# Jump Game II in Python

class Solution:
def jump(self, nums: List[int]) -> int:
"""
Function to find the minimum number of jumps to reach the last index.

The function uses a greedy algorithm approach where it iteratively identifies the farthest it
can reach from the current position and makes a jump to the position that gives the maximum
reach.

Args:
nums (List[int]): List of non-negative integers representing the maximum jump length at each position.

Returns:
int: The minimum number of jumps needed to reach the last index.
"""
jumps = 0  # Number of jumps needed
current_jump_end = 0  # End of the range that we can jump to
farthest = 0  # Farthest point that we can reach

# We don't need to consider the last element in nums, as we can't jump from there
for i in range(len(nums) - 1):
# Update the farthest point we can reach
farthest = max(farthest, i + nums[i])

# If we've reached the end of the current jump,
# increase the jump count and set new current jump end to farthest
if i == current_jump_end:
jumps += 1
current_jump_end = farthest

return jumps