3489. Zero Array Transformation IV

Problem Link

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):

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

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):

  <ul>
  	<li>Decrement the values at indices <code>[0, 1]</code> by <code><font face="monospace">1</font></code>.</li>
  	<li>The array will become <code>[0, 1, 3, 2, 1]</code>.</li>
  </ul>
  </li>
  <li><strong>For query 1 (l = 1, r = 2, val = 1):</strong>
  <ul>
  	<li>Decrement the values at indices <code>[1, 2]</code> by 1.</li>
  	<li>The array will become <code>[0, 0, 2, 2, 1]</code>.</li>
  </ul>
  </li>
  <li><strong>For query 2 (l = 2, r = 3, val = 2):</strong>
  <ul>
  	<li>Decrement the values at indices <code>[2, 3]</code> by 2.</li>
  	<li>The array will become <code>[0, 0, 0, 0, 1]</code>.</li>
  </ul>
  </li>
  <li><strong>For query 3 (l = 3, r = 4, val = 1):</strong>
  <ul>
  	<li>Decrement the value at index 4 by 1.</li>
  	<li>The array will become <code>[0, 0, 0, 0, 0]</code>. Therefore, the minimum value of <code>k</code> is 4.</li>
  </ul>
  </li>
  

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

Solution

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Python3

class Solution:
    def minZeroArray(self, nums: List[int], queries: List[List[int]]) -> int:
        N = len(nums)
        M = len(queries)
        ans = -inf
 
        for i, x in enumerate(nums):
 
            @cache
            def go(index, curr):
                if curr == 0:
                    return index
                    
                if index >= M or curr < 0:
                    return inf
 
                res = go(index + 1, curr)
                l, r, val = queries[index]
                if l <= i <= r:
                    res = min(res, go(index + 1, curr - val))
 
                return res
 
            minIndex = go(0, x)
 
            if minIndex == inf:
                return -1
 
            ans = max(ans, minIndex)
 
        return ans