diff --git a/guide/english/algorithms/sorting-algorithms/bubble-sort/index.md b/guide/english/algorithms/sorting-algorithms/bubble-sort/index.md index 850d73e9fe..d139cbd844 100644 --- a/guide/english/algorithms/sorting-algorithms/bubble-sort/index.md +++ b/guide/english/algorithms/sorting-algorithms/bubble-sort/index.md @@ -10,36 +10,36 @@ This is a very slow sorting algorithm compared to algorithms like quicksort, wit ### Example: #### First Pass: -( 5 1 4 2 8 ) –> ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1. +( **5 1** 4 2 8 ) –> ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1. -( 1 5 4 2 8 ) –> ( 1 4 5 2 8 ), Swap since 5 > 4 +( 1 **5 4** 2 8 ) –> ( 1 4 5 2 8 ), Swap since 5 > 4 -( 1 4 5 2 8 ) –> ( 1 4 2 5 8 ), Swap since 5 > 2 +( 1 4 **5 2** 8 ) –> ( 1 4 2 5 8 ), Swap since 5 > 2 -( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ), Now, since these elements are already in order (8 > 5), algorithm does not swap them. +( 1 4 2 **5 8** ) –> ( 1 4 2 5 8 ), Now, since these elements are already in order (8 > 5), algorithm does not swap them. #### Second Pass: -( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ) +( **1 4** 2 5 8 ) –> ( 1 4 2 5 8 ) -( 1 4 2 5 8 ) –> ( 1 2 4 5 8 ), Swap since 4 > 2 +( 1 **4 2** 5 8 ) –> ( 1 2 4 5 8 ), Swap since 4 > 2 -( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) +( 1 2 **4 5** 8 ) –> ( 1 2 4 5 8 ) -( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) +( 1 2 4 **5 8** ) –> ( 1 2 4 5 8 ) Now, the array is already sorted, but our algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted. #### Third Pass: -( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) +( **1 2** 4 5 8 ) –> ( 1 2 4 5 8 ) -( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) +( 1 **2 4** 5 8 ) –> ( 1 2 4 5 8 ) -( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) +( 1 2 **4 5** 8 ) –> ( 1 2 4 5 8 ) -( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) +( 1 2 4 **5 8** ) –> ( 1 2 4 5 8 ) #### Properties - Space complexity: O(1)