debug

content/1_Intro/Intro_About.md

@@ -31,7 +31,7 @@ order: 1
 
 ## Module Organization
 
-Written with [markdown](https://www.markdownguide.org/cheat-sheet/).
+Written with [Markdown](https://www.markdownguide.org/cheat-sheet/). Can use [StackEdit](https://stackedit.io/) to check latex.
 
 ### Lesson
 

content/1_Intro/Intro_RunningCpp.md

@@ -18,6 +18,7 @@ Using C++ both online and locally (currently for Mac only).
    * make sure your code is not public
    * sometimes randomly erases your code when you first create it (so get in the habit of copying your code before creating it!)
  * [OnlineGDB](https://www.onlinegdb.com/)
+   * compiler and debugger tool
 
 Of course, you can't use File I/O on these websites (or do a lot of other stuff ...).
 
@@ -27,7 +28,9 @@ Of course, you can't use File I/O on these websites (or do a lot of other stuff
 
 ## Installation
 
-Open **Terminal** and run
+Open **Terminal**. First, familiarize yourself with some basic commands given [here](https://blog.teamtreehouse.com/introduction-to-the-mac-os-x-command-line).
+
+Run
 
 ```sh
 brew install gcc
@@ -110,11 +113,13 @@ If you want to read input from `inp.txt` and write to `out.txt`, then use the fo
 ./name < inp.txt > out.txt
 ```
 
-See "Introductory Problems" for how to do file input and output within the program.
+See "Intro - Introductory Problems" for how to do file input and output within the program.
 
 ### Adding Shortcuts
 
-Retyping this command gets tedious once we start adding many [command line options](https://developers.redhat.com/blog/2018/03/21/compiler-and-linker-flags-gcc/). See "General - Debugging" for more information about compilation options.
+[Aliases in Terminal](https://jonsuh.com/blog/bash-command-line-shortcuts/)
+
+Retyping the commands for compiling and running gets tedious once we start adding many [command line options](https://developers.redhat.com/blog/2018/03/21/compiler-and-linker-flags-gcc/). See "General - Debugging" for more information about compilation options.
 
 Open your bash profile with a text editor such as gedit (or sublime text).
 
@@ -145,6 +150,7 @@ Note that all occurrences of `$1` are replaced with `name`.
  * [Geany](https://www.geany.org/)
    * used at IOI
  * [Visual Studio Code](https://code.visualstudio.com/)
+   * haven't used personally
  * [XCode](https://developer.apple.com/xcode/)
    * Mac only
  * [Codeblocks](http://www.codeblocks.org/)
@@ -160,11 +166,4 @@ I mostly just use sublime text.
    * [Sublime Snippets](https://www.granneman.com/webdev/editors/sublime-text/top-features-of-sublime-text/quickly-insert-text-and-code-with-sublime-text-snippets)
    * [Symlink](https://www.sublimetext.com/docs/3/osx_command_line.html) 
      * Using `/usr/local/bin/subl` instead of `~/bin/subl` worked for me on OS X Mojave.
- * [Atom](https://atom.io/)
-
-## Other Useful Links
-
- * [Intro to Command Line](http://blog.teamtreehouse.com/introduction-to-the-mac-os-x-command-line)
- * [Command Line Shortcuts](https://jonsuh.com/blog/bash-command-line-shortcuts/)
- * [Run Python Script](https://stackoverflow.com/questions/7855996/cant-run-python-py-files-from-terminal-on-mac)
- * [Competitive C++ Style Guide](https://codeforces.com/blog/entry/64218)
+ * [Atom](https://atom.io/)

content/2_General/6_Debugging.md

@@ -5,14 +5,15 @@ author: Benjamin Qi, Aaron Chew
 order: 6
 ---
 
- - Compilation Options
- - CppIO Template
- - Stress Testing
- - Using a Debugger
- 
+Detecting issues within your program and figuring out how to avoid them in the first place.
+
 <!-- END DESCRIPTION -->
 
-(what is debugging?)
+## Style Guide
+
+[Swift](https://codeforces.com/blog/entry/64218)
+
+## Compilation
 
 As mentioned in "Running C++," I use the following to compile and run.
 
