Determine reachability and minimum jumps

Given an array of non-negative integers nums of length n, where nums[i] is the maximum number of steps you can move forward from index i: ( 1) Determine whether you can reach index n-1 starting from index 0. ( 2) If reachable, compute the minimum number of jumps required to reach index n-1. Aim for an O(n) time, O( 1) extra space solution if possible. Explain the algorithm, prove its correctness, analyze time/space complexity, and discuss edge cases (e.g., zeros that block progress, n=1, very large jump values, and cases where the last index is unreachable).