实现多项式的JAVA类

  1 package practice;
  2 //http://introcs.cs.princeton.edu/java/92symbolic/Polynomial.java.html
  3 /*************************************************************************
  4  *  Compilation:  javac Polynomial.java
  5  *  Execution:    java Polynomial
  6  *
  7  *  Polynomials with integer coefficients.
  8  *
  9  *  % java Polynomial
 10  *  zero(x) =     0
 11  *  p(x) =        4x^3 + 3x^2 + 2x + 1
 12  *  q(x) =        3x^2 + 5
 13  *  p(x) + q(x) = 4x^3 + 6x^2 + 2x + 6
 14  *  p(x) * q(x) = 12x^5 + 9x^4 + 26x^3 + 18x^2 + 10x + 5
 15  *  p(q(x))     = 108x^6 + 567x^4 + 996x^2 + 586
 16  *  0 - p(x)    = -4x^3 - 3x^2 - 2x - 1
 17  *  p(3)        = 142
 18  *  p'(x)       = 12x^2 + 6x + 2
 19  *  p''(x)      = 24x + 6
 20  *
 21  *************************************************************************/
 22 public class Polynomial {
 23     private int[] coef; //coefficients 系数
 24     private int deg;//degree of polynomial (0 for the zero polynomial)
 25     
 26     //a*x^b
 27     public Polynomial(int a, int b){
 28         coef = new int[b+1];
 29         coef[b] = a;
 30         deg = degree();
 31     }
 32     
 33     // return the degree of this polynomial (0 for the zero polynomial)
 34     public int degree(){
 35         int d = 0;
 36         for(int i = 0; i<coef.length; i++)
 37             if(coef[i]!=0)
 38                 d = i;
 39 
 40         return d;
 41     }
 42     
 43     //return c = a+b
 44     public Polynomial plus(Polynomial b){
 45         Polynomial a = this;
 46         Polynomial c = new Polynomial(0, Math.max(a.deg, b.deg));
 47         for(int i = 0; i <= a.deg; i++)
 48             c.coef[i] += a.coef[i];
 49         for(int i = 0; i <= b.deg; i++)
 50             c.coef[i] += b.coef[i];
 51         c.deg = c.degree();
 52         return c;
 53     }
 54     
 55     // return (a - b)
 56     public Polynomial minus(Polynomial b) {
 57         Polynomial a = this;
 58         Polynomial c = new Polynomial(0, Math.max(a.deg, b.deg));
 59         for (int i = 0; i <= a.deg; i++) c.coef[i] += a.coef[i];
 60         for (int i = 0; i <= b.deg; i++) c.coef[i] -= b.coef[i];
 61         c.deg = c.degree();
 62         return c;
 63     }
 64 
 65     // return (a * b)
 66     public Polynomial times(Polynomial b) {
 67         Polynomial a = this;
 68         Polynomial c = new Polynomial(0, a.deg + b.deg);
 69         for (int i = 0; i <= a.deg; i++)
 70             for (int j = 0; j <= b.deg; j++)
 71                 c.coef[i+j] += (a.coef[i] * b.coef[j]);
 72         c.deg = c.degree();
 73         return c;
 74     }
 75 
 76     // return a(b(x))  - compute using Horner's method
 77     public Polynomial compose(Polynomial b) {
 78         Polynomial a = this;
 79         Polynomial c = new Polynomial(0, 0);
 80         for (int i = a.deg; i >= 0; i--) {
 81             Polynomial term = new Polynomial(a.coef[i], 0);
 82             c = term.plus(b.times(c));
 83         }
 84         return c;
 85     }
 86 
 87 
 88     // do a and b represent the same polynomial?
 89     public boolean eq(Polynomial b) {
 90         Polynomial a = this;
 91         if (a.deg != b.deg) return false;
 92         for (int i = a.deg; i >= 0; i--)
 93             if (a.coef[i] != b.coef[i]) return false;
 94         return true;
 95     }
 96 
 97 
 98     // use Horner's method to compute and return the polynomial evaluated at x
 99     public int evaluate(int x) {
100         int p = 0;
101         for (int i = deg; i >= 0; i--)
102             p = coef[i] + (x * p);
103         return p;
104     }
105 
106     // differentiate this polynomial and return it
107     public Polynomial differentiate() {
108         if (deg == 0) return new Polynomial(0, 0);
109         Polynomial deriv = new Polynomial(0, deg - 1);
110         deriv.deg = deg - 1;
111         for (int i = 0; i < deg; i++)
112             deriv.coef[i] = (i + 1) * coef[i + 1];
113         return deriv;
114     }
115     public String toString(){
116         if(deg == 0)
117             return "" + coef[0];
118         if(deg == 1)
119             return coef[1] + "x + " + coef[0];
120         
121         String s = coef[deg] + "x^" + deg;
122         for(int i = deg-1; i >= 0; i--){
123             if(coef[i] == 0)
124                 continue;
125             else if(coef[i] > 0)
126                 s = s + " + " + ( coef[i]);
127             else if(coef[i] < 0)
128                 s = s + " - " + (-coef[i]);
129             if(i== 1)
130                 s = s + "x";
131             else if(i > 1)
132                 s = s +"x^" + i;
133         }
134         return s;
135     }
136     
137     public static void main(String[] args) { 
138         Polynomial zero = new Polynomial(0, 0);
139 
140         Polynomial p1   = new Polynomial(4, 3);
141         Polynomial p2   = new Polynomial(3, 2);
142         Polynomial p3   = new Polynomial(1, 0);
143         Polynomial p4   = new Polynomial(2, 1);
144         Polynomial p    = p1.plus(p2).plus(p3).plus(p4);   // 4x^3 + 3x^2 + 1
145 
146         Polynomial q1   = new Polynomial(3, 2);
147         Polynomial q2   = new Polynomial(5, 0);
148         Polynomial q    = q1.plus(q2);                     // 3x^2 + 5
149 
150 
151         Polynomial r    = p.plus(q);
152 //        Polynomial s    = p.times(q);
153 //        Polynomial t    = p.compose(q);
154 
155         System.out.println("zero(x) =     " + zero);
156         System.out.println("p(x) =        " + p);
157         System.out.println("q(x) =        " + q);
158         System.out.println("p(x) + q(x) = " + r);
159 //        System.out.println("p(x) * q(x) = " + s);
160 //        System.out.println("p(q(x))     = " + t);
161 //        System.out.println("0 - p(x)    = " + zero.minus(p));
162 //        System.out.println("p(3)        = " + p.evaluate(3));
163 //        System.out.println("p'(x)       = " + p.differentiate());
164 //        System.out.println("p''(x)      = " + p.differentiate().differentiate());
165    }
166 }