Minimum Jumps to Reach the End

Problem Given an array nums[] where nums[i] is the maximum forward jump length from index i, return the minimum number of jumps needed to reach the last index. You are guaranteed to be able to reach it.

Input / Output

• Input: an integer array nums[].
• Output: the minimum number of jumps from index 0 to index n-1.

Constraints

• 1 <= nums.length <= 10^4, 0 <= nums[i] <= 1000.
• The last index is always reachable.
• Input is large enough that materialising the implied graph and traversing every edge is too slow — the intended solution is linear.

Example

• nums = [2,3,1,1,4] → 2. Jump 0→1, then 1→4.
• Tricky case: nums = [2,3,0,1,4] → 2. The naive "jump as far as possible" sends you 0→2, a near dead end; the correct move is 0→1, the position within reach that opens up the furthest subsequent reach.