Patching Array

arraygreedy

Problem Statement

Given a sorted integer array nums and an integer n , add/patch elements to the array such that any number in the range [1, n] inclusive can be formed by the sum of some elements in the array.

Return the minimum number of patches required .

Examples

Example 1

Input: nums = [1,3], n = 6
Output: 1
Combinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4.
Now if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,3], [1,2,3].
Possible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6].
So we only need 1 patch.

Example 2

Input: nums = [1,5,10], n = 20
Output: 2
The two patches can be [2, 4].

Example 3

Input: nums = [1,2,2], n = 5
Output: 0

Constraints

1 <= nums.length <= 1000

1 <= nums[i] <= 10 ^4

nums is sorted in ascending order .

1 <= n <= 2 ^31 - 1

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy