1+ public class KataSolution {
2+
3+ public static String expand (String expr ) {
4+ // The corresponding values will be stored in these variables
5+ int n , a = Integer .MIN_VALUE , b = Integer .MIN_VALUE ;
6+ char letter = ' ' ;
7+
8+ // We get the value of a, b, n and the letter of the expression
9+ StringBuilder sb = new StringBuilder ();
10+ for (int i = 1 ; i < expr .length (); ++i ) {
11+ if (expr .charAt (i ) == '-' || isNumber (String .valueOf (expr .charAt (i )))) {
12+ sb .append (expr .charAt (i ));
13+ } else if (isNumber (sb .toString ()) || sb .toString ().equals ("-" )) {
14+ if (sb .toString ().equals ("-" ))
15+ sb .append ("1" );
16+
17+ if (a == Integer .MIN_VALUE ) {
18+ a = Integer .parseInt (sb .toString ());
19+ letter = expr .charAt (i );
20+ } else
21+ b = Integer .parseInt (sb .toString ());
22+
23+ sb .setLength (0 );
24+ }
25+ }
26+ // If the coefficient a == 1, then we adjust the values
27+ if (b == Integer .MIN_VALUE ) {
28+ b = a ;
29+ a = 1 ;
30+ letter = expr .charAt (1 );
31+ }
32+ // We get the value of the degree
33+ n = Integer .parseInt (sb .toString ());
34+
35+ // If the coefficient b == 0, then we return the result of the expression (a*letter)^n
36+ if (b == 0 )
37+ return getPolyUnit (1 , n , 0 , a , b , letter , true );
38+
39+ // If the degree is == 0, then return 1
40+ if (n == 0 )
41+ return "1" ;
42+
43+ sb .setLength (0 );
44+
45+ // Otherwise, we calculate the value of each term of the polynomial using Pascal's triangle
46+ long nFac = getFactorial (n );
47+ for (int k = 0 ; k < n + 1 ; ++k ) {
48+ // Calculate the coefficient C_n^k
49+ long c = nFac / (getFactorial (k ) * getFactorial (n - k ));
50+
51+ // If the leading element is missing + before the number
52+ if (sb .isEmpty ()) {
53+ sb .append (getPolyUnit (c , n , k , a , b , letter , true ));
54+ } else
55+ sb .append (getPolyUnit (c , n , k , a , b , letter , false ));
56+ }
57+
58+ return sb .toString ();
59+ }
60+
61+
62+ // The method allows you to determine whether a sequence is a number
63+ private static boolean isNumber (String str ) {
64+ try {
65+ Integer .parseInt (str );
66+ return true ;
67+ } catch (Exception e ) {
68+ return false ;
69+ }
70+ }
71+
72+
73+ // The method allows you to get the factorial of a number
74+ private static long getFactorial (int f ) {
75+ long result = 1 ;
76+ for (long i = 1 ; i <= f ; i ++) {
77+ result = result * i ;
78+ }
79+ return result ;
80+ }
81+
82+
83+ // The method allows you to get a correct representation of the next term of the polynomial
84+ private static String getPolyUnit (long c , int n , int k , int a , int b , char letter , boolean isLead ) {
85+ StringBuilder result = new StringBuilder ();
86+
87+ // We raise the coefficients a and b to the appropriate degrees
88+ long newA = (long ) Math .pow (a , n - k );
89+ long newB = (long ) Math .pow (b , k );
90+
91+ // If the product is different from zero
92+ if (c * newA * newB != 0 ) {
93+ // If the coefficient of a non-leading element is positive
94+ if (c * newA * newB > 0 && !isLead )
95+ result .append ("+%d" .formatted (c * newA * newB ));
96+ // If the coefficient in front of the leading element == -1
97+ else if (c * newA * newB == -1 && isLead )
98+ result .append ("-" );
99+ // If the value of the coefficient modulus is != 1 or the last element is being processed
100+ else if (Math .abs (c * newA * newB ) != 1 || n - k == 0 )
101+ result .append (c * newA * newB );
102+ }
103+
104+ // Processing the display of the letter in the expression. It is present in the expression if
105+ // the coefficient is not zero, or it is not the last element
106+ if (n - k != 0 && c * newA * newB != 0 ) {
107+ // If the last element is added, add a letter without a degree
108+ if (n - k == 1 )
109+ result .append (letter );
110+ // Otherwise, with a degree
111+ else
112+ result .append ("%s^%d" .formatted (letter , n - k ));
113+ }
114+
115+ return result .toString ();
116+ }
117+ }
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