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Data Structures for Coding Interviews in Java

Solution: Big O of a Nested Loop with Subtraction

Explore how to analyze the time complexity of nested loops where the outer loop decrements by 3 and the inner loop counts down linearly. This lesson breaks down execution counts per statement, leading to a clear calculation of the quadratic time complexity O(n²). Gain insight into evaluating algorithm performance with nested loops in Java.

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Given Code

Java
class NestedLoop {
  public static void main(String[] args) {
    int n = 10; // O(time complexity of the called function)
    int sum = 0; //O(1)
    double pie = 3.14; //O(1)
    
    
    for (int var = n; var >= 1; var = var - 3) { // O(n/3)
      System.out.println("Pie: " + pie); // O(n/3)
      
      for (int j = n; j >= 0; j = j - 1) { // O((n/3)*(n+1))
        sum++; // O((n/3)*(n+1))
      }
    } //end of outer for loop
  System.out.println("Sum: " + sum);//O(1)
  } //end of main
} //end of class

Solution Breakdown

On line 8 in the outer loop, int var=n; runs once, var>=1; gets executed n3+1 ...