# Find the Wavy Words!

(Note: this is an easier spin-off of my previous challenge Find the Infinity Words!, which is a spin-off of my other previous challenge Find the Swirling Words! :) )

### Definition of a Wavy Word:

1. If you connect with curves all the characters of a Wavy Word on the alphabet (A-Z) you obtain the path of a wave continuously going toward right or toward left and never changing direction, like in the diagrams below.
2. A Wavy Word can be:
• Raising if each consecutive character is at the right (on the alphabet) of the previous one.
• Decreasing if each consecutive character is at the left (on the alphabet) of the previous one.
3. All the even connection must be down, all the odd connections must be up.
4. You can ignore upper/lowercase or consider/convert all to upper case or all to lower case.
5. The input words are only characters in the alphabet range of A-Z, no spaces, no punctuation, or symbols.
6. If a word has double characters, like "SPOON", you must collapse the doubles to one character: "SPOON" > "SPON" (because if you go from O to O is zero distance).
7. The Wavy Words will contain at least 3 distinct characters (even after doubles collapsing).

### Here there are some examples:

Write a full program or function that will take a word from standard input and will output if it is a Wavy Word or not, and in positive case, output if it is raising or decreasing. The output can be True/False/Null, 2/1/0, 1/Null/0, -1/0/1, NO/WR/WD, etc, you decide how to represent it.

### Test cases:

WAVY WORDS:
ADEPT, BEGIN, BILL, BOSS, BOOST, CHIMP,
KNOW, SPONGE, SPOON, TROLL, WOLF

BEGIN  > YES > RAISING
BILL   > YES > RAISING
BOSS   > YES > RAISING
BOOST  > YES > RAISING
CHIMP  > YES > RAISING
KNOW   > YES > RAISING
SPONGE > YES > DECREASING
SPOON  > YES > DECREASING
TROLL  > YES > DECREASING
WOLF   > YES > DECREASING

NOT WAVY WORDS:
WATCH, EARTH, NINON, FOO, BAR, WAVE, SELECTION,
YES, NO, DEFINITION, WATER, WINE, CODE, AAAHHHH, I, MM, ABCA


### Rules:

• Shortest code wins.

Find, as a list, as many Wavy Words as you can in an English dictionary, and the longest as well. You can take for example as reference the complete list of English words here.

• How did you make the pictures? – Oliver Ni Oct 28 '16 at 16:57
• @Oliver With Illustrator because I have it for work, but is possible to obtain similar results with Gimp or Inkskape, or others. – Mario Oct 28 '16 at 17:01
• NO and FOO aren't valid inputs by your rules. – PurkkaKoodari Oct 28 '16 at 17:27
• @Pietu1998 They're in the NOT WAVY WORDS section though, which is correct.. – Kade Oct 28 '16 at 17:32
• @xnor #5 you can assume all the input words are as described, no need to validate. #7 this is the minimum number of letters to make a wave shape. For the rest you decide the output as you prefer. – Mario Oct 28 '16 at 21:13

# 05AB1E, 11 9 bytes (Thanks to Adnan)

Dg2›iÇü‹Ù


Try it online!

Wavy Cases:

0 - Decreasing Wavy

1 - Increasing Wavy

Not Wavy Cases:

[0,1] - Not wavy, initially decreasing, but then has an increase/equality that broke the pattern.

[1,0] - Not wavy, initially increasing, but then has a decrease/equality that broke the pattern

Input String - Not possible to be wavy in the first place due to length.

Explanation:

Dg2›iÇü‹Ù   # Full program

D           # Push 2 copies of input.
g2›i       # If length is greater than 2.
Ç      # Push ASCII values for all characters in the string.
ü     # Push pairwise array.
‹    # Vectorize 1 if negative difference, 0 if positive difference.
Ù   # Uniquify using right most unique values first.
# Else just print the string back, letting them know it's not valid input.

• @JonathanAllan Dangit... I just saw the comments and changes... I took The input words will contain at least 3 distinct characters to mean that I didn't have to handle less than 3 char words. Working on changes, may take awhile; this is my first answer I was able to do in 05AB1E. – Magic Octopus Urn Oct 28 '16 at 19:12
• @JonathanAllan Fixed :)! But now you're beating me ;). – Magic Octopus Urn Oct 28 '16 at 19:30
• Very nice! One tip, ü‹ is the same as ü-0‹ :) – Adnan Oct 29 '16 at 14:11
• Hehehe... Man, I may just have to learn python and start helping to expand 05AB1E. This language is impressive. Thanks for the tip! – Magic Octopus Urn Oct 30 '16 at 3:40

# Jelly, 10 bytes

OIṠḟ0µL’aQ


Returns:
[1] for wavy increasing
[-1] for wavy decreasing
something else otherwise ([], [0], [-1,1], or [1,-1])

(Declared as unnecessary: For a single value for each OIṠḟ0µL’aQS (11 bytes) will return 1, -1, and 0 respectively.)

