Problem Statement |
| | A power series takes the form:
f(x) = a0 + a1x + a2x2 + a3x3 + ...
If we had another power series
g(x) = b0 + b1x + b2x2 + b3x3 + ...
then we compute the product as follows:
f(x)g(x) = a0b0 + (a0b1 + a1b0)x + (a0b2 + a1b1 + a2b0)x2 + ...
More formally, we have
ck = sum (i = 0 to k) aibk-i
where ck is a coefficient of the power series for the product.
Given the series f(x) you must determine g(x) such that f(x)g(x) = 1 + 0x + 0x2 + ...
The first few a-values will be given in a int[] start. The remaining a-values will be an infinitely repeating sequence of the terms in repeat. For example, if start = { 1, 2 } and repeat = { 3, 4, 5 } then the resulting power series is
1 + 2x + 3x2 + 4x3 + 5x4 + 3x5 + 4x6 + 5x7 + ...
You will return the first n terms of g(x) as a String[] where the first element is b0, the second is b1 and so forth. Each bi should be given in the form "p/q" where p and q are integers with no common factors (other than 1), and q is positive. If bi equals 0, then use the string "0/1". Neither p nor q should have extra leading zeros, and if p is negative, it should have a single leading '-'. |
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Definition |
| | | Class: | CauchyProduct | | Method: | findInverse | | Parameters: | int[], int[], int | | Returns: | String[] | | Method signature: | String[] findInverse(int[] start, int[] repeat, int n) | | (be sure your method is public) |
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Constraints |
| - | start will contain between 1 and 50 elements, inclusive. |
| - | repeat will contain between 1 and 50 elements, inclusive. |
| - | Each element of start will be between -20 and 20, inclusive. |
| - | Each element of repeat will be between -20 and 20, inclusive. |
| - | Element 0 of start will not be 0. |
| - | n will be between 1 and 1000, inclusive. |
| - | Each integer in each element of the return value will be between -100000 and 100000, inclusive. |
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Examples |
| 0) | |
| | | Returns: {"1/1", "-1/1", "0/1", "0/1", "0/1" } | |
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| 1) | |
| | | Returns: {"1/1", "-2/1", "2/1", "-2/1", "2/1" } | |
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| 2) | |
| | | Returns:
{"1/1",
"-2/1",
"1/1",
"0/1",
"0/1",
"3/1",
"-9/1",
"9/1",
"0/1",
"-9/1",
"18/1",
"-36/1",
"45/1",
"-9/1",
"-63/1",
"126/1",
"-171/1",
"180/1",
"-36/1",
"-333/1" } | |
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| 3) | |
| | | Returns:
{"1/1",
"-2/1",
"1/1",
"0/1",
"0/1",
"3/1",
"-9/1",
"9/1",
"0/1",
"-9/1",
"18/1",
"-36/1",
"45/1",
"-9/1",
"-63/1",
"126/1",
"-171/1",
"180/1",
"-36/1",
"-333/1",
"747/1",
"-927/1",
"720/1",
"99/1",
"-1818/1",
"3960/1",
"-4923/1",
"3123/1",
"2097/1",
"-10674/1",
"20457/1",
"-24552/1",
"13464/1",
"17379/1",
"-62865/1" } | |
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| 4) | |
| | | Returns: {"1/2", "-3/4", "1/8", "1/16", "1/32" } | |
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| 5) | |
| | {-19,14,-8,-2,-19,12,-4} | {-6,-6,2,14,-5,-18,17,-8,8,
-16,-2,-12,11,16,-12,-17,5,
1,11,11,0,10,-14,8,1,4,
-8,1,-16,16,19,-4,18,4,
-11,-15,9,4,-8,10,-5,-9,9,-9,16,10} | 3 |
| Returns: {"-1/19", "-14/361", "-44/6859" } | |
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