Problem context and objectives
Mission briefing
Puzzle systems engineer · A game mechanic is behaving incorrectly
Treat each jump as one breadth layer: The Fewest Leaps.
Brute force may pass the demo but fail when the world fills with players.
How you win
- 1Recognize when Greedy jump frontier matches the clues
- 2Keep this true after every move: currentEnd is the farthest index reachable with `jumps` moves and farthest is the next layer boundary
- 3Reach the result within O(n)
Rules and pressure
- Target cost: O(n)
- State rule: currentEnd is the farthest index reachable with `jumps` moves and farthest is the next layer boundary
Lesson 1 of 3
Live algorithm trace
Greedy jump frontier
Complete execution1 of 6
Before jumping, only index 0 belongs to the current launch layer.
1
jumps = 0; currentEnd = 02
farthest = max(farthest, i + nums[i])3
when i reaches currentEnd4
jumps += 15
currentEnd = farthest6
stop once the end is coveredjumps = 0currentEnd = 0farthest = 0
Truth to preserve / Cost target
Truth to preserve
currentEnd is the farthest index reachable with `jumps` moves and farthest is the next layer boundary
Cost target
O(n)
All indices reachable with the current jump form one range. Scan that range for the farthest next reach, then commit one jump only when the current range ends.
Your call · What should guide every step of this algorithm?