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ashawkey · Dec 29, 2023 · 4d9e89c · 4d9e89c
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diff --git a/docs/algorithm/advanced/final_exam_prep.md b/docs/algorithm/advanced/final_exam_prep.md
@@ -181,7 +181,6 @@ int main() {
 ```
 
 
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 ### BIT
 
 ##### apple tree
@@ -275,7 +274,6 @@ int main() {
 ```
 
 
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 ### Segment Tree
 
 ##### Balanced Lineup 
@@ -352,7 +350,6 @@ int main() {
 ```
 
 
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 ##### integers
 
 ```c++
@@ -458,7 +455,6 @@ int main() {
 ```
 
 
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 ##### kth-Number
 
 ```c++
@@ -544,7 +540,6 @@ int main() {
 ```
 
 
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 ##### Mayor's Poster
 
 ```c++
@@ -640,9 +635,6 @@ int main() {
 ```
 
 
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 ### Trie
 
 ##### Proto
@@ -736,7 +728,6 @@ int main() {
 ```
 
 
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 ### Directed Tarjan
 
 ##### popular cows
@@ -840,7 +831,6 @@ int main() {
 ```
 
 
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 ### Shortest Path
 
 ###### candies
@@ -929,7 +919,6 @@ int main() {
 ```
 
 
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 ##### currency exchange
 
 ```c++
@@ -1000,7 +989,6 @@ int main() {
 ```
 
 
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 ##### Warmholes
 
 ```c++
@@ -1075,7 +1063,6 @@ int main() {
 ```
 
 
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 ##### cow contest
 
 ```c++
@@ -1153,17 +1140,13 @@ int main() {
 ```
 
 
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 ----
 
 ### Undirected Tarjan
 
 ···
 
 
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 ### Maximum Flow
 
 ##### Alice's Chance
@@ -1425,9 +1408,6 @@ int main() {
 ```
 
 
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 ### Geometry
 
 ##### TOYS
@@ -1987,11 +1967,6 @@ int main() {
 ```
 
 
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 ### Suffix Array
 
 ##### Substrings
@@ -2112,6 +2087,3 @@ int main() {
 ```
 
 
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diff --git a/docs/algorithm/advanced/后缀数组.md b/docs/algorithm/advanced/后缀数组.md
@@ -15,7 +15,6 @@ sa[5] = 2	nana
 ```
 
 
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 ### $O(n \log n)$ Method to find SA
 
 * **j-suffix** 
@@ -68,7 +67,6 @@ sa[5] = 2	nana
   ```
 
 
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 ### RMQ (Sparse Table)
 
 Range Maximum/Minimum Query. `RMQ(arr, i, j)`
@@ -165,9 +163,6 @@ int main() {
 ```
 
 
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 ### 最长公共前缀数组
 
 任给两个后缀，O(1)求其最长公共前缀（LCP）的长度。
@@ -196,20 +191,26 @@ LCPL(i, j) = min{height[i+1, ..., j]} // RMQ O(1)
 
 * LCP引理1
   
+
 $$
+\displaylines{
 
   LCPL(i, j) = min\{LCPL(k, k+1)| k=i, ..., j-1\}
   
+}
 $$
 
 
 * LCP引理2
   
+
 $$
+\displaylines{
 
   \forall i \le k \lt j \\
   LCPL(k, j) \ge LCPL(i, j)
   
+}
 $$
 
 
@@ -221,19 +222,16 @@ $$
 
   `i>0 && Rank[i]>0`时：
   
+
 $$
+\displaylines{
 
   H[i] \ge H[i-1] -1
   
+}
 $$
 
 
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 ```c++
 int Rank[maxn], height[maxn];
 void buildHeight(char* str, int n, int* sa){
@@ -252,11 +250,9 @@ buildHeight("abcd", 5, sa);
 ```
 
 
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 ### Applications
 
 
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 ###### POJ2774 Long Long Message
 
 求两个字符串的最长公共子串。
@@ -345,7 +341,6 @@ int main() {
 ```
 
