1. First row
Every cell in the first row has one path.
const dp = Array(n).fill(1)Typorithm · medium
Unique Paths
▷ Interactive algorithm labunique-paths-dpdynamic-programminggridcountingspace-optimized
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Full lesson · 8 learning steps Open any exercise for focused practice
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Step 1 of 8 · intro card
Learn Unique Paths
Dynamic Programming
Unique Paths counts grid routes using the fact that each cell is reached from top or left.
The robot only moves right or down.
Each cell adds paths from top and left.
A single row array stores the previous row plus current left value.
Preparing algorithm lab…
01
State: paths to current column.
02
Base: first row and column have one path.
03
Transition: top + left.
04
Space O(n).
function uniquePaths(m, n) {
const dp = Array(n).fill(1);
for (let row = 1; row < m; row++) {
for (let col = 1; col < n; col++) {
dp[col] += dp[col - 1];
}
}
return dp[n - 1];
}Read the implementation
Connect each part of the code to the concept before you type.
2. Process rows
Start after the first row base case.
for (let row = 1; row < m; row++)3. Top plus left
Current paths are from top plus left.
dp[col] += dp[col - 1]A complete learning loop
01
Understand
Read the concept map and follow the code breakdown.
02
Reconstruct
Type the implementation, repair mistakes and work through every recall exercise.
03
Verify
Use the final check without hints; revisit weak concepts in short practice sessions.