1785. Minimum Elements to Add to Form a Given Sum
Description
You are given an integer array nums
and two integers limit
and goal
. The array nums
has an interesting property that abs(nums[i]) <= limit
.
Return the minimum number of elements you need to add to make the sum of the array equal to goal
. The array must maintain its property that abs(nums[i]) <= limit
.
Note that abs(x)
equals x
if x >= 0
, and -x
otherwise.
Example 1:
Input: nums = [1,-1,1], limit = 3, goal = -4 Output: 2 Explanation: You can add -2 and -3, then the sum of the array will be 1 - 1 + 1 - 2 - 3 = -4.
Example 2:
Input: nums = [1,-10,9,1], limit = 100, goal = 0 Output: 1
Constraints:
1 <= nums.length <= 105
1 <= limit <= 106
-limit <= nums[i] <= limit
-109 <= goal <= 109
Solutions
Solution 1: Greedy
First, we calculate the sum of the array elements $s$, and then calculate the difference $d$ between $s$ and $goal$.
The number of elements to be added is the absolute value of $d$ divided by $limit$ and rounded up, that is, $\lceil \frac{|d|}{limit} \rceil$.
Note that in this problem, the data range of array elements is $[-10^6, 10^6]$, the maximum number of elements is $10^5$, the total sum $s$ and the difference $d$ may exceed the range of 32-bit integers, so we need to use 64-bit integers.
The time complexity is $O(n)$, and the space complexity is $O(1)$. Here, $n$ is the length of the array $nums$.
1 2 3 4 |
|
1 2 3 4 5 6 7 8 9 10 11 |
|
1 2 3 4 5 6 7 8 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
|
1 2 3 4 5 |
|
1 2 3 4 5 6 7 8 9 10 11 12 |
|
1 2 3 4 5 6 7 8 |
|