Jump Game II

Jump Game II

You are given a 0-indexed array of integers nums of length n. You are initially positioned at nums[0].

Each element nums[i] represents the maximum length of a forward jump from index i. In other words, if you are at nums[i], you can jump to any nums[i + j] where:

• 0 <= j <= nums[i], and
• i + j < n

Return the minimum number of jumps to reach nums[n - 1].

The test cases are generated such that you can always reach nums[n - 1].

Examples

Example 1:

Input: nums = [2, 3, 1, 1, 4]
Output: 2
Explanation: The minimum number of jumps to reach the last index is 2.
  Jump 1 step from index 0 to 1, then 3 steps to the last index.

Example 2:

Input: nums = [2, 3, 0, 1, 4]
Output: 2
Explanation: Jump 1 step from index 0 to 1, then 3 steps to the last index.

Example 3:

Input: nums = [1]
Output: 0
Explanation: You are already at the last index. No jumps needed.

Constraints

• 1 <= nums.length <= 10^4
• 0 <= nums[i] <= 1000
• It is guaranteed that you can reach nums[n - 1].

Expected Complexity

• Time: O(n)
• Space: O(1)