30 Days of LeetCode: Day 10 - Decoding Jump Game II from LeetCode Language

Today, let's explore how to translate a LeetCode challenge from its formal language into something more digestible. Sometimes the biggest challenge is understanding what the problem is actually asking us to do; and for me, this either means overthinking what is said, or not completely understanding the directives.

The Original Challenge

Here's how LeetCode presents the problem:

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].

Let's break down why this language might be confusing:

1. "0-indexed array" - What does that mean?

2. "nums[i] represents maximum length" - Maximum of what?

3. "jump to any nums[i + j] where 0 <= j <= nums[i]" - That's a lot of mathematical notation!

4. "nums[n - 1]" - Why not just say "last position"?

The Challenge in Plain English

Think of it like a game of hopscotch where:

• You start at square one("0-indexed array")

• Each square has a number("nums[i] represents maximum length")

• That number tells you how many squares you're ALLOWED to hop forward("jump to any nums[i + j] where 0 <= j <= nums[i]")

• You want to reach the end in the fewest hops("nums[n - 1]")

Example: [2,3,1,1,4]

Copy[2] [3] [1] [1] [4]
 ^
Start

Key Points to Understand

1. "Maximum Length of Jump" means:

   • If square says 2, you can jump 1 OR 2 spaces

   • Not required to use full jump

   • Like having a limit, not a requirement

2. "0-indexed" means:

   • First position is position 0

   • Second position is position 1

   • Just how we count positions, not important for understanding

3. "Minimum number of jumps" means:

   • Find shortest path to end

   • Like finding shortest route on a map

   • Multiple paths might work, we want shortest

Common Misunderstandings

1. "I must use the exact number shown"

   • No! If it shows 3, you can jump 1, 2, OR 3 spaces

   • It's a maximum, not an exact requirement

2. "I need to check if I can reach the end"

   • No! Problem guarantees we can reach the end

   • We just need to find shortest way

3. "I should always take biggest jump possible"

   • Not necessarily!

   • Sometimes smaller jumps lead to better positions

Practical Example

Let's play it out with [2,3,1,1,4]:

1. Start at first number (2):

   • Can jump 1 or 2 spaces ahead

   • Like standing at start of hopscotch

2. If we jump to second number (3):

   • Now can jump up to 3 spaces

   • More options opened up

3. Each position gives new options:

   • Like having different paths on a map

   • Need to find quickest route

Questions to Ask Yourself

1. "From where I am now..."

   • How far can I jump?

   • What positions can I reach?

2. "For each possible landing spot..."

   • What new options does it give me?

   • Does it get me closer to goal?

3. "Among all possible paths..."

   • Which uses fewest jumps?

   • Like finding shortest route through a city

Why the Language Matters

LeetCode's formal language serves a purpose - it's precise and unambiguous. But that precision can make it hard to grasp the core concept. By translating it into familiar terms, we can:

1. Better visualize what we're trying to do

2. Think about the problem more intuitively

3. Come up with solutions based on understanding, not just parsing instructions

Conclusion

Before diving into code, take time to:

• Read the formal problem carefully

• Translate it into simple terms you understand

• Visualize it with real-world analogies

• Make sure you understand what success looks like