```
public class JumpGameV {
public int jump(int[] nums) {
if (nums == null || nums.length == 0) return 0;
int jumps = 0;
int currentEnd = 0;
int farthest = 0;
for (int i = 0; i < nums.length - 1; i++) {
// Update the farthest point that can be reached
farthest = Math.max(farthest, i + nums[i]);
// If we have reached the end of the current jump range
if (i == currentEnd) {
jumps++;
currentEnd = farthest;
}
}
return jumps;
}
}
```

### Key Parts of the Code
- `farthest = Math.max(farthest, i + nums[i]);`: This line updates the farthest point that can be reached from the current index.
- `if (i == currentEnd)`: This condition checks if the current index has reached the end of the current jump range, prompting an increment in the jump count.
## Complexity Analysis
- **Time Complexity**: O(n), where n is the length of the array. The array is traversed once.
- **Space Complexity**: O(1), as no additional space proportional to the input size is used.
## Edge Cases
- **Single Element Array**: The output should be 0 as no jumps are needed.
- **Unreachable End**: Arrays where the end cannot be reached should be handled gracefully.
### Example Edge Cases
- Input: `[0]`, Output: `0`
- Input: `[1, 0, 1]`, Output: `1`
## Testing
To test the solution comprehensively:
- Use a variety of test cases, including simple, complex, and edge cases.
- Example test cases:
- `[2, 3, 1, 1, 4]` should return `2`.
- `[1, 1, 1, 1]` should return `3`.
- `[0]` should return `0`.
## Thinking and Problem-Solving Tips
- Break down the problem into smaller parts and understand the role of each element in the array.
- Practice similar problems to improve problem-solving skills and familiarity with greedy algorithms.
## Conclusion
Understanding and solving the Jump Game V problem helps in developing skills in greedy algorithms and dynamic programming. Practice and exploration of similar problems can further enhance problem-solving abilities.
## Additional Resources
- [LeetCode Problems](https://leetcode.com/problemset/all/)
- [GeeksforGeeks Greedy Algorithms](https://www.geeksforgeeks.org/greedy-algorithms/)
- [Introduction to Algorithms by Cormen et al.](https://mitpress.mit.edu/books/introduction-algorithms)
By mastering this problem, you can improve your algorithmic thinking and be better prepared for coding interviews and competitive programming. Happy coding!