0045__jump_game_2.py

"""
LeetCode link: https://leetcode.com/problems/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 reach
nums[n - 1].

## 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

## Constraints

* 1 <= nums.length <= 10^4
* 0 <= nums[i] <= 1000
"""
from typing import List
from unittest import TestCase


class Solution(TestCase):
    def test_example_1(self):
        self.assertEqual(2, self.jump([2, 3, 1, 1, 4]))

    def test_example_2(self):
        self.assertEqual(2, self.jump([2, 3, 0, 1, 4]))

    def jump(self, nums: List[int]) -> int:
        dp = [0] * len(nums)
        for i in range(len(nums) - 2, -1, -1):
            if nums[i] > 0:
                dp[i] = 1 + min(dp[i + 1:i + nums[i] + 1])
            else:
                dp[i] = len(nums) + 1

        return dp[0]