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3489. Zero Array Transformation IV

Description

You are given an integer array nums of length n and a 2D array queries, where queries[i] = [li, ri, vali].

Each queries[i] represents the following action on nums:

  • Select a subset of indices in the range [li, ri] from nums.
  • Decrement the value at each selected index by exactly vali.

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.

 

Example 1:

Input: nums = [2,0,2], queries = [[0,2,1],[0,2,1],[1,1,3]]

Output: 2

Explanation:

  • For query 0 (l = 0, r = 2, val = 1):
    • Decrement the values at indices [0, 2] by 1.
    • The array will become [1, 0, 1].
  • For query 1 (l = 0, r = 2, val = 1):
    • Decrement the values at indices [0, 2] by 1.
    • The array will become [0, 0, 0], which is a Zero Array. Therefore, the minimum value of k is 2.

Example 2:

Input: nums = [4,3,2,1], queries = [[1,3,2],[0,2,1]]

Output: -1

Explanation:

It is impossible to make nums a Zero Array even after all the queries.

Example 3:

Input: nums = [1,2,3,2,1], queries = [[0,1,1],[1,2,1],[2,3,2],[3,4,1],[4,4,1]]

Output: 4

Explanation:

  • For query 0 (l = 0, r = 1, val = 1):
    • Decrement the values at indices [0, 1] by 1.
    • The array will become [0, 1, 3, 2, 1].
  • For query 1 (l = 1, r = 2, val = 1):
    • Decrement the values at indices [1, 2] by 1.
    • The array will become [0, 0, 2, 2, 1].
  • For query 2 (l = 2, r = 3, val = 2):
    • Decrement the values at indices [2, 3] by 2.
    • The array will become [0, 0, 0, 0, 1].
  • For query 3 (l = 3, r = 4, val = 1):
    • Decrement the value at index 4 by 1.
    • The array will become [0, 0, 0, 0, 0]. Therefore, the minimum value of k is 4.

Example 4:

Input: nums = [1,2,3,2,6], queries = [[0,1,1],[0,2,1],[1,4,2],[4,4,4],[3,4,1],[4,4,5]]

Output: 4

 

Constraints:

  • 1 <= nums.length <= 10
  • 0 <= nums[i] <= 1000
  • 1 <= queries.length <= 1000
  • queries[i] = [li, ri, vali]
  • 0 <= li <= ri < nums.length
  • 1 <= vali <= 10

Solutions

Solution 1

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