An algorithm rearranges a sequence of numbers following a specific rule in each step. Following is an illustration of input and the subsequent steps of rearrangement.
Input: 98 31 06 72 63 59 36 12 84
Step 1: 98 31 36 72 63 59 06 12 84
Step 2: 84 31 36 72 63 59 06 12 98
Step 3: 84 31 36 63 72 59 06 12 98
Step 4: 84 31 12 63 72 59 06 36 98
Using the same rule, trace the steps for the following input sequence:
Input: 12 31 59 36 63 72 98 84 06
The sum of the numbers for the given sequence whose positions remain unaltered through all the steps as in the input is:
- A94
- B103
- C129
- D131
Solution & Step-by-step Explanation
The rearrangement rules based on the index swaps are:
* Step 1: Swap index 3 and index 7.
* Step 2: Swap index 1 and index 9.
* Step 3: Swap index 4 and index 5.
* Step 4: Swap index 3 and index 8.
Let's trace the given input across all steps step-by-step:
* Step 1 (Swap index 3 and 7):
* Step 2 (Swap index 1 and 9):
* Step 3 (Swap index 4 and 5):
* Step 4 (Swap index 3 and 8):
Now let's check which elements tracking positions to remained completely unchanged from Input through all four subsequent steps:
* Position 2 held the value consistently throughout.
* Position 6 held the value consistently throughout.
All other positions experienced a mutation in at least one step.
* Step 1: Swap index 3 and index 7.
* Step 2: Swap index 1 and index 9.
* Step 3: Swap index 4 and index 5.
* Step 4: Swap index 3 and index 8.
Let's trace the given input across all steps step-by-step:
* Step 1 (Swap index 3 and 7):
* Step 2 (Swap index 1 and 9):
* Step 3 (Swap index 4 and 5):
* Step 4 (Swap index 3 and 8):
Now let's check which elements tracking positions to remained completely unchanged from Input through all four subsequent steps:
* Position 2 held the value consistently throughout.
* Position 6 held the value consistently throughout.
All other positions experienced a mutation in at least one step.