Problem Description
You are given an integer array nums of length n and a 2D array queries, where queries[i] = [l_i, r_i, val_i]. Each queries[i] represents the following action on nums:
- Select a subset of indices in the range
[l_i, r_i]fromnums. - Decrement the value at each selected index by exactly
val_i.
A Zero Array is an array with all its elements equal to 0. Return the minimum possible non-negative value of k, such that after processing the first k queries in sequence, nums becomes a Zero Array. If no such k exists, return -1.
Key Insights
- You need to determine the minimum number of queries needed to turn all elements of
numsto zero. - Each query allows you to decrement values over a specific range, so careful selection of which queries to apply is crucial.
- The problem can be explored using a greedy or binary search approach to find the minimum
k.
Space and Time Complexity
Time Complexity: O(n * q), where n is the length of nums and q is the length of queries. This is because, in the worst case, we might need to apply each query to all elements of nums.
Space Complexity: O(n), for storing the modified state of the nums array during processing.
Solution
To solve the problem, we can use a simulation approach. We will iterate through the queries, applying them to the nums array while maintaining a count of how many queries have been applied. For each query, we will check if applying it can potentially lead to a Zero Array. If at any point all elements become zero, we record that number of queries. If we exhaust all queries without achieving a Zero Array, we return -1.