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Topics: Array, Greedy, Prefix Sum, Difference Array
You are given an integer array nums of even length n and an integer limit.
In one move, you can replace any integer from nums with another integer between 1 and limit (inclusive).
An array is called complementary if for every index i:
nums[i] + nums[n - 1 - i] = constant
That means every mirrored pair in the array must have the same sum.
[1, 2, 3, 4]
Pair sums:
| Pair | Sum |
|---|---|
| 1 + 4 | 5 |
| 2 + 3 | 5 |
✅ All pair sums are equal, so the array is complementary.
nums = [1,2,4,3]
limit = 4
1
In 1 move, we can change the array to:
[1,2,2,3]
Now the mirrored pair sums become:
| Pair | Sum |
|---|---|
| 1 + 3 | 4 |
| 2 + 2 | 4 |
✅ Every pair has the same sum.
Therefore, the minimum number of moves is:
nums = [1,2,2,1]
limit = 2
2
One possible complementary array:
[2,2,2,2]
Pair sums:
| Pair | Sum |
|---|---|
| 2 + 2 | 4 |
| 2 + 2 | 4 |
Since values cannot exceed limit = 2, this requires 2 moves.
nums = [1,2,1,2]
limit = 2
0
The array already satisfies:
| Pair | Sum |
|---|---|
| 1 + 2 | 3 |
| 2 + 1 | 3 |
✅ No changes are needed.
| Constraint | Value |
|---|---|
2 <= n <= 10^5 | ✅ |
1 <= nums[i] <= limit <= 10^5 | ✅ |
n is even | ✅ |
For every mirrored pair:
(nums[i], nums[n - 1 - i])
we try to make all pair sums equal using the minimum moves.
The target sum can range from:
2 <= target sum <= 2 * limit
Efficient solutions use:
to compute the answer in:
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