Asked in: Meesho
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All Testcases Passed ✔
Solution
def solve(A):
def helper(arr):
left = 0
// ... rest of solution available after purchaseExplanation
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To approach this problem, begin by fully understanding the game mechanics and the objective. You are given an array of integers, and two players, Alex and Bob, who pick numbers from opposite ends of the array in turns until the array is empty. The twist is that each player chooses a side (start or end) at the beginning of the game and sticks to that side for the entire duration. Alex always starts first.
Your goal is not to simulate every single possible game play but rather to find the **minimum absolute difference** between the sum of numbers collected by both players, considering **all possible side selections** (S for start, E for end) each could make.
Since each player can only pick from one fixed end of the array, the possible configurations are:
1. Alex picks from the start (S), Bob from the end (E)
2. Alex picks from the end (E), Bob from the start (S)
These are the only two valid configurations since both can't pick from the same end; otherwise, one would have no legal move.
Now, for each configuration, simulate the game turn by turn:
- Initialize two pointers or indices representing Alex’s and Bob’s sides.
- On each turn, alternate between Alex and Bob.
- Each player picks from their respective side and accumulates the value.
- Adjust the current end of the array accordingly, removing the element that was picked.
- Continue this process until the array is empty.
At the end of the simulation, compute the absolute difference between the sum of the elements collected by Alex and Bob. Do this for both configurations and retain the minimum absolute difference from the two.
To make this efficient and avoid duplication of logic, think about using a two-pointer approach. One pointer starts from the beginning, the other from the end. For configuration 1, Alex always picks from the front and Bob from the back. For configuration 2, it's reversed. On each turn, simulate the pick, update the pointer on that side, and switch turns. Also, maintain two running sums: one for Alex and one for Bob.
Now, shift your thinking to how turn order affects the outcome. Since Alex always starts, she will get to pick the first, third, fifth, etc., elements (i.e., all odd-numbered turns), while Bob picks the second, fourth, sixth, etc. So if there are an odd number of elements, Alex will always get one more element than Bob.
This is important because the array size (N) affects who gets how many turns. So during your simulation, be mindful of how many turns each player will get and ensure you're updating the correct player's sum on each turn.
Another useful perspective is symmetry. You only need to simulate the two valid configurations described above because they fully cover all strategic possibilities the players can take given the game rules. Any other variation, like both picking from the same side, breaks the game rules.
To make this simulation more organized, you could also consider writing a helper function that accepts parameters like:
- The array
- Which side Alex and Bob are choosing
- Whose turn it is
This function can then return the final sums and you compute the difference.
Finally, for each test case (since the input mentions multiple test cases), repeat the process: simulate both valid configurations, compute the absolute differences in scores, and keep the minimum one.
Edge cases to consider:
- If the array has only one element, Alex will take it, Bob gets nothing, and the absolute difference is just the value of that element.
- If the array has two elements, Alex takes one, Bob takes the other — the difference is the absolute difference of the two elements.
- If all elements in the array are equal, the minimum absolute difference will naturally be 0 or close to 0, depending on the number of elements.
In conclusion, the key strategy is to simulate both valid gameplay configurations using a turn-based, pointer-driven approach, compute the resulting sums for each player, and then find the minimum absolute difference. Being systematic with turns, careful with pointer movement, and mindful of edge cases will help ensure a correct and efficient solution.
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