# Fibonacci with dynamic programming

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Section titled Problem

## Problem

The Fibonacci numbers, commonly denoted `F(n)` form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from `0` and `1`. That is,

``````F(0) = 0, F(1) = 1
F(n) = F(n - 1) + F(n - 2), for n > 1.
``````

Given `n`, calculate `F(n)`.

Example 1:

``````Input: n = 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
``````

Example 2:

``````Input: n = 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
``````

Example 3:

``````Input: n = 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
``````

Constraints:

• `0 <= n <= 30`
Section titled Solution

## Solution

Section titled Recursion

### Recursion

• Find a base recursive call, in this case is condition where input equals with 0 will return 0 and 1 will return 1
• Then from the description above, call the recursive with F(n-1) + F(n-2)
``````
func fibonacci(n int) int{
if n==0 || n==1{
return n
}

return fibonacci(n-1)+fibonacci(n-2)
}``````
Section titled Dynamic%20programming

### Dynamic programming

• First step similar with recursive, early return if n equals 0 or 1
• Use memoize to compose calculation
``````func fib(n int) int {
if n==0 || n==1{
return n
}

dp:=make([]int, n+1)
dp[0]=0
dp[1]=1
for i:=2;i<n+1;i++{
dp[i] = dp[i-2]+dp[i-1]
}

return dp[n]
}``````

But let’s remove unnecessary array

``````func fib(n int) int {
if n==0 || n==1{
return n
}

a, b, ans:= 0, 1, 0

for i:= 1; i < n; i++{
ans = a + b;
a = b;
b = ans;
}

return ans;
}``````
go puzzle snippets cp