Minimum Cost Path in Grid with Teleportation | 3D DP + Teleport Optimization | 28 Jan 2026
LeetCode POTD (28th Jan 2026)
Educational Insight
The "Minimum Cost Path in Grid with Teleportation Allowed" problem is a rich example of stateful DP on grids, where each cell’s cost depends not only on position but also on how many teleports you have left.
A naive recursion over all teleport destinations explodes, so the accepted solution relies on memoized / bottom‑up DP combined with optimized teleport transitions over preprocessed cell groups.
Key Implementation Details
Define dp[i][j][t] as the minimum cost to reach (i, j) using exactly t teleports, initialized with large values.
Transitions: pay grid cost for right/down moves, and sometimes use a teleport (t → t+1) to jump to cells with value ≤ current.
Precompute data structures that let you jump/relax multiple teleport destinations efficiently instead of scanning the entire grid.
Answer is min over dp[n−1][n−1][t] for all allowed teleport counts.
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