2145-count-the-hidden-sequences.js

/**
 * 2145. Count the Hidden Sequences
 * https://leetcode.com/problems/count-the-hidden-sequences/
 * Difficulty: Medium
 *
 * You are given a 0-indexed array of n integers differences, which describes the differences
 * between each pair of consecutive integers of a hidden sequence of length (n + 1). More formally,
 * call the hidden sequence hidden, then we have that differences[i] = hidden[i + 1] - hidden[i].
 *
 * You are further given two integers lower and upper that describe the inclusive range of values
 * [lower, upper] that the hidden sequence can contain.
 *
 * - For example, given differences = [1, -3, 4], lower = 1, upper = 6, the hidden sequence is a
 *   sequence of length 4 whose elements are in between 1 and 6 (inclusive).
 *   - [3, 4, 1, 5] and [4, 5, 2, 6] are possible hidden sequences.
 *   - [5, 6, 3, 7] is not possible since it contains an element greater than 6.
 *   - [1, 2, 3, 4] is not possible since the differences are not correct.
 *
 * Return the number of possible hidden sequences there are. If there are no possible sequences,
 * return 0.
 */

/**
 * @param {number[]} differences
 * @param {number} lower
 * @param {number} upper
 * @return {number}
 */
var numberOfArrays = function(differences, lower, upper) {
  let minValue = 0;
  let maxValue = 0;
  let current = 0;

  for (const diff of differences) {
    current += diff;
    minValue = Math.min(minValue, current);
    maxValue = Math.max(maxValue, current);
  }

  const range = upper - lower;
  const validRange = range - (maxValue - minValue);

  return validRange >= 0 ? validRange + 1 : 0;
};