Minimum length of jumps to avoid given array of obstacles

We are given coordinates of obstacles on a straight line. We start jumping from point 0, we need to reach end avoiding all obstacles. Length of every jump has to be same (For example, if we jump from 0 to 4, then we must make next jump from 4 to 8). We need to find the minimum length of jump so that we can reach end and we avoid all obstacles.

Examples:

```Input : obs[] = [5, 3, 6, 7, 9]
Output : 4
Obstacles are at points 3, 5, 6, 7 and 9
We jump from 0 to 4, then 4 to 8, then 4
to 12. This is how we reach end with jumps
of length 4. If we try lower jump lengths,
we cannot avoid all obstacles.

Input : obs[] = [5, 8, 9, 13, 14]
Output : 6
```

*

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We insert locations of all obstacles in a hash table. We also find maximum value of obstacle. Then we try all possible jump sizes from 1 to maximum. If any jump size leads to a obstacle, we do not consider that jump.

Java

 `// Java program to find length of a jump ` `// to reach end avoiding all obstacles ` `import` `java.util.*; ` ` `  `public` `class` `obstacle { ` `    ``static` `int` `avoidObstacles(``int``[] obs) ` `    ``{ ` `        ``// Insert all array elements in a hash table ` `        ``// and find the maximum value in the array ` `        ``HashSet hs = ``new` `HashSet(); ` `        ``int` `max = obs[``0``]; ` `        ``for` `(``int` `i=``0``; i max)  ` `                ``return` `i;          ` `        ``} ` ` `  `        ``return` `max+``1``; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `a[] = ``new` `int``[] { ``5``, ``3``, ``6``, ``7``, ``9` `}; ` `        ``int` `b = avoidObstacles(a); ` `        ``System.out.println(b); ` `    ``} ` `} `

Python3

 `# Python3 program to find length of a jump ` `# to reach end avoiding all obstacles ` `def` `avoidObstacles(obs): ` `     `  `    ``# sort the list in ascending order ` `    ``obs ``=` `sorted``(obs) ` `     `  `    ``# set jump distance to 1 ` `    ``jump_dist ``=` `1` `     `  `    ``# flag to check if current jump distance  ` `    ``# hits an obstacle ` `    ``obstacle_hit ``=` `True` ` `  `    ``while``(obstacle_hit): ` `         `  `        ``obstacle_hit ``=` `False` `        ``jump_dist ``+``=` `1` `         `  `        ``# checking if jumping with current length ` `        ``# hits an obstacle ` `        ``for` `i ``in` `range``(``0``, ``len``(obs)): ` `            ``if` `obs[i] ``%` `jump_dist ``=``=` `0``: ` `                 `  `                ``# if obstacle is hit repeat process ` `                ``# after increasing jump distance ` `                ``obstacle_hit ``=` `True` `                ``break` ` `  `    ``return` `jump_dist ` `     `  `# Driver Code ` `a ``=` `[``5``, ``3``, ``6``, ``7``, ``9``] ` `b ``=` `avoidObstacles(a) ` `print``(b) ` ` `  `# This code is contributed by ViratJoshi `

C#

 `// C# program to find length of a jump ` `// to reach end avoiding all obstacles ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `public` `class` `obstacle  ` `{ ` `    ``static` `int` `avoidObstacles(``int``[] obs) ` `    ``{ ` `        ``// Insert all array elements in a hash table ` `        ``// and find the maximum value in the array ` `        ``HashSet<``int``> hs = ``new` `HashSet<``int``>(); ` `        ``int` `max = obs[0]; ` `        ``for` `(``int` `i = 0; i < obs.Length; i++) ` `        ``{ ` `            ``hs.Add(obs[i]); ` `            ``max = Math.Max(max, obs[i]); ` `        ``} ` ` `  `        ``// checking for every possible length which ` `        ``// yield us solution ` `        ``for` `(``int` `i = 1; i <= max; i++)  ` `        ``{ ` `            ``int` `j; ` `            ``for` `(j = i; j <= max; j = j + i) ` `            ``{ ` ` `  `                ``// if there is obstacle, break the loop. ` `                ``if` `(hs.Contains(j))  ` `                    ``break``; ` `            ``} ` ` `  `            ``// If above loop did not break ` `            ``if` `(j > max)  ` `                ``return` `i;          ` `        ``} ` `        ``return` `max+1; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]a = ``new` `int``[] { 5, 3, 6, 7, 9 }; ` `        ``int` `b = avoidObstacles(a); ` `        ``Console.WriteLine(b); ` `    ``} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```4
```

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