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Algorithms for Coding Interviews in C++

Solution: Big (O) of Nested Loop with Addition

Explore how to calculate the Big O time complexity of nested loops with addition by examining execution counts line by line. Understand the method to simplify expressions and identify the dominant term, equipping you to analyze algorithm efficiency confidently in coding interviews.

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Solution:

C++
int main(){
  int n = 10;
  int sum = 0;     
  float pie = 3.14;   
  for (int i=1; i<n; i+=3){  // O(n/3)
    cout << pie << endl;        // O(n/3)
    for (int j=1; j<n; j+=2){    // O((n/3)*(n/2)) 
      sum += 1;        // O((n/3)*(n/2))
      cout << sum << endl;   // O((n/3)*(n/2))
    }
  }
}

On line 6 in the outer loop, int i=1; runs once, i<n; gets executed n3+1\frac{n}{3}+1 ...