Problem context and objectives
Mission briefing
Dungeon strategy engineer · A robot must cross a tiled dungeon
Store enough solved tile states to plan the complete route: The Balloon Vault.
A greedy step can trap the robot; recomputing every route is too expensive.
How you win
- 1Recognize when Burst balloons interval DP matches the clues
- 2Keep this true after every move: dp[left][right] is the maximum coins from bursting only balloons strictly between the boundaries
- 3Reach the result within O(n cubed) time and O(n squared) space
Rules and pressure
- Target cost: O(n cubed) time and O(n squared) space
- State rule: dp[left][right] is the maximum coins from bursting only balloons strictly between the boundaries
Lesson 1 of 3
Live algorithm trace
Burst balloons interval DP
Complete execution1 of 5
1
left
3
1
5
8
1
right
Pad the original values with permanent boundary ones.
1
pad values with boundary ones2
grow open interval widths3
try every last balloon k4
coins = left boundary * k * right boundary5
add solved left and right intervals6
keep the maximum and return full intervalpadded = [1,3,1,5,8,1]
Truth to preserve / Cost target
Truth to preserve
dp[left][right] is the maximum coins from bursting only balloons strictly between the boundaries
Cost target
O(n cubed) time and O(n squared) space
Choosing a first balloon changes its neighbors unpredictably. Choosing the final balloon inside an interval fixes both boundary multipliers, splitting the remaining work into independent left and right intervals.
Your call · What should guide every step of this algorithm?