How to resolve the algorithm Display a linear combination step by step in the Groovy programming language

Published on 12 May 2024 09:40 PM
#Groovy

How to resolve the algorithm Display a linear combination step by step in the Groovy programming language

Table of Contents

Problem Statement

Display a finite linear combination in an infinite vector basis

(

e

1

,

e

2

, … )

{\displaystyle (e_{1},e_{2},\ldots )}

. Write a function that, when given a finite list of scalars

(

α

1

,

α

2

, … )

{\displaystyle (\alpha ^{1},\alpha ^{2},\ldots )}

, creates a string representing the linear combination

∑

i

α

i

e

i

{\displaystyle \sum {i}\alpha ^{i}e{i}}

in an explicit format often used in mathematics, that is: where

α

i

k

≠ 0

{\displaystyle \alpha ^{i_{k}}\neq 0}

The output must comply to the following rules:

Show here output for the following lists of scalars:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Display a linear combination step by step in the Groovy programming language

Source code in the groovy programming language

class LinearCombination {
    private static String linearCombo(int[] c) {
        StringBuilder sb = new StringBuilder()
        for (int i = 0; i < c.length; ++i) {
            if (c[i] == 0) continue
            String op
            if (c[i] < 0 && sb.length() == 0) {
                op = "-"
            } else if (c[i] < 0) {
                op = " - "
            } else if (c[i] > 0 && sb.length() == 0) {
                op = ""
            } else {
                op = " + "
            }
            int av = Math.abs(c[i])
            String coeff = av == 1 ? "" : "" + av + "*"
            sb.append(op).append(coeff).append("e(").append(i + 1).append(')')
        }
        if (sb.length() == 0) {
            return "0"
        }
        return sb.toString()
    }

    static void main(String[] args) {
        int[][] combos = [
                [1, 2, 3],
                [0, 1, 2, 3],
                [1, 0, 3, 4],
                [1, 2, 0],
                [0, 0, 0],
                [0],
                [1, 1, 1],
                [-1, -1, -1],
                [-1, -2, 0, -3],
                [-1]
        ]

        for (int[] c : combos) {
            printf("%-15s  ->  %s\n", Arrays.toString(c), linearCombo(c))
        }
    }
}

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