### How?

OIṠḟ0µL’aQ - Main link: s
O          - cast to ordinals
I         - incremental differences
Ṡ        - sign (-1 for decreasing, 0 for no change, 1 for increasing)
ḟ0      - filter out zeros
L    - length
’   - decremented
a  - and
Q - unique items

• Are you allowed to have 3 different possible outputs for the neither case? – xnor Oct 28 '16 at 19:36
• I took "you decide how to represent it" to mean yes, so long as they are different. However your question about rule #5 could invalidate this (and probably every other entry). – Jonathan Allan Oct 28 '16 at 19:55
• Added an solution to that if need be. – Jonathan Allan Oct 28 '16 at 20:08
• Can you not just sum the list? – xnor Oct 28 '16 at 20:13
• Oh, yes, of course >_< thanks. – Jonathan Allan Oct 28 '16 at 20:15

## Python 2, 54 bytes

lambda s:[2<len(set(s))<s[::b]==sorted(s)for b in-1,1]


Takes input as a list of characters. Outputs:

[False, True] for ascending
[True, False] for descending
[False, False] for neither


Checks if the sorted input string equals its original or reverse. Does so by slicing with step sizes of 1 and -1. At the same time, we check whether the word has at least 2 distinct letters.

If "exit with error" can be used an output for the neither case, we can go down to 51 bytes:

lambda s:[s,s[::-(len(set(s))>2)]].index(sorted(s))


# Python 3, 77 75 bytes

lambda x:(len(set(x))>2)*(list(x)==sorted(x)or(list(x)==sorted(x)[::-1])*2)


Assumes all letters are of the same case.

Returns:

• 0 if not wavy
• 1 if forwards wavy
• 2 if backwards wavy

Removed unnecessary spaces thanks @ETHproductions

• Welcome to PPCG, and nice first answer! However, you also need to make sure that there are at least three distinct chars in the string; if not, it's not a wavy word no matter what. – ETHproductions Oct 28 '16 at 19:22
• Ah, right. Should've looked closer at the definition of a wavy word. Fixed. – C. Smith Oct 28 '16 at 20:16
• Nice! I'm not a Python expert, but I think you can remove the space on either side of the or. – ETHproductions Oct 28 '16 at 20:36
• Yep, you're right. Forgot to remove them after surrounding the expressions with parentheses. Thanks for the catch! – C. Smith Oct 28 '16 at 21:38

