JOIN

 Problem Statement

Problem Statement for ConstructLCSEasy

### Problem Statement

A string S is a subsequence of a string T if we can obtain S from T by erasing some (possibly all or none) of its characters. For example, "000" is a subsequence of "01010".

The longest common subsequence (LCS) of two strings A and B is a string C that is a subsequence of each of them and has the largest length among all strings with this property. Let f(A,B) be the length of the LCS of strings A and B. For example, we have f("101", "111000") = 2, f("101", "110011") = 3, and f("00", "1111") = 0.

You are given three small positive integers ab, bc, and ca. Please find three strings A, B, C such that:
• Each of the strings contains only the characters '0' and '1'.
• The length of each string is between 1 and 1,000, inclusive.
• f(A, B) = ab
• f(B, C) = bc
• f(C, A) = ca
Return a String formed as follows: A + " " + B + " " + C. (I.e., the returned string should contain the three strings A, B, C, separated by single spaces.)

You may assume that a solution always exist. If there are multiple solutions you may return any of them.

### Definition

 Class: ConstructLCSEasy Method: construct Parameters: int, int, int Returns: String Method signature: String construct(int ab, int bc, int ca) (be sure your method is public)

### Constraints

-ab will be between 1 and 50, inclusive.
-bc will be between 1 and 50, inclusive.
-ca will be between 1 and 50, inclusive.
-ab <= bc <= ca.

### Examples

0)

 `2` `3` `4`
`Returns: "1111 101 1010101"`
 The returned string corresponds to the following solution: A = "1111" B = "101" C = "1010101" We can easily verify that the only LCS of A and B is "11", the only LCS of B and C is "101", and the only LCS of C and A is "1111".
1)

 `4` `4` `7`
`Returns: "10101010 1011 1010101"`
 Another solution is: a = "0000111", b = "0000", c = "0000111".
2)

 `6` `7` `8`
`Returns: "10101010 1111010 110101010"`
3)

 `7` `8` `8`
`Returns: "10101010 010101101 110101001011"`
4)

 `15` `17` `19`
`Returns: "000100101101111011000 11110111010011101010 100100001010101001010101000011111"`
5)

 `50` `50` `50`
```Returns:
"11111111111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111111111"```

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This problem was used for:
Single Round Match 716 Round 1 - Division II, Level Two