Divide and conquer - minor addition to preconditions

omkarbajaj073 · omkarbajaj073 · commit 75f32b0c87a5 · 2022-04-27T17:13:52.000+05:30
diff --git a/src/dynamic_programming/divide-and-conquer-dp.md b/src/dynamic_programming/divide-and-conquer-dp.md
@@ -4,8 +4,8 @@ Divide and Conquer is a dynamic programming optimization.
 
 ### Preconditions
 Some dynamic programming problems have a recurrence of this form: $$dp(i, j) =
-\min_{0 \leq k \leq j} \\{ dp(i - 1, k - 1) + C(k, j) \\}$$ Where $C(k, j)$ is a cost
-function and $dp(i, j) = 0$ when $j \lt 0$.
+\min_{0 \leq k \leq j} \\{ dp(i - 1, k - 1) + C(k, j) \\}$$, where $C(k, j)$ is a cost
+function and $dp(i, j) = 0$ when $j \lt 0$. Further, $C(i, j)$ must satisfy the quadrangle inequality, i.e., $C(b, c) \leq C(a, d)$ for all $a \leq b \leq c \leq d$.
 
 Say $0 \leq i \lt m$ and $0 \leq j \lt n$, and evaluating $C$ takes $O(1)$
 time. Then the straightforward evaluation of the above recurrence is $O(m n^2)$. There
