Bottom-Up Build

Tabulation

Tabulation is DP done in dependency order. You fill the table from base cases upward so every state is available when needed.

Orderdeterministic

Storagetable

The “frontier” is the next state whose dependencies are already computed.

Tabulation avoids call-stack overhead and makes progress easy to inspect.

DP Table

dp[0] = dp[0] + dp[0]

dp[0]0

dp[1]?

dp[2]?

dp[3]?

dp[4]?

dp[5]?

dp[6]?

dp[7]?

dp[8]?

dp[9]?

dp[10]?