Memoization in action
See how values propagate
Break down complexity
Build from smaller solutions
Select a problem and click "Visualize DP" to see the table being filled.
Build up solutions from smallest subproblems - often more efficient than top-down.
// Fibonacci with tabulation
function fib(n) {
const dp = [0, 1];
for (let i = 2; i <= n; i++) {
dp[i] = dp[i-1] + dp[i-2];
}
return dp[n];
} // O(n) time, O(n) spaceWithout memoization, you'll solve the same subproblems repeatedly.
// Without memoization - O(2^n)!
function fib(n) {
if (n <= 1) return n;
return fib(n-1) + fib(n-2);
}
// fib(5) recalculates fib(3) twice!Look for: 1) Optimal substructure - optimal solution uses optimal sub-solutions. 2) Overlapping subproblems - same subproblems solved multiple times. Keywords like "minimum", "maximum", "count ways", "longest" often indicate DP.
Top-down (memoization) is often easier to write and only computes needed subproblems. Bottom-up (tabulation) avoids recursion overhead and can be more space-efficient with optimization.
If dp[i] only depends on dp[i-1] and dp[i-2], you only need to store 2 values instead of the full array. This reduces O(n) space to O(1).