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Algorithm Complexity - Binary Search

    lower_bound
{
  unsigned int   low  = 0;
  unsigned int   mid;
  unsigned int   hih = size;
  while (low < hih)
  {
    mid =  (low + hih) / 2;  
    if (v[mid] < t)          
      low = mid + 1;         
    else                     
      hih = mid;             
  }  
  return low;
}
  • notion of input size: n = size of container
  • atomic computation: comparison
    (call to operator <())
  • f(n) = (1 compare) x (no. of iterations of loop body)
       = (1) x (log n)
       = Θ(log n)
  • algorithm complexity = Θ(log n)

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