 
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 ###### 最长公共子串（多序列）
 
 [ref](https://www.xuebuyuan.com/3226411.html)
@@ -357,7 +352,6 @@ int main() {
 * 最坏复杂度$O(l L\log L)$，在所有字符串都只含有同一个字符时达到。
 
 
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 ###### POJ3450 Corporate Identity
 
 ```c++
@@ -487,7 +481,6 @@ int main() {
 ```
 
 
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 ###### Musical Theme POJ
 
 不重叠的最长重复子串。
@@ -589,7 +582,6 @@ int main() {
 ```
 
 
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 ##### Milk Pattern
 
 可重叠的至少k次的最长重复子序列。

diff --git a/docs/algorithm/advanced/图的连通性.md b/docs/algorithm/advanced/图的连通性.md
@@ -245,7 +245,6 @@
     ```
 
 
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 ### 无向连通图
 
 * 割点&桥
@@ -759,4 +758,3 @@
   ```
 
 
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diff --git a/docs/algorithm/advanced/并查集.md b/docs/algorithm/advanced/并查集.md
@@ -366,4 +366,3 @@
     ```
 
 
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diff --git a/docs/algorithm/advanced/最短路算法.md b/docs/algorithm/advanced/最短路算法.md
@@ -14,11 +14,15 @@
 
   时间复杂度分析：
 
+
 $$
+\displaylines{
   T(n) = O(E)*dk_Q + O(V)*em_Q
   
+}
 $$
 
+
   $dk_Q$ means **Decrease Key**, we need to sort all edges once in the whole algo.
 
   $em_Q$ means Extract Min, for each vertex, we calculate the next shortest edge once.
@@ -170,9 +174,6 @@ int main() {
 ```
 
 
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 ### Examples
 
 * Currency Exchange

diff --git a/docs/algorithm/advanced/树状数组.md b/docs/algorithm/advanced/树状数组.md
@@ -42,8 +42,11 @@
 
   $O(N)$: build time complexity
   
+
 $$
+\displaylines{
   C[k] = sum(k)-sum(k-lowbit(k))
+}
 $$
 
 
@@ -215,7 +218,6 @@ int query(int i, int j) {
 ```
 
 
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 * Examples
 
   * 最长上升子序列

diff --git a/docs/algorithm/advanced/线段树.md b/docs/algorithm/advanced/线段树.md
@@ -26,12 +26,16 @@ struct node{
 
   Not a complete tree, but nearly.
 
+
 $$
+\displaylines{
 
   2*2^{ceil(log_2(n))}-1 \le 4n-1
   
+}
 $$
 
+
   so it is safe if we assign `[4 * maxn]` nodes, then we can use $2*i+1, 2*i+2$ instead of `node*`
 
 ### Operations

diff --git a/docs/algorithm/advanced/线段树2.md b/docs/algorithm/advanced/线段树2.md
@@ -291,7 +291,6 @@
   保证边重合的情况，两边不都算。
 
 
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   ```c++
   #include <iostream>
   #include <algorithm>
@@ -419,9 +418,6 @@
   ```
 
 
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 #### 二维线段树
 
 * Matrix

diff --git a/docs/algorithm/advanced/线段树总结.md b/docs/algorithm/advanced/线段树总结.md
@@ -75,9 +75,6 @@ int main() {
 ```
 
 
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 ### 动态线段树：区间最值替换
 
 **替换**某个区间的最值为某个数。而非增加到某个数（见下）。也不是取当前值与目标值的最大值（无法实现）。
@@ -153,7 +150,6 @@ void modify(int rt, int l, int r, int v) {
 ```
 
 
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 ###### LeetCode 699 Falling Squares
 
 ```c++
@@ -251,9 +247,6 @@ public:
 ```
 
 
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 ### 动态线段树：区间加减
 
 支持区间求和、求最值。
@@ -363,4 +356,3 @@ int main() {
 ```
 
 
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