minimum-elements-to-add-to-form-a-given-sum

< Previous 　　　　　　　　　　　　　　　　 Next >

1785. Minimum Elements to Add to Form a Given Sum (Medium)

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

Related Topics

[Greedy]

Hints

Hint 1

Try thinking about the problem as if the array is empty. Then you only need to form goal using elements whose absolute value is <= limit.

Hint 2

You can greedily set all of the elements except one to limit or -limit, so the number of elements you need is ceil(abs(goal)/ limit).

Hint 3

You can "normalize" goal by offsetting it by the sum of the array. For example, if the goal is 5 and the sum is -3, then it's exactly the same as if the goal is 8 and the array is empty.

Hint 4

The answer is ceil(abs(goal-sum)/limit) = (abs(goal-sum)+limit-1) / limit.