# R, 96 95 bytes

function(x,d=diff(rle(utf8ToInt(x))$v))if(any(d>0)&any(d<0)|sum(1|d)<2)3 elseif(all(d<1),2,1)  Returns: • 1 for wavy and raising • 2 for wavy and decreasing • 3 for non-wavy Explained • d=diff(rle(utf8ToInt(x))$v): Generates a variable d by first converting the string into it's ASCII values using utf8ToInt which conveniently returns a vector. Subsequently perform run length encoding using rle. rle(...)$v returns the non-repeating values of the sequence (i.e. collapsing all runs). Finally take the difference. • if(any(d>0)&any(d<0)|sum(1|d)<2)3: If at least one of the differences are positive and at least one negative, or if the difference sequence has less than 2 elements (equivalent to the original word having less than 3 characters), the word is non-wavy and return 3 • elseif(all(d<1),2,1): Else if all differences are negative, return 2 for wavy and decreasing, else return 1 for wavy and raising. Try all the test cases at R-fiddle (note that it's named such that it can be vectorized for the test cases). ## JavaScript (ES6), 84 81 bytes s=>(new Set(t=[...s]).size>2)*(!t.some((c,i)=>c>s[i+1])-!t.some((c,i)=>c<s[i+1]))  Assumes the input is all in the same case. Returns 1 for raising wavy, -1 for decreasing wavy, 0 or -0 (both are falsy) for not wavy. Edit: Saved 3 bytes thanks to @RobertHickman. • I'm not an expert on the newer features, but can you remove new? – Cyoce Oct 29 '16 at 17:28 • @Cyoce Annoyingly the newer features require you to use new. – Neil Oct 29 '16 at 18:05 • @Neil, I believe, You can save a byte by initializing another variable inside of the Set() function t=[...s] and using t instead of [...s] in those two spots you have it. – Robert Hickman Nov 1 '16 at 19:36 ## Javascript (ES6), 8480 78 bytes i=>new Set(s=[...i]).size>2?[i,s.reverse().join].indexOf(s.sort().join):-1  Where wavy increasing is 0, decreasing is 1, and -1 is not wavy. Thanks to @Neil for helping me save 2 bytes. • new Set(s=[...i]) saves you 2 bytes. (It works by iterating i, turning it into an array, iterating the array, and turning that into a set. Convoluted but you don't worry about that sort of thing when you're golfing.) – Neil Nov 1 '16 at 22:05 # Pyth, 12 bytes x*<2lrQ8_BQS  # Python 2, 5352 50 bytes Expects input enclosed in quotes, e.g. "watch" As unnamed lambda: lambda s:(sum(map(cmp,s[1:],s))+1)/min(len(s)-1,3)  Sums the sign of difference between each letters and integer-divides by len-1. If all were 1 (increasing) the sum is len-1 it displays 1, similar for decreasing -1 and for mixed 1,-1 the sum is smaller than len-1 so it displays 0. -1 byte for changing cmp,s[1:],s[:-1]) to cmp,s[1:],s)+1 • Will return 1 for "NO" – Jonathan Allan Oct 28 '16 at 20:57 • @JonathanAllan LMNOP so O is after N which means increasing which means 1 – Karl Napf Oct 28 '16 at 21:05 • Yep, but any word of less than 3 characters (after removing any duplicate letters) was defined as not wavy ("NO" is in the not wavy test cases). – Jonathan Allan Oct 28 '16 at 21:06 • @JonathanAllan fixed the len issue, but i the repeating chars are still a problem – Karl Napf Oct 28 '16 at 22:10 # Ruby, 54 bytes ->w{c=w.chars.uniq;c==(s=c.sort)?2:(c==s.reverse)?1:0}  Returns 0 if the word is not wavy, 1 if backwards wavy, and 2 if forwards wavy. # Groovy - 56 bytes {d=it[0];c=[0]*3;it.each{a->c[(a<=>d)]=1;d=a};c[1..-1]} Outputs [1,0] for raising wavy, [0,1] for decreasing wavy, [0,0] for single character input or [1,1] for non-wavy. NOTE: Assumes input is either a String or a char[] and all letters are of the same case. # PHP, 96 Bytes for(;($t=$argv[1])[++$i];)$s+=$r[]=$t[$i-1]<=>$t[$i];echo(max($r)-min($r)<2)*(0<=>$s)*(1<$s*$s);  or 98 Bytes $s=str_split($t=$argv[1]);sort($s);echo(-($t==strrev($j=join($s)))|$t==$j)*!!count_chars($t,3)[2];  0 not wavy 1 raising -1 decreasing • - instead of 2* (-1 for decreasing: -1 byte). *(!!...) needs no parentheses. (-2) – Titus Oct 29 '16 at 14:37 • $s*$s>1 instead of abs($s)>1 (-2) – Titus Oct 30 '16 at 8:34
• @Titus Done Thank You – Jörg Hülsermann Oct 30 '16 at 9:27

