Find product of all the elements in the array except self. (without division)

ProductExceptSelf.js

var leftArray = rightArray = prod = []

var leftHashMap = rightHashMap = {}

function constructLeftArrayElement (arr, i) {
    if (i <= 0) {
        leftHashMap[i] = 1
        return 1
    } else {
        if (leftHashMap.hasOwnProperty(i-1)) {
            var val = leftHashMap[i-1] * arr[i-1]
            leftHashMap[i] = val
            return val
        } else {
            var val = constructLeftArrayElement(arr, i-1) * arr[i-1]
            leftHashMap[i] = val
            return val
        }

    }
}

function constructRightArrayElement (arr, i) {
    if (i >= arr.length-1) {
        rightHashMap[i] = 1
        return 1
    } else {
        if (rightHashMap.hasOwnProperty(i+1)) {
            var val = rightHashMap[i+1] * arr[i+1]
            rightHashMap[i] = val
            return val
        } else {
            var val = constructRightArrayElement(arr, i+1) * arr[i+1]
            rightHashMap[i] = val
            return val
        }
    }
}

var productExceptSelf = function(nums) {
    var leftArray = []
    var rightArray = []
    var prod = []
    leftHashMap = {}
    rightHashMap = {}
    var i = 0
    for(i = 0; i < nums.length; i++) {
        leftArray[i] = constructLeftArrayElement(nums, i)
    }
    for(i = 0; i < nums.length; i++) {
        rightArray[i] = constructRightArrayElement(nums, i)
    }
    for(i = 0; i < nums.length; i++) {
        prod[i] = leftArray[i] * rightArray[i]
    }
    return prod
}