You are given an integer array nums. Start by selecting a starting position curr such that nums[curr] == 0, and choose a movement direction of either left or right. After that, you repeat the following process: If curr is out of the range [0, n -

countValidSelections.js

/**
 * Counts how many zero positions in the array can lead to all elements being reduced to zero
 * by moving forward or backward and decrementing non-zero values.
 *
 * @param {number[]} nums - Array of non-negative integers
 * @return {number} - Total number of valid selections from zero positions
 */
var countValidSelections = function (nums) {
    // Collect indices where the value is zero
    const zeroIndexArr = nums.reduce((acc, cur, idx) => {
        if (cur === 0) acc.push(idx);
        return acc;
    }, []);

    // If there are no zero positions, no valid selections are possible
    if (zeroIndexArr.length === 0) return 0;

    let validSelections = 0;

    /**
     * Checks if all elements in the array are zero
     * @param {number[]} arr
     * @return {boolean}
     */
    const isArrayZero = (arr) => arr.every((val) => val === 0);

    /**
     * Simulates movement from a starting index in a given direction,
     * toggling direction whenever a non-zero element is decremented.
     *
     * @param {number} cur - Starting index
     * @param {number[]} nums - Copy of the original array
     * @param {"forward"|"backward"} direction - Initial movement direction
     * @return {boolean} - True if all elements become zero during traversal
     */
    const moveLogic = (cur, nums, direction) => {
        while (cur >= 0 && cur < nums.length) {
            // Move in the current direction
            cur = direction === "forward" ? cur + 1 : cur - 1;

            // If within bounds and value is positive, decrement and flip direction
            if (cur >= 0 && cur < nums.length && nums[cur] > 0) {
                nums[cur]--;
                direction = direction === "forward" ? "backward" : "forward";
            }
        }
        return isArrayZero(nums);
    };

    // Try each zero index as a starting point in both directions
    zeroIndexArr.forEach((z) => {
        if (moveLogic(z, [...nums], "forward")) validSelections++;
        if (moveLogic(z, [...nums], "backward")) validSelections++;
    });

    return validSelections;
};