# PHP, 100 bytes

$n=$m=$l=str_split($argv[1]);sort($n);rsort($m);echo(($n==$l)-($m==$l))*(count(array_unique($l))>2);  Returns: • -1 for wavy, decreasing. • 0 for not wavy. • 1 for wavy, raising. • !!array_unique($s)[2] instead of count(array_unique($l))>2 – Jörg Hülsermann Oct 29 '16 at 13:14 • Actually, the problem with that is that array_unique will preverse keys. Thus an input like aaabc will falsely output 0 when using array_unique. – chocochaos Oct 30 '16 at 11:36 # C, 164 bytes main(){char s[99];scanf("%s",s);char *c=&s;int p=*c;while(*c^0){if(p>*c){if(c-&s[0]>1)return 0;while(*c^0){if(p<*c)return 0;p=*c;c++;}return 2;}p=*c;c++;}return 1;}  Returns 0 if not wawy, 1 if wawy and raising, 2 if decreasing. ## Racket 321 bytes (let*((ld(λ(sl)(for/list((i(sub1(length sl))))(-(list-ref sl(add1 i))(list-ref sl i)))))(l(ld(remove-duplicates(map (λ(x)(char->integer x))(string->list s)))))(am andmap)(N"Not WAVY")(d displayln))(cond[(<(length l)2)(d N)][(am(λ(x)(>= x 0))l) (d"YES; RAISING")][(am(λ(x)(<= x 0))l)(d"YES; DECREASING")][else(d N)])))  Ungolfed: (define (f s) (let* ((ld (lambda(sl) ; sub-fn to get differences in list elements (for/list ((i (sub1(length sl)))) (- (list-ref sl (add1 i)) (list-ref sl i) ) ))) (l (ld (remove-duplicates (map (lambda(x) (char->integer x)) (string->list s))))) (am andmap) (N "Not WAVY") (d displayln)) (cond [(< (length l) 2)(d N)] [(am (lambda(x) (>= x 0)) l) (d "YES; RAISING")] [(am (lambda(x) (<= x 0)) l) (d "YES; DECREASING")] [else (d N)] )))  Testing: (f "ADEPT"); > YES > RAISING (f "BEGIN"); > YES > RAISING (f "BILL"); > YES > RAISING (f "BOSS"); > YES > RAISING (f "BOOST"); > YES > RAISING (f "CHIMP"); > YES > RAISING (f "KNOW"); > YES > RAISING (f "SPONGE"); > YES > DECREASING (f "SPOON"); > YES > DECREASING (f "TROLL"); > YES > DECREASING (f "WOLF"); > YES > DECREASING (f "WATCH") (f "EARTH") (f "NINON") (f "FOO") (f "BAR") (f "WAVE") (f "SELECTION")  Output: YES; RAISING YES; RAISING YES; RAISING YES; RAISING YES; RAISING YES; RAISING YES; RAISING YES; DECREASING YES; DECREASING YES; DECREASING YES; DECREASING Not WAVY Not WAVY Not WAVY Not WAVY Not WAVY Not WAVY Not WAVY  # Java 7, 254 240 bytes import java.util.*;int c(String s){char[]a=s.toCharArray(),x=a.clone();Arrays.sort(x);return s.replaceAll("(.)\\1{1,}","$1").length()<3?0:Arrays.equals(a,x)|Arrays.equals(x,(new StringBuffer(s).reverse()+"").toCharArray())?a[0]>a[1]?1:2:0;}


Outputs 0 if the input string isn't wavy, 1 if it's a raising wave, and 2 if it's a decreasing wave.

Ungolfed & test code:

Try it here.

import java.util.*;
class M{
static int c(String s){
char[] a = s.toCharArray(),
x = a.clone();
Arrays.sort(x);
return s.replaceAll("(.)\\1{1,}", "\$1").length() < 3
? 0
: Arrays.equals(a, x) | Arrays.equals(x, (new StringBuffer(s).reverse()+"").toCharArray())
? a[0] > a[1]
? 1
: 2
: 0;
}

public static void main(String[] a){
System.out.print(c("BEGIN") + ", ");
System.out.print(c("BILL") + ", ");
System.out.print(c("BOSS") + ", ");
System.out.print(c("BOOST") + ", ");
System.out.print(c("CHIMP") + ", ");
System.out.println(c("KNOW"));

System.out.print(c("SPONGE") + ", ");
System.out.print(c("SPOON") + ", ");
System.out.print(c("TROLL") + ", ");
System.out.println(c("WOLF"));

System.out.print(c("WATCH") + ", ");
System.out.print(c("EARTH") + ", ");
System.out.print(c("NINON") + ", ");
System.out.print(c("FOO") + ", ");
System.out.print(c("BAR") + ", ");
System.out.print(c("WAVE") + ", ");
System.out.print(c("SELECTION") + ", ");
System.out.print(c("YES") + ", ");
System.out.print(c("NO") + ", ");
System.out.print(c("DEFINITION") + ", ");
System.out.print(c("WATER") + ", ");
System.out.print(c("WINE") + ", ");
System.out.print(c("CODE") + ", ");
System.out.print(c("AAAHHHH") + ", ");
System.out.print(c("I") + ", ");
System.out.print(c("MM") + ", ");
System.out.println(c("ABCA"));
}
}


Output:

2, 2, 2, 2, 2, 2, 2
1, 1, 1, 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

• int c(char[]s){int t=s[0],f=s.length,a=1,b=1,i;for(i=1;i<f;){if(s[i]-s[i-1]>=0)++a;if(s[i]-s[i++-1]<1)++b;}return a==f?1:b==f?-1:0;}(132 bytes) – Numberknot Oct 31 '16 at 12:55
• Output 1 if wavy raising,output -1 if wavy decreasing,0 if not wavy – Numberknot Oct 31 '16 at 12:56