Watch 10 video solutions for Zero Array Transformation III, a medium level problem involving Array, Greedy, Sorting. This walkthrough by codestorywithMIK has 11,473 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
You are given an integer array nums of length n and a 2D array queries where queries[i] = [li, ri].
Each queries[i] represents the following action on nums:
[li, ri] in nums by at most 1.A Zero Array is an array with all its elements equal to 0.
Return the maximum number of elements that can be removed from queries, such that nums can still be converted to a zero array using the remaining queries. If it is not possible to convert nums to a zero array, return -1.
Example 1:
Input: nums = [2,0,2], queries = [[0,2],[0,2],[1,1]]
Output: 1
Explanation:
After removing queries[2], nums can still be converted to a zero array.
queries[0], decrement nums[0] and nums[2] by 1 and nums[1] by 0.queries[1], decrement nums[0] and nums[2] by 1 and nums[1] by 0.Example 2:
Input: nums = [1,1,1,1], queries = [[1,3],[0,2],[1,3],[1,2]]
Output: 2
Explanation:
We can remove queries[2] and queries[3].
Example 3:
Input: nums = [1,2,3,4], queries = [[0,3]]
Output: -1
Explanation:
nums cannot be converted to a zero array even after using all the queries.
Constraints:
1 <= nums.length <= 1050 <= nums[i] <= 1051 <= queries.length <= 105queries[i].length == 20 <= li <= ri < nums.lengthProblem Overview: You are given an array nums and a list of range queries. Each query can decrease every element in its range by 1. The goal is to determine how many queries can be removed while still being able to apply the remaining queries to make the entire array become zero.
Approach 1: Difference Array Technique (O((n + q) log q) time, O(n + q) space)
This approach simulates applying only the necessary queries using a difference array to track how many decrements are currently active at each index. Sort queries by their starting index and iterate through nums from left to right. Maintain a max heap of candidate queries whose start index is ≤ the current position. If the active decrement count is smaller than nums[i], repeatedly pick the query with the farthest right boundary from the heap and apply it. Applying a query increases the active decrement count and schedules its end using the difference array (diff[r+1]--). This ensures decrements automatically stop after the range ends. If no valid query covers the index while more decrements are needed, the transformation is impossible. The number of used queries determines how many can be removed.
The key insight is that applying the query with the farthest r maximizes coverage for future indices. This greedy choice reduces the total number of queries needed and works well with prefix-sum style tracking using a prefix sum or difference array.
Approach 2: Greedy with Priority Queue (O((n + q) log q) time, O(q) space)
This method focuses directly on greedy selection using a max heap. First sort queries by their left boundary. While scanning the array, push all queries whose l ≤ i into a max heap ordered by r. Track how many decrement operations are currently active at index i. If nums[i] requires more decrements than currently active, repeatedly pop the query with the largest r and activate it. Queries that end before i cannot help and indicate failure if additional decrements are still required.
The greedy choice works because a query with a larger right boundary contributes decrements to more future elements. This approach combines concepts from greedy algorithms and priority queues. By always extending coverage as far as possible, you minimize the number of queries used.
Recommended for interviews: The greedy priority queue solution is what most interviewers expect. It clearly demonstrates reasoning about optimal choices and efficient data structure usage. Showing the difference-array tracking alongside it demonstrates strong understanding of range updates and array prefix techniques.
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Difference Array + Heap | O((n + q) log q) | O(n + q) | When tracking active range effects efficiently with prefix sums |
| Greedy with Priority Queue | O((n + q) log q) | O(q) | General case; interview-preferred approach using greedy selection |