From 8c240a639d1c86bb1b1aeebe747fb428ad753190 Mon Sep 17 00:00:00 2001 From: Thomas Zeger Date: Sun, 5 Jan 2025 10:06:11 -0500 Subject: [PATCH] Fix sentence structure in fft.md --- src/algebra/fft.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/algebra/fft.md b/src/algebra/fft.md index 2e6532558..38ed620a5 100644 --- a/src/algebra/fft.md +++ b/src/algebra/fft.md @@ -97,7 +97,7 @@ It is easy to see that $$A(x) = A_0(x^2) + x A_1(x^2).$$ -The polynomials $A_0$ and $A_1$ are only half as much coefficients as the polynomial $A$. +The polynomials $A_0$ and $A_1$ have only half as many coefficients as the polynomial $A$. If we can compute the $\text{DFT}(A)$ in linear time using $\text{DFT}(A_0)$ and $\text{DFT}(A_1)$, then we get the recurrence $T_{\text{DFT}}(n) = 2 T_{\text{DFT}}\left(\frac{n}{2}\right) + O(n)$ for the time complexity, which results in $T_{\text{DFT}}(n) = O(n \log n)$ by the **master theorem**. Let's learn how we can accomplish that.