JS: DP rod cutting . A recurrence doesn't go further than i = 1 in "for cycle"

Question

I have met some difficulties with the understanding how works cycle "for" and recurrence together. I tried to implement the rod cutting problem in JavaScript. (the original code was written in Java).

Problem: The problem is that the recurrence goes down in each cycle i = 1 to bottom until it reaches the lowest value but then it doesn't execute next cycle i=2. What is wrong in this code?

Code:

var p = [2,5,8,9,10,17,17,20,24,30];
function cut_rod(p,n){
        console.log("           level=",n); 
        if(n == 0){
            return 0;
        } 
        q = Number.MIN_VALUE;

        for(i = 1; i <= n; i++){
            console.log("           i=",i);
            q = Math.max(q, p[i-1] + cut_rod(p, n-i));
            console.log("           q=",q);         
        }         
        return q;
}
console.log(cut_rod(p,10));

The same problem was met when I decided to implement the recurrence which just execute each step of each cycle. (just for the understanding of recurrence without solving some problem).

code:

function test(sum){
    console.log("i'm here sum",sum);
    if (sum < 1) {
        console.log("       ",sum," is less then 1, return",1);
        return x=1;
    }
    else{
        for(i=1;i<=3;i++){
            console.log("           i=",i);
            x = test(sum-i)+1;
            console.log("           x=",x)
        }       
    }
    return x;
} 

console.log("----------------->start"); 
console.log("answer",test(5));  

Thank you very much.

Answer 1

This is a scope issue. Your i and q variables are global variables, not local variables.

Change for(i = 1; i <= n; i++){ ... to for(var i = 1; i <= n; i++){ ...

and q = Number.MIN_VALUE; to var q = Number.MIN_VALUE;.