Update Lagrange.mdx

Author: A1exL1ang

content/6_Advanced/Lagrange.mdx

@@ -66,7 +66,7 @@ because we either begin a new subarray or we continue an existing subarray.
 
 Let $v$ be the maximal achievable sum with $\lambda$ penalty and $c$ be the number of subarrays used to achieve $v$. Then the **maximal possible sum achievable if we use exactly $c$ subarrays is $v+\lambda c$**. Note that we add $\lambda c$ to undo the penalty.
 
-Our goal is to find some $\lambda$ such that $c=k$. As we increase $\lambda$, it makes sense for $c$ to decrease since we are penalizing subarrays more. Thus, we can try to binary search for $\lambda$ to make $c=k$ and set our answer to be $v+\lambda c$ at the optimal $\lambda$.
+Our goal is to find some $\lambda$ such that $c=K$ (assuming $K$ is at most the number of positive elements). As we increase $\lambda$, it makes sense for $c$ to decrease since we are penalizing subarrays more. Thus, we can try to binary search for $\lambda$ to make $c=K$ and set our answer to be $v+\lambda c$ at the optimal $\lambda$.
 
 This idea almost works but there are still some very important caveats and conditions that we have not considered.