Minimum Operations to Make Array Equal - Problem
You start with a special array where each element follows the pattern arr[i] = (2 * i) + 1. This creates an array of consecutive odd numbers: [1, 3, 5, 7, 9, ...].
Your goal is to make all elements equal using the minimum number of operations. In each operation, you can:
- Choose any two indices
xandy - Subtract 1 from
arr[x] - Add 1 to
arr[y]
This is essentially redistributing values between array elements. The total sum remains constant, but you're trying to balance the array perfectly.
Example: For n = 3, the array is [1, 3, 5]. The target value is 3 (average), so you need 2 operations to transform it to [3, 3, 3].
Input & Output
example_1.py — Small Array
$
Input:
n = 3
›
Output:
2
💡 Note:
Array is [1, 3, 5]. Target is 3. Element 1 needs +2, element 5 gives -2. Total: 2 operations.
example_2.py — Even Length
$
Input:
n = 6
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Output:
9
💡 Note:
Array is [1, 3, 5, 7, 9, 11]. Target is 6. Left half deficits: 5+3+1 = 9 operations needed.
example_3.py — Single Element
$
Input:
n = 1
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Output:
0
💡 Note:
Array is [1]. Already equal, no operations needed.
Constraints
- 1 ≤ n ≤ 104
-
Array elements follow the pattern
arr[i] = (2 * i) + 1 - All elements can be made equal using the given operations
Visualization
Tap to expand
Understanding the Visualization
1
Initial State
Tanks have levels 1, 3, 5, 7, ... (consecutive odd numbers)
2
Target Level
All tanks should reach level n (the middle value)
3
Transfer Operations
Left tanks need water, right tanks provide it
4
Minimum Operations
Sum of all deficits = n²/4 transfers needed
Key Takeaway
🎯 Key Insight: The array is perfectly symmetric around its middle value n, so we only need to calculate how much the first half is 'short' and that equals our minimum operations.
💡
Explanation
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