Zero Array Transformation I

Problem Description

You are given an integer array nums of length n and a 2D array queries, where queries[i] = [l_i, r_i]. For each queries[i], select a subset of indices within the range [l_i, r_i] in nums and decrement the values at the selected indices by 1. A Zero Array is an array where all elements are equal to 0. Return true if it is possible to transform nums into a Zero Array after processing all the queries sequentially, otherwise return false.

Key Insights

• Each query allows decrementing the values in a specified range of the array.
• The sum of all elements in nums must equal the total number of decrements possible from all queries combined.
• The total decrements can be calculated by summing the lengths of the ranges specified in queries.
• If the total sum of nums equals the total possible decrements, then transforming nums into a Zero Array is feasible.

Space and Time Complexity

Time Complexity: O(q), where q is the number of queries, since we need to iterate through each query to compute the total decrements.
Space Complexity: O(1), as we are using a constant amount of extra space.

Solution

To solve the problem, we can follow these steps:

1. Calculate the total sum of elements in the nums array.
2. For each query, determine the total number of decrements possible by summing the lengths of the ranges specified in queries.
3. If the total sum of nums is equal to the total possible decrements, return true; otherwise, return false.

The algorithm primarily relies on basic arithmetic and the counting of indices from the query ranges.

Code Solutions