@@ -21,8 +22,6 @@ co() { g++ -std=c++11 -O2 -o $1 $1.cpp -Wall -Wextra -Wshadow -DLOCAL -Wl,-stack
 run() { co $1 && ./$1 & fg; }
 ```
 
-## Compilation
-
 ### Warnings
 
 See [here](https://gcc.gnu.org/onlinedocs/gcc/Warning-Options.html).

content/3_Bronze/6_Bronze_Pairs.md

@@ -5,9 +5,15 @@ author: ?
 order: 6
 ---
 
-## [Pair](http://www.cplusplus.com/reference/utility/pair/pair/)
+A **pair** is a structure that holds two values, not necessarily of the same type.
 
-A structure that holds two values, not necessarily of the same type (not built into java!). 
+(tuple?)
+
+<!-- END DESCRIPTION -->
+
+(is this present in Java?)
+
+## [C++](http://www.cplusplus.com/reference/utility/pair/pair/)
 
  - `make_pair(a, b)`: Returns a pair with values a, b.
  - `pair.first`: The first value of the pair.

content/3_Bronze/8_Bronze_Complete.md

@@ -2,7 +2,7 @@
 slug: /bronze/complete-search
 title: "Complete Search"
 author: Unknown
-order: 7
+order: 8
 ---
 
 See 6 of https://www.overleaf.com/project/5e73f65cde1d010001224d8a

content/4_Silver/6_Silver_Psum.md

@@ -47,7 +47,7 @@ Given a 2-dimensional array of size $NxM$, answer $Q$ queries of the following f
 ### Prefix Minimum, XOR, etc.
 
 Similar to prefix sums, you can also take prefix minimum or maximum; but *you cannot* answer min queries over an arbitrary range with prefix minimum. (This is because minimum doesn't have an inverse operation, the way subtraction is to addition.)
-On the other hand, XOR is its own inverse operation...
+On the other hand, XOR is its own inverse operation, meaning that the XOR of any number with itself is zero.
 
  - [USACO My Cow Ate My Homework](http://usaco.org/index.php?page=viewproblem2&cpid=762)
  - [CSES Range XOR Queries](https://cses.fi/problemset/task/1650)
@@ -56,15 +56,16 @@ On the other hand, XOR is its own inverse operation...
 
 Instead of storing just the values themselves, you can also take a prefix sum over $i\cdot a_i$, or $10^i \cdot a_i$, for instance. Some math is usually helpful for these problems; don't be afraid to get dirty with algebra!
 
-For instance, let's see how to quickly answer the following type of query: Find $1\cdot a_l+2\cdot a_{l+1}+3\cdot a_{l+2}+\cdots+(r-l+1)\cdot a_{r}$.
+For instance, let's see how to quickly answer the following type of query: Find 
+$$1\cdot a_l+2\cdot a_{l+1}+3\cdot a_{l+2}+\cdots+(r-l+1)\cdot a_{r}.$$
 First, define the following:
-$ps[i] = a_1+a_2+a_3+a_4+\cdots+a_i$
-$ips[i] = 1\cdot a_1+2\cdot a_2+\cdots+i\cdot a_i$
+$$ps[i] = a_1+a_2+a_3+a_4+\cdots+a_i$$
+$$ips[i] = 1\cdot a_1+2\cdot a_2+\cdots+i\cdot a_i$$
 Then, we have:
-$l\cdot a_l + (l+1) \cdot a_{l+1} + \cdots + r \cdot a_r = ips[r]-ips[l-1]$
-$(l-1) \cdot a_l + (l-1) \cdot a_{l+1} + \cdot + (l-1) \cdot a_r = (l-1)(ps[r]-ps[l-1])$
+$$l\cdot a_l + (l+1) \cdot a_{l+1} + \cdots + r \cdot a_r = ips[r]-ips[l-1]$$
+$$(l-1) \cdot a_l + (l-1) \cdot a_{l+1} + \cdot + (l-1) \cdot a_r = (l-1)(ps[r]-ps[l-1])$$
 And so,
-$1\cdot a_l + 2 \cdot a_{l+1} + \cdots + (r-l+1) \cdot a_r = ips[r]-ips[l-1]-(l-1)(ps[r]-ps[l-1])$
+$$1\cdot a_l + 2 \cdot a_{l+1} + \cdots + (r-l+1) \cdot a_r = ips[r]-ips[l-1]-(l-1)(ps[r]-ps[l-1])$$
 Which is what we were looking for!
 
  - [AtCoder Multiple of 2019](https://atcoder.jp/contests/abc164/tasks/abc164_d) (You may want to solve the below problem "Subsequences Summing to Seven" before doing this one.)