Perfect Squares - Implementation (The code)

Here's the dynamic programming solution:

function numSquares(n)
    dp := array of size (n + 1) filled with infinity
    dp[0] := 0
    for i from 1 to n
        j := 1
        while j * j ≤ i
            dp[i] := min(dp[i], dp[i - j * j] + 1)
            j := j + 1
    return dp[n]

You build up $dp$ from $0$ to $n$. For each $i$, you try all perfect squares $j^2 \leq i$ and take the minimum. The answer is $dp[n]$.