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Algorithms for Coding Interviews in Java

Solution: Big (O) of Nested Loop with Multiplication

Understand how to analyze the time complexity of nested loops involving multiplication using logarithmic iterations and geometric series. Learn to derive the Big O notation of O(n) by examining loop execution patterns and their upper and lower bounds. This lesson equips you to evaluate nested loop complexities effectively in coding challenges.

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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)
		int var = 1;
	
		while(var < n) {  // O(log n)
			System.out.println("Pie: " + pie); // O(log n)
			
			for (int j = 0; j < var; j++) {  // 2n
				sum++;  //  (2n-1)
			}
			var *= 2; // O(log n)
		} //end of while loop
		
		System.out.println("Sum: " + sum); //O(1)
	} //end of main
} //end of class

Explanation

The answer is O(n) ...

Time Complexity

The above slides give a detailed, step-by-step analysis of the code. Here, we provide a more summarized version.

The outer loop here runs log(n)log(n) ...