range_addition

Problem

Assume you have an array of length n initialized with all 0's and are given k update operations. Each operation is represented as a triplet: [startIndex, endIndex, inc] which increments each element of subarray A[startIndex ... endIndex] (startIndex and endIndex inclusive) with inc. Return the modified array after all k operations were executed.

Example:

Given:
length = 5,
updates = [
  [1,  3,  2],
  [2,  4,  3],
  [0,  2, -2]
]
                                
Output: [-2, 0, 3, 5, 3]

Initial state: [ 0, 0, 0, 0, 0 ]

After applying operation [1, 3, 2]: [ 0, 2, 2, 2, 0 ]

After applying operation [2, 4, 3]: [ 0, 2, 5, 5, 3 ]

After applying operation [0, 2, -2]: [-2, 0, 3, 5, 3 ]

Solution

• Similar to segment tree
• View interval as two operations: one to increase [start, n), another to decrease [end+1, n)
• Pre-process all segments before carrying out increments
• Half-open, half-close intervals are easier to manage