The given Python code defines a method, `jump`, inside a...

The given Python code defines a method, jump, inside a class Solution. The method computes the minimum number of jumps required to reach the last index of a given list, nums, starting from the first index. Each element in the array, nums[i], represents the maximum number of indices that can be jumped forward from that position.

Here’s a detailed step-by-step explanation of what the code does:

Input:

• nums: A list of non-negative integers, where each value represents the maximum range you can jump forward from that position.

Algorithm Explanation:

1. Initialization:

   • n: The length of the array nums.
   • jumps: A counter to track the number of jumps made, initialized to 0.
   • curr_end: Marks the farthest point that can be reached with the current number of jumps, initialized to 0.
   • farthest: Tracks the farthest point that can be reached while iterating through the array, initialized to 0.

2. Iterating through the array:

   • The loop runs from i = 0 to n-2 (not including the last element) because you don't need to jump beyond the last index.
   • For each index i, the code updates farthest to the maximum possible position that can be reached (max(farthest, i + nums[i])).

3. Making a new jump:

   • If the current index i reaches curr_end (the current jump boundary), a jump is required:
     • Increment jumps as a new jump is made.
     • Update curr_end to the value of farthest, which represents the next farthest point reachable.
   • This ensures that the minimum number of jumps are used.

4. Return the result:

   • The method finally returns jumps, the minimum number of jumps required to reach the last index.

Key Observations:

• This approach uses a greedy algorithm to minimize the number of jumps.
• It updates curr_end (current jump boundary) only when necessary, ensuring the smallest possible number of jumps.

Complexity:

• Time Complexity: O(n), where n is the length of the array. Each index is processed once.
• Space Complexity: O(1), as only a constant amount of extra space is used.

Example:

Input:

nums = [2, 3, 1, 1, 4]

Execution:

1. Initial state: jumps = 0, curr_end = 0, farthest = 0.
2. Iterate through nums:
   • i = 0: Update farthest = max(0, 0 + 2) = 2.
     • Since i == curr_end, increment jumps to 1 and update curr_end = 2.
   • i = 1: Update farthest = max(2, 1 + 3) = 4.
     • No jump yet because i != curr_end.
   • i = 2: Update farthest = max(4, 2 + 1) = 4.
     • Since i == curr_end, increment jumps to 2 and update curr_end = 4.
3. End the loop, and return jumps = 2.

Output:

2

This means it takes a minimum of 2 jumps to reach the end of the array [2, 3, 1, 1, 4].

In Summary:

The code calculates the minimum number of jumps needed to reach the last index of the nums list using a greedy approach.