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

numberOfArrays.js

/**
 * This function calculates the number of valid arrays that can be reconstructed
 * from a given list of differences within a specified range.
 *
 * @param {number[]} differences - An array of differences between consecutive elements.
 * @param {number} lower - The lower bound of the valid range.
 * @param {number} upper - The upper bound of the valid range.
 * @return {number} - The number of valid arrays that can be reconstructed.
 */
var numberOfArrays = function(differences, lower, upper) {
    // Initialize the lower and upper bounds of the array values
    let low = lower, high = upper;

    // Iterate through the differences array in reverse order
    for (let i = differences.length - 1; i >= 0; i--) {
        // Adjust the current bounds by subtracting the current difference
        low = low - differences[i];
        high = high - differences[i];

        // Check if the adjusted bounds are completely out of the valid range
        if ((low < lower && high < lower) || (low > upper && high > upper)) {
            return 0; // No valid array can be formed
        }

        // Clamp the bounds to the valid range
        low = Math.max(low, lower);
        high = Math.min(high, upper);
    }

    // Return the number of possible values for the first element in the valid range
    return (high - low) + 1;
};