June 2018 Update

Task/Polynomial-long-division/Java/polynomial-long-division.java

@@ -0,0 +1,118 @@
+import java.util.Arrays;
+
+public class PolynomialLongDivision {
+    private static class Solution {
+        double[] quotient, remainder;
+
+        Solution(double[] q, double[] r) {
+            this.quotient = q;
+            this.remainder = r;
+        }
+    }
+
+    private static int polyDegree(double[] p) {
+        for (int i = p.length - 1; i >= 0; --i) {
+            if (p[i] != 0.0) return i;
+        }
+        return Integer.MIN_VALUE;
+    }
+
+    private static double[] polyShiftRight(double[] p, int places) {
+        if (places <= 0) return p;
+        int pd = polyDegree(p);
+        if (pd + places >= p.length) {
+            throw new IllegalArgumentException("The number of places to be shifted is too large");
+        }
+        double[] d = Arrays.copyOf(p, p.length);
+        for (int i = pd; i >= 0; --i) {
+            d[i + places] = d[i];
+            d[i] = 0.0;
+        }
+        return d;
+    }
+
+    private static void polyMultiply(double[] p, double m) {
+        for (int i = 0; i < p.length; ++i) {
+            p[i] *= m;
+        }
+    }
+
+    private static void polySubtract(double[] p, double[] s) {
+        for (int i = 0; i < p.length; ++i) {
+            p[i] -= s[i];
+        }
+    }
+
+    private static Solution polyLongDiv(double[] n, double[] d) {
+        if (n.length != d.length) {
+            throw new IllegalArgumentException("Numerator and denominator vectors must have the same size");
+        }
+        int nd = polyDegree(n);
+        int dd = polyDegree(d);
+        if (dd < 0) {
+            throw new IllegalArgumentException("Divisor must have at least one one-zero coefficient");
+        }
+        if (nd < dd) {
+            throw new IllegalArgumentException("The degree of the divisor cannot exceed that of the numerator");
+        }
+        double[] n2 = Arrays.copyOf(n, n.length);
+        double[] q = new double[n.length];
+        while (nd >= dd) {
+            double[] d2 = polyShiftRight(d, nd - dd);
+            q[nd - dd] = n2[nd] / d2[nd];
+            polyMultiply(d2, q[nd - dd]);
+            polySubtract(n2, d2);
+            nd = polyDegree(n2);
+        }
+        return new Solution(q, n2);
+    }
+
+    private static void polyShow(double[] p) {
+        int pd = polyDegree(p);
+        for (int i = pd; i >= 0; --i) {
+            double coeff = p[i];
+            if (coeff == 0.0) continue;
+            if (coeff == 1.0) {
+                if (i < pd) {
+                    System.out.print(" + ");
+                }
+            } else if (coeff == -1.0) {
+                if (i < pd) {
+                    System.out.print(" - ");
+                } else {
+                    System.out.print("-");
+                }
+            } else if (coeff < 0.0) {
+                if (i < pd) {
+                    System.out.printf(" - %.1f", -coeff);
+                } else {
+                    System.out.print(coeff);
+                }
+            } else {
+                if (i < pd) {
+                    System.out.printf(" + %.1f", coeff);
+                } else {
+                    System.out.print(coeff);
+                }
+            }
+            if (i > 1) System.out.printf("x^%d", i);
+            else if (i == 1) System.out.print("x");
+        }
+        System.out.println();
+    }
+
+    public static void main(String[] args) {
+        double[] n = new double[]{-42.0, 0.0, -12.0, 1.0};
+        double[] d = new double[]{-3.0, 1.0, 0.0, 0.0};
+        System.out.print("Numerator   : ");
+        polyShow(n);
+        System.out.print("Denominator : ");
+        polyShow(d);
+        System.out.println("-------------------------------------");
+        Solution sol = polyLongDiv(n, d);
+        System.out.print("Quotient    : ");
+        polyShow(sol.quotient);
+        System.out.print("Remainder   : ");
+        polyShow(sol.remainder);
+    }
+}