Calculate the Coefficient

Slug: calculate-the-coefficient

Difficulty: Medium

Id: 710077

Summary

The problem is about calculating the coefficient of a polynomial expression given its coefficients. The key concepts involved are polynomial manipulation and arithmetic operations.

Detailed Explanation

To solve this problem, we can use the concept of polynomial multiplication and addition. The coefficient of the polynomial expression a0 + a1*x + a2*x^2 + ... + an*x^n is an, where n is the degree of the polynomial.

Here's a step-by-step breakdown of the solution:

Parse the input string to extract the coefficients and their corresponding powers.
Initialize the coefficient to 0.
Iterate through the input string, multiplying each term by its corresponding power and adding it to the current coefficient.
Return the calculated coefficient.

Here's an ASCII art diagram illustrating the polynomial expression:

a0 + a1*x + a2*x^2 + ... + an*x^n
  |         |
  v         v
  a1*x     a2*x^2
  |         |
  v         v
  a0

Time complexity: O(n), where n is the number of terms in the polynomial expression. Space complexity: O(1), as we only require a constant amount of space to store the coefficient.

Optimized Solutions

Java

public class CoefficientCalculator { public static int calculateCoefficient(String polynomial) { int coefficient = 0; for (String term : polynomial.split("\\+")) { String[] parts = term.trim().split(" "); int power = Integer.parseInt(parts[1].substring(1)); int value = Integer.parseInt(parts[0]); coefficient += value * (int) Math.pow(x, power); } return coefficient; } }