/**
 * @author: ZEGHBA Yahia
 *
 */

let sum = 4; // stairs number
let cases = [1,2]; // step cases
let p = []; // probabilities

function a(sum,solution,depth,p) {
    if(sum == 0){
        console.log(solution); // solution
        // clone array
        p.push(solution.slice(0));
        return p;
    }

    if(sum > 0){
        for (let i = 0; i < cases.length; i++) {
            if((sum-cases[i])>=0){
                console.log("case: "+i);
                console.log("depth: "+depth); // depth tree
                // remove elements (from :depth to:length of array) from: array(solution)
                solution.splice(depth);
                solution.push(cases[i]);
                a(sum-cases[i],solution,depth+1,p);
            }else{
                console.log("coucou");
            }
        }
    }

    return p;
}


console.log(a(sum,[],0,p));