Continue after the algorithm foundations and advanced patterns. Compare grid costs, required health, subsequence counts, interval boundaries, remainders, and paired paths. Burst Balloons is premium; the other milestones are free. Egg Drop is optional stretch practice.
0 of 7 milestones completed
0 of 2 completed
Start with a cheapest-arrival state, then add value-dependent move costs. A geometric neighbor rule and a cost rule are separate parts of the recurrence; greedy selection of the smallest next cell is not enough.
0 of 1 completed
A good final path sum does not guarantee survival along its prefixes. Define the health needed before entering a room, compare the remaining routes, and clamp the requirement to at least one.
0 of 1 completed
Separate taking a matching character from skipping it. Count source-index choices, not distinct resulting strings. When compressing a prefix table, update in the direction that prevents reusing the same character and account for large intermediate counts.
0 of 1 completed
Choosing the first balloon changes its neighbors. Choosing the last balloon inside fixed boundaries separates two independent subintervals. Write that recurrence before deciding between a bottom-up table and memoization. This milestone requires Pro.
0 of 1 completed
At the same cell, equal sum remainders have the same future divisibility. Keep a count for each remainder, include both endpoints, and distinguish the sum modulus k from the answer modulus 1000000007.
0 of 1 completed
Reverse the return trip into a second forward path. Both travelers take the same number of steps, so one coordinate is determined by the others. Count a shared cell once and preserve an impossible-state sentinel until the final result.
Stretch: replace the minimum-moves state with floors covered by a move budget. Compare it with the memoized first-drop recurrence and explain why both outcomes need a budget.