t = function() {
	var tdata = [];
	for(var j = 0 ; j < this.dim[1] ; j++){ //these 2 loops very similar to the mult method
		for(var i=0 ; i < this.dim[0]; i++){
			tdata.push(this.data[j+this.dim[1]*i] );
		}
	}
	return new Matrix([this.dim[1],this.dim[0]], tdata,this.name+"†") ;
}

// We were not ask to do so, but for consistency we would need to modify 'mult' in order
// to deal properly with the name of the matrix, as was done in the vector case.
Matrix.prototype.mult = function(B){
	if( this.dim[1] != B.dim[0] ) {
		var msg = "<p>ERROR: Can't multiply. #columns doesn't match #rows! </p>" ;
		document.body.innerHTML +=  msg ;
		console.log(msg);
		return -1;
	}

	var dim = [this.dim[0] , B.dim[1] ] ;
	var data = [] ;

	//
	for(var i = 0 ; i < this.dim[0] ; i++ ) { //loop over rows of caller matrix ('A', aka. the 'this' matrix)
		for(var j = 0 ; j < B.dim[1] ; j++) { // loop over columns of callee matrix ('B')
			var sum=0;
			for(var k = 0 ; k < this.dim[1] ; k++ ) { //multiply row i of 'this' with column j of 'B'
				sum += this.data[i*this.dim[1] + k] * B.data[k*B.dim[1] + j] ;
			}
			data.push( sum ) ;
		}
	}
        var nname = "("+this.name+")("+B.name+")" 
	return new Matrix( dim, data , nname) ; //dealing with the new name
}