Binary Search Practice Test

A database stores sorted usernames array "adam", "bella", "carlos", "dina", "eli", "fatima", "gwen", "hugo", "ivan" and searches for target "fatima" using iterative binary search; midpoint is $\lfloor(\text{low}+\text{high})/2\rfloor$, comparing strings alphabetically. Steps: low=0, high=8, mid=4 ("eli") < "fatima" so low=5; next mid=$\lfloor(5+8)/2\rfloor$=6 ("gwen") > "fatima" so high=5; next mid=$\lfloor(5+5)/2\rfloor$=5 ("fatima") found. Refer to the array provided above. How many iterations are required to locate the target element using binary search?

A nearly complete sorted sequence is stored as array 101, 102, 103, 104, 105, 106, 108, 109, 110, 111; exactly one integer is missing. Students use iterative binary search on the expected range 101–111, using midpoint $\lfloor(\text{low}+\text{high})/2\rfloor$ and comparing arraymid to expected value (101+mid). Steps: low=0, high=9, mid=4: array4=105 matches expected 105 so low=5; mid=$\lfloor(5+9)/2\rfloor$=7: array7=109 but expected 108 so high=6; mid=$\lfloor(5+6)/2\rfloor$=5: array5=106 matches expected 106 so low=6; mid=$\lfloor(6+6)/2\rfloor$=6: array6=108 but expected 107, so missing value is 107. Refer to the array provided above. What is the position of the target element in the array after applying binary search?