Dynamic Programming has a reputation as
the hardest interview topic in CS.
The reputation disappears when you see
it visually.
The One Principle
Never calculate the same thing twice.
\`javascript
// Without DP — 1900+ calculations
function fibNaive(n) {
if (n <= 1) return n;
return fibNaive(n-1) + fibNaive(n-2); // recalculates everything
}
// With DP — 16 calculations
const memo = {};
function fibDP(n) {
if (n <= 1) return n;
if (memo[n]) return memo[n]; // instant lookup
memo[n] = fibDP(n-1) + fibDP(n-2);
return memo[n];
}
`\
The Numbers
fibNaive(15): 1946 function calls
fibDP(15): 16 unique calculations
Same answer. 1900 vs 16.
Two Properties to Identify DP
Overlapping subproblems — same smaller
problems appear multiple times. Check:
does fib(10) appear more than once?
Optimal substructure — optimal solution
builds from optimal subproblems. Check:
does fib(15) depend on optimal fib(14)?
Both true for Fibonacci. Both true for
most DP interview problems.
Watch It
What Is Next
This is Video 10 — the final algorithm
in the series. Next: AI and Machine
Learning visualized the same way.
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