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.lengthIn #3362 Zero Array Transformation III, the goal is to determine whether a sequence of range operations can transform an array into all zeros. The challenge lies in efficiently applying and tracking the effect of multiple interval updates without repeatedly modifying each element.
A common strategy is to use a difference array or prefix sum technique to simulate range updates efficiently. Instead of applying every operation directly, maintain cumulative effects so that each index reflects the total decrement applied by previous operations. While iterating through the array, you can track whether the current position has received enough operations to reduce its value to zero.
Some optimized approaches also combine greedy processing with priority queues or interval tracking to select the most useful operations when multiple ranges overlap. This avoids unnecessary operations and ensures coverage of required indices.
With careful bookkeeping of active operations, the algorithm can run in roughly O(n log n) time (depending on data structures used) and O(n) space.
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Difference Array / Prefix Sum Simulation | O(n + q) | O(n) |
| Greedy with Priority Queue for Range Selection | O((n + q) log q) | O(n) |
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Use these hints if you're stuck. Try solving on your own first.
Sort the queries.
We need to greedily pick the queries with farthest ending point first.
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Problems similar to Zero Array Transformation III appear in interviews at large tech companies. They test understanding of greedy strategies, range updates, and efficient data structure usage. Mastering prefix sums and interval processing is particularly useful for such questions.
Common data structures used include difference arrays, prefix sums, and priority queues. These structures help track the cumulative impact of range operations efficiently. They also allow quick decisions about which operations should be applied while scanning the array.
The optimal approach usually combines a greedy strategy with efficient range update tracking such as a difference array or prefix sums. This allows the algorithm to simulate multiple interval operations without repeatedly updating each element. In some implementations, a priority queue helps choose the most beneficial ranges when overlaps occur.
A difference array allows range updates to be recorded in constant time instead of modifying every element within the range. Later, prefix sums reconstruct the actual values after all updates. This significantly reduces the overall complexity when many interval operations are involved.