Difference between revisions of "TADM2E 3.28"
From Algorithm Wiki
| Line 2: | Line 2: | ||
1. Calculate cumulative production P and Q:<br> | 1. Calculate cumulative production P and Q:<br> | ||
| − | <math>P_0 = | + | <math>P_0 = 3 |
| + | , P_k=X_k P_{k-1}=\prod_{i=1}^kx_i</math><br> | ||
<math>Q_n = 1, Q_k=X_k Q_{k+1}=\prod_{i=k}^nx_i</math> | <math>Q_n = 1, Q_k=X_k Q_{k+1}=\prod_{i=k}^nx_i</math> | ||
Revision as of 10:17, 27 July 2020
We need two passes over X:
1. Calculate cumulative production P and Q:
$ P_0 = 3 , P_k=X_k P_{k-1}=\prod_{i=1}^kx_i $
$ Q_n = 1, Q_k=X_k Q_{k+1}=\prod_{i=k}^nx_i $
2. Calculate M:
$ M_k=P_{k-1}Q_{k+1}, k\in[1,n] $
Using Iteration:
Java example:
public class Multiplication { public static int[] product(int[] x) { int[] M = new int[x.length]; for (int i = 0; i < x.length; i++) { M[i] = product(x, M, i + 1, x.length); } return M; } private static int product(int[] x, int[] y, int i, int length) { if (i == length) return productLeft(x, i - 2, length); return x[i] * productLeft(x, i - 2, length) * productRight(x, i + 1, length); } private static int productLeft(int[] x, int i, int length) { if (i < 0) return 1; return x[i] * productLeft(x, i - 1, length); } private static int productRight(int[] x, int i, int length) { if (i >= length) return 1; return x[i] * productRight(x, i + 1, length); } }
