Problem Description
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.
Key Insights
- The problem requires us to find the minimum number of additional integers needed to represent every integer from 1 to n using the sums of elements in the given sorted array.
- We can utilize a greedy approach where we try to cover the range incrementally.
- If we can create sums up to a certain value
maxReach, then we can determine the next integer we need to add to the array to extend our reach.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The solution uses a greedy algorithm to determine how many patches (new integers) are needed. We maintain a variable maxReach that represents the maximum sum we can form with the current elements and any patches added. We iterate through the nums array and try to extend maxReach using the elements of nums. If we reach a point where maxReach is less than the next integer we need to form, we add that integer as a patch and increment our count of patches. This process continues until we can form all numbers up to n.