The first version of Dijkstra's algorithm, which uses an array implementation without binary heap, $($lazy$)$ binomial heap, or Fibonacci heap, has a time complexity of o$(*$n$).$ In which type of graph would this version of Dijkstra's algorithm have a lower time complexity compared to a version implemented with a binomial heap? Please explain your answer.

Please sequentially draw the result of adding the following data to a binomial heap: $5,1,3,4,6,8,2,9.($There$\text{'}$s no need to draw the array storing the roots$).$