- 1
Read Up, Read Left
DP goes 2D: each cell combines its UP and LEFT neighbors, the first row and column seed the table, and row-major fill delivers the answer to the far corner.
Multiple choice - 2
Unique Paths
A robot walks right/down across an m x n grid — every path's last move enters from UP or LEFT, so dp[i][j] = dp[i-1][j] + dp[i][j-1] counts them all.
Complete codeDebugMultiple choiceTrace - 3
Unique Paths II
Drop obstacles into the grid: a blocked cell counts 0 paths, and — the trap — edge cells AFTER an obstacle become unreachable too.
Complete codeDebugMultiple choiceTrace - 4
Minimum Path Sum
Minimization on the counting skeleton: dp[i][j] = grid[i][j] + min(up, left), edge rows and columns accumulate instead of counting 1s, and the corner holds the cheapest path.
Complete codeDebugMultiple choiceTrace - 5
Triangle
The bottom-up collapse: seed dp with the last row, fold each row upward with dp[j] = t[i][j] + min(dp[j], dp[j+1]), and the whole triangle converges to a single answer at dp[0] — no ragged-edge special cases.
Complete codeMultiple choiceTrace - 6
Count Square Submatrices
One cell, three witnesses: dp[i][j] = side of the largest all-ones square ending at (i,j) = min(up, left, diagonal) + 1 — and summing every dp value counts every square exactly once.
Complete codeDebugMultiple choiceTrace - 7
Grid DP CheckpointCheckpoint
No new concepts — carry the island's grid moves onto unseen ground: values falling with three parents, two robots whose harvests must be planned jointly, a dungeon that yields only to backward filling, and a square allowed one repaired hole.
Complete codeMultiple choiceTrace - 8
Grid DP ReviewReview
Mixed recap of the island: the up/left dependency shape and every fill order it permits, base edges as counts of one versus accumulated costs, obstacle zeroing and its shadow, the bottom-up collapse that tames ragged shapes, min-of-three square geometry, and the rolling row that shrinks O(mn) space to one row.
Code orderMultiple choice - 9
Boss: Maximal SquareBoss
The island's final test: the largest all-ones square in a binary matrix. One min-of-three recurrence certifies every square at once — and the boss's traps are trusting only two neighbors and returning the side when the problem demands the area.
Complete codeDebugCode orderMultiple choiceTrace
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