Step by Step solution about How to resolve the algorithm Polynomial long division step by step in the Go programming language

The code snippet you provided is an implementation of the polynomial long division algorithm in Go.

The pld function takes two input polynomials, nn and dd, and returns the quotient q, the remainder r, and a boolean indicating whether the division was successful (ok).

The first step in the algorithm is to check if the degree of the divisor polynomial dd is negative. If it is, the function returns with all ok set to false to indicate that the division cannot be performed.

If the degree of dd is non-negative, the function appends the remainder r to the dividend nn and checks if the degree of nn is greater than or equal to the degree of dd. If it is, the function creates a slice q to store the quotient and iterates through the terms of nn until the degree of nn is less than the degree of dd.

In each iteration, the function creates a slice d to hold the terms of the divisor polynomial, copies the terms of dd into d, and divides the leading coefficient of nn by the leading coefficient of d. The result of the division is stored in the corresponding element of q.

The function then subtracts the product of d and q from nn. This effectively removes the leading term of nn from the polynomial and reduces its degree by one.

The loop continues until the degree of nn is less than the degree of dd. At this point, the remaining terms of nn are the remainder r.

The function returns the quotient q, the remainder r, and a boolean ok set to true indicating that the division was successful.

Here is an example of how to use the pld function:

package main

import "fmt"

func main() {
   n := []float64{-42, 0, -12, 1}
   d := []float64{-3, 1}
   
   q, r, ok := pld(n, d)
   if ok {
       fmt.Println("Q:", q)
       fmt.Println("R:", r)
   } else {
       fmt.Println("error")
   }
}

This will print the following output:

Q: [14 4]
R: [0]

package main

import "fmt"

func main() {
    n := []float64{-42, 0, -12, 1}
    d := []float64{-3, 1}
    fmt.Println("N:", n)
    fmt.Println("D:", d)
    q, r, ok := pld(n, d)
    if ok {
        fmt.Println("Q:", q)
        fmt.Println("R:", r)
    } else {
        fmt.Println("error")
    }
}

func degree(p []float64) int {
    for d := len(p) - 1; d >= 0; d-- {
        if p[d] != 0 {
            return d
        }
    }
    return -1
}

func pld(nn, dd []float64) (q, r []float64, ok bool) {
    if degree(dd) < 0 {
        return
    }
    nn = append(r, nn...)
    if degree(nn) >= degree(dd) {
        q = make([]float64, degree(nn)-degree(dd)+1)
        for degree(nn) >= degree(dd) {
            d := make([]float64, degree(nn)+1)
            copy(d[degree(nn)-degree(dd):], dd)
            q[degree(nn)-degree(dd)] = nn[degree(nn)] / d[degree(d)]
            for i := range d {
                d[i] *= q[degree(nn)-degree(dd)]
                nn[i] -= d[i]
            }
        }
    }
    return q, nn, true
}