# 1. Introduction

"Jump Game II" is a dynamic and engaging problem that tests one's ability in array manipulation and optimal decision-making. The problem involves finding the minimum number of jumps needed to reach the end of an array, where each element represents the maximum jump length from that position. This challenge is great for understanding greedy algorithms and dynamic programming concepts.

## Problem

Given a 0-indexed array of integers nums of length n, where you start at the first element, each element nums[i] represents the maximum length of a forward jump from index i. The task is to return the minimum number of jumps required to reach the last element in the array. It is guaranteed that the end of the array can be reached.

# 2. Solution Steps

1. Initialize a variable to keep track of the current end of the jump, another for the farthest reachable point, and a jump counter.

2. Iterate through the array, excluding the last element.

3. Update the farthest reachable point at each step.

4. If you reach the current end of the jump, increase the jump counter and update the end of the jump to the farthest point reached.

5. Continue the process until you reach the end of the array.

6. Return the jump counter as the result.

# 3. Code Program

``````def jump(nums):
jumps, current_end, farthest = 0, 0, 0

for i in range(len(nums) - 1):
farthest = max(farthest, i + nums[i])
if i == current_end:
jumps += 1
current_end = farthest

return jumps

# Example Usage
print(jump([2,3,1,1,4]))
print(jump([2,3,0,1,4]))
``````

```2
2
```

### Explanation:

1. Iterative Approach: The function iterates through the array to determine the minimum jumps.

2. Farthest Reach: At each step, it calculates the farthest point that can be reached.

3. Jump Update: When the current end of a jump is reached, the jump count is incremented.

4. End of Jump Update: The end of the current jump is updated to the farthest point reached so far.

5. Greedy Algorithm: This approach uses a greedy strategy to always jump to the farthest reachable point.

6. Result: The function returns the minimum number of jumps needed to reach the end of the array.