273. Integer to English Words (Hard)

Convert a non-negative integer to its english words representation. Given input is guaranteed to be less than 2^31- 1.

For example,

123 -> "One Hundred Twenty Three"
12345 -> "Twelve Thousand Three Hundred Forty Five"
1234567 -> "One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven"

Solution 1: StringBuilder O(1); O(1)

Create 3 arrays to store strings used to represent the English words.
为了使用append，不用insert，应该从高位开始计算。

    /**
     * Try to find the pattern first.
     * The numbers less than 1000, e.g. xyz, can be x Hundred y"ty" z.
     * The numbers larger than 1000, we need to add thousand or million or billion.
     * Given a number n, we pronounce the most significant digits (highest order bit) first. So...
     * Then append the result of next three most significant digits to the end of current result.
     * Next result of num = current result of num + the pronunciation of next three digits 
     * Each time, we handle 3 digits according to the rule of English words representation.
     */    
    final String[] LESS_THAN_20 = {"", "One", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine", "Ten", 
    "Eleven", "Twelve", "Thirteen", "Fourteen", "Fifteen", "Sixteen", "Seventeen", "Eighteen", "Nineteen"};
    final String[] TENS = {"", "Ten", "Twenty", "Thirty", "Forty", "Fifty", "Sixty", "Seventy", "Eighty", "Ninety"};
    final String[] THOUSANDS = {"Billion", "Million", "Thousand", ""};
    final int[] radix = {1000000000, 1000000, 1000, 1}; //modulus

    public String numberToWords(int num) {
        if (num == 0) return "Zero";

        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < radix.length; i++) {
            if (num / radix[i] == 0) continue;

            sb.append(trans(num / radix[i])).append(THOUSANDS[i]).append(' '); //handle 3 digits
            num %= radix[i]; //update the num by letting num mod the radix
        }
        return sb.toString().trim(); //The string's tail may have extra whitespace.
    }

    private String trans(int num) {
        if (num == 0) return "";
        if (num < 20) return LESS_THAN_20[num] + " "; //return corresponding English words
        if (num < 100) return TENS[num / 10] + " " + trans(num % 10);
        return LESS_THAN_20[num / 100] + " Hundred " + trans(num % 100);
    }

Solution 2: String O(1); O(1)

    private final String[] belowTwenty = {"", "One", "Two", "Three", "Four", "Five", "Six", "Seven", "Eight", "Nine", "Ten",
            "Eleven", "Twelve", "Thirteen", "Fourteen", "Fifteen", "Sixteen", "Seventeen",
            "Eighteen", "Nineteen"};
    private final String[] tens = {"", "Ten", "Twenty", "Thirty", "Forty", "Fifty", "Sixty", "Seventy", "Eighty", "Ninety"};
    private final String[] thousands = {"", "Thousand", "Million", "Billion"};

    public String numberToWords(int num) {
        if (num == 0) {
            return "Zero";
        }

        String words = "";
        int count = 0;
        while (num > 0) {
            if (num % 1000 != 0) {
                words = helper(num % 1000) + thousands[count] + " " + words;
            }
            num /= 1000;
            count++;
        }
        return words.trim();
    }

    private String helper(int num) {
        if (num == 0) {
            return "";
        } else if (num < 20) {
            return belowTwenty[num] + " ";
        } else if (num < 100) {
            return tens[num / 10] + " " + helper(num % 10);
        } else {
            return belowTwenty[num / 100] + " Hundred " + helper(num % 100);
        }
    }