Given a 0-indexed array nums where nums[i] represents the maximum jump length from index i, return the minimum number of jumps to reach the last index.
You can assume you can always reach the last index.
Example
Input
2,3,1,1,4
Output
2
Reasoning
We start at index 0 with a jump length of 2, allowing us to reach indices 1 or 2.
From index 1, we have a jump length of 3, which enables us to reach indices 2, 3, or 4, but we can only reach index 4 in two jumps if we first jump to index 1 and then to index 4.
The optimal path is 0→1→4, resulting in a total of 2 jumps.
This path is the minimum number of jumps required to reach the last index, so the output is 2.
The Jump Game II problem is a classic example of a Dynamic Programming problem. Dynamic Programming is a method for solving complex problems by breaking them down into simpler subproblems, solving each subproblem only once, and storing the solutions to subproblems to avoid redundant computation. In the context of this problem, we need to understand how to model the problem as a sequence of decisions, where each decision represents a jump from one index to another. We also need to understand the concept of optimal substructure, which means that the optimal solution to the overall problem can be constructed from the optimal solutions of its subproblems.
The problem can be viewed as a graph traversal problem, where each index in the array represents a node, and the maximum jump length from each index represents the edges between nodes. We need to find the shortest path from the starting node (index 0) to the ending node (the last index). This requires understanding of graph theory and how to apply it to solve the problem. Additionally, we need to consider the greedy approach, which involves making the locally optimal choice at each step with the hope that it will lead to a globally optimal solution.
To solve this problem, we need to have a good understanding of array manipulation and iteration techniques, as we will be iterating over the array and updating the minimum number of jumps to reach each index. We also need to be familiar with conditional statements and looping constructs, as we will be using them to implement the logic of the solution.
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