1. Blocked unknowns
Infinity prevents invalid directions from winning.
const dp = Array(cols).fill(Infinity)Typorithm · medium
Minimum Path Sum
▷ Interactive algorithm labminimum-path-sum-dpdynamic-programminggridminimization
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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 Minimum Path Sum
Dynamic Programming
Minimum Path Sum chooses the cheaper path to each grid cell from top or left.
Each cell has a path cost.
The transition reads top and left because moves are right/down.
A one-row dp array stores top and current-left costs.
Preparing algorithm lab…
01
State: minimum cost to current cell.
02
Invalid left edge uses Infinity.
03
Transition: cell + min(top, left).
04
Space O(cols).
function minPathSum(grid) {
const rows = grid.length;
const cols = grid[0].length;
const dp = Array(cols).fill(Infinity);
dp[0] = 0;
for (let row = 0; row < rows; row++) {
for (let col = 0; col < cols; col++) {
dp[col] = grid[row][col] + Math.min(dp[col], col > 0 ? dp[col - 1] : Infinity);
}
}
return dp[cols - 1];
}Read the implementation
Connect each part of the code to the concept before you type.
2. Start before first cell
The first cell adds to zero cost.
dp[0] = 03. Min top/left
Current cost plus cheaper of top or left.
grid[row][col] + Math.min(dp[col], col > 0 ? dp[col - 1] : Infinity)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.