Find the maximum sum path in a triangle (bottom-up DP)?

Short answer: public int MaximumTotal(IList<IList<int>> triangle) { int n = triangle.Count; int[] dp = new int[n]; for (int i = 0; i < n; i++) dp[i] = triangle[n - 1][i]; for (int layer = n - 2; layer >= 0; layer--) { for (int i = 0; i <= layer; i++) { dp[i] = triangle[layer][i] + Math.Max(dp[i], dp[i + 1]); } } return dp[0]; } Explanation: Start from bottom row, keep updating max path sums up to the top.

Example code

public int MaximumTotal(IList<IList<int>> triangle) {
int n = triangle.Count;
int[] dp = new int[n];
for (int i = 0; i < n; i++) dp[i] = triangle[n - 1][i];
for (int layer = n - 2; layer >= 0; layer--) {
for (int i = 0; i <= layer; i++) {
dp[i] = triangle[layer][i] + Math.Max(dp[i], dp[i + 1]);
}
}
return dp[0];
} Explanation: Start from bottom row, keep updating max path sums up to the top.

Real-world example (ShopNest)

In coding rounds, state complexity aloud, write a clear ShopNest-flavored example (orders, carts), then handle edge cases (empty list, null, overflow).

Say this in the interview

1. Define — one clear sentence (the short answer above).
2. Example — relate it to a project like ShopNest or your real work.
3. Trade-off — when you would not use it.