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What is tabulation?

Fill a table bottom-up to solve sub-problems.

What is tabulation?

Tabulation solves subproblems by filling a table bottom-up.

Loops replace recursion; each cell is a subproblem's result.

Tabulation is the bottom-up counterpart of memoization; no stack overflow risk.

Bottom-up approach

Tabulation solves the smallest subproblems first, then uses them to build larger ones.

There is no recursion; all computation happens in a loop.

This approach prevents stack overflow on deep recursion; it suits large n values.

Practice Fibonacci tabulation

Write fib_tab(n). Compute Fibonacci with a table. Print 55 with print(fib_tab(10)).

Starter code

solution.py
def fib_tab(n):
    # Fibonacci tabulation

Sample solution

solution.py
def fib_tab(n):
    # Fibonacci tabulation
    if n <= 1:
        return n
    dp = [0] * (n + 1)
    dp[1] = 1
    for i in range(2, n + 1):
        dp[i] = dp[i - 1] + dp[i - 2]
    return dp[n]
print(fib_tab(10))

Expected output

55

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Which direction does tabulation work in?

  • Top-down
  • Bottom-up Correct answer
  • From sides
  • Random

Explanation: Bottom-up.

2 Table structure

Question 
dp = [0] * (____ + 1)
Answer 
dp = [0] * (n + 1)

Explanation: n is right.

3 What is tabulation: match the terms

Term Meaning
tabulation Bottom-up
table Table
loop Loop
no recursion No recursion

All lessons in Advanced

1 DP - Memoization

  1. What is memoization?
  2. Fibonacci memoization
  3. Dict-based cache
  4. Summary - Memoization

2 DP - Tabulation

  1. What is tabulation?
  2. Building the table
  3. Fibonacci tabulation
  4. Summary - Tabulation

3 LCS

  1. LCS definition
  2. DP table
  3. Backtracking the table
  4. Summary - LCS

4 Knapsack

  1. Knapsack problem
  2. 0/1 knapsack DP
  3. Decision table
  4. Summary - Knapsack

5 DP project

  1. Project: Overview
  2. Cost table
  3. DP solution
  4. Print the result

6 Matrix chain

  1. Multiplication order
  2. DP table
  3. Split point
  4. Summary - Matrix chain

7 Floyd-Warshall

  1. All pairs
  2. Triple loop
  3. Table update
  4. Summary - Floyd-Warshall

8 Dijkstra

  1. Single source
  2. Priority queue
  3. Relaxation
  4. Summary - Dijkstra

9 Bellman-Ford

  1. Negative weights
  2. Edge relaxation loop
  3. Negative cycle
  4. Summary - Bellman-Ford

10 Kruskal

  1. Minimum spanning tree
  2. Edge sorting
  3. Cycle check
  4. Summary - Kruskal

11 Prim

  1. Prim idea
  2. Priority queue
  3. Visited set
  4. Summary - Prim

12 Topological sort

  1. Dependency order
  2. DFS-based sort
  3. Kahn algorithm
  4. Summary - Topological sort

13 Union-find, trie, segment tree

  1. Union-find
  2. Trie
  3. Segment tree
  4. Summary - Advanced structures

14 Advanced final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4