Merge branch 'main' into patch-1

adamant-pwn · web-flow · commit 38982cb5217d · 2024-10-15T12:08:03.000+02:00
diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
@@ -12,7 +12,7 @@ jobs:
 
     steps:
       - name: Checkout repository
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
         with:
           fetch-depth: 0
           submodules: recursive
diff --git a/.github/workflows/delete-preview.yml b/.github/workflows/delete-preview.yml
@@ -1,15 +1,15 @@
 name: Delete PR Preview
 
 on:
-  pull_request:
+  pull_request_target:
     types: [closed]
 
 jobs:
   delete_pr_preview:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout gh-pages branch
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
         with:
           ref: gh-pages
 
diff --git a/.github/workflows/deploy-cloud-function.yml b/.github/workflows/deploy-cloud-function.yml
@@ -10,7 +10,7 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout repository
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
 
       - uses: dorny/paths-filter@v2
         id: changes
diff --git a/.github/workflows/deploy-prod.yml b/.github/workflows/deploy-prod.yml
@@ -12,7 +12,7 @@ jobs:
     if: github.event.workflow_run.conclusion == 'success' && github.event.workflow_run.event == 'push'
     steps:
       - name: Checkout repository
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
 
       - name: Download pages
         uses: actions/download-artifact@v4
@@ -49,7 +49,7 @@ jobs:
     if: github.event.workflow_run.conclusion == 'success'
     steps:
       - name: Checkout repository
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
 
       - name: Download pages
         uses: actions/download-artifact@v4
@@ -75,13 +75,19 @@ jobs:
           publish_branch: gh-pages
           destination_dir: ${{ steps.get-pr-number.outputs.pr_number }}
 
-      
+      - name: Find PR comment
+        uses: peter-evans/find-comment@v3
+        id: fc
+        with:
+          issue-number: ${{ steps.get-pr-number.outputs.pr_number }}
+          comment-author: github-actions[bot]
+          body-includes: Preview the changes for PR
+
       - name: Create or update PR comment
         if: steps.get-pr-number.outputs.pr_number != 'main'
-        uses: peter-evans/create-or-update-comment@v3
+        uses: peter-evans/create-or-update-comment@v4
         with:
-          token: ${{ github.token }}
+          comment-id: ${{ steps.fc.outputs.comment-id }}
           issue-number: ${{ steps.get-pr-number.outputs.pr_number }}
-          body: 'Preview the changes for PR #${{ steps.get-pr-number.outputs.pr_number }} (${{ github.event.workflow_run.head_sha }}) [here](https://gh.cp-algorithms.com/${{ steps.get-pr-number.outputs.pr_number }}/).'
-          body-includes: 'Preview the changes for PR'
-          mode: replace
+          body: 'Preview the changes for PR #${{ steps.get-pr-number.outputs.pr_number }} (for commit ${{ github.event.workflow_run.head_sha }}) at https://gh.cp-algorithms.com/${{ steps.get-pr-number.outputs.pr_number }}/.'
+          edit-mode: replace
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
@@ -11,7 +11,7 @@ jobs:
 
     steps:
       - name: Checkout repository
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
       - name: Set up Python
         uses: actions/setup-python@v2
         with:
diff --git a/README.md b/README.md
@@ -16,6 +16,8 @@ Compiled pages are published at [https://cp-algorithms.com/](https://cp-algorith
 
 ## Changelog
 
+- October, 2024: Welcome new maintainers: [jxu](https://github.com/jxu), [mhayter](https://github.com/mhayter) and [kostero](https://github.com/kostero)!
+- October, 15, 2024: GitHub pages based mirror is now served at [https://gh.cp-algorithms.com/](https://gh.cp-algorithms.com/), and an auxiliary competitive programming library is available at [https://lib.cp-algorithms.com/](https://lib.cp-algorithms.com/).
 - July 16, 2024: Major overhaul of the [Finding strongly connected components / Building condensation graph](https://cp-algorithms.com/graph/strongly-connected-components.html) article.
 - June 26, 2023: Added automatic RSS feeds for [new articles](https://cp-algorithms.com/feed_rss_created.xml) and [updates in articles](https://cp-algorithms.com/feed_rss_updated.xml).
 - December 20, 2022: The repository name and the owning organizations were renamed! Now the repo is located at [https://github.com/cp-algorithms/cp-algorithms](https://github.com/cp-algorithms/cp-algorithms). It is recommended to update the upstream link in your local repositories, if you have any.
diff --git a/src/algebra/linear-diophantine-equation.md b/src/algebra/linear-diophantine-equation.md
@@ -27,10 +27,10 @@ A degenerate case that need to be taken care of is when $a = b = 0$. It is easy
 
 When $a \neq 0$ and $b \neq 0$, the equation $ax+by=c$ can be equivalently treated as either of the following:
 
-\begin{gather}
-ax \equiv c \pmod b,\newline
-by \equiv c \pmod a.
-\end{gather}
+\begin{align}
+ax &\equiv c \pmod b \\
+by &\equiv c \pmod a
+\end{align}
 
 Without loss of generality, assume that $b \neq 0$ and consider the first equation. When $a$ and $b$ are co-prime, the solution to it is given as
 
@@ -51,6 +51,12 @@ y = \frac{c-ax}{b}.
 
 ## Algorithmic solution
 
+**Bézout's lemma** (also called Bézout's identity) is a useful result that can be used to understand the following solution. 
+
+> Let $g = \gcd(a,b)$. Then there exist integers $x,y$ such that $ax + by = g$.
+> 
+> Moreover, $g$ is the least such positive integer that can be written as $ax + by$; all integers of the form $ax + by$ are multiples of $g$. 
+
 To find one solution of the Diophantine equation with 2 unknowns, you can use the [Extended Euclidean algorithm](extended-euclid-algorithm.md). First, assume that $a$ and $b$ are non-negative. When we apply Extended Euclidean algorithm for $a$ and $b$, we can find their greatest common divisor $g$ and 2 numbers $x_g$ and $y_g$ such that:
 
 $$a x_g + b y_g = g$$
@@ -119,7 +125,7 @@ $$y = y_0 - k \cdot \frac{a}{g}$$
 
 are solutions of the given Diophantine equation.
 
-Moreover, this is the set of all possible solutions of the given Diophantine equation.
+Since the equation is linear, all solutions lie on the same line, and by the definition of $g$ this is the set of all possible solutions of the given Diophantine equation.
 
 ## Finding the number of solutions and the solutions in a given interval
 
diff --git a/src/graph/dinic.md b/src/graph/dinic.md
@@ -106,7 +106,7 @@ struct Dinic {
             int v = q.front();
             q.pop();
             for (int id : adj[v]) {
-                if (edges[id].cap - edges[id].flow < 1)
+                if (edges[id].cap == edges[id].flow)
                     continue;
                 if (level[edges[id].u] != -1)
                     continue;
@@ -125,7 +125,7 @@ struct Dinic {
         for (int& cid = ptr[v]; cid < (int)adj[v].size(); cid++) {
             int id = adj[v][cid];
             int u = edges[id].u;
-            if (level[v] + 1 != level[u] || edges[id].cap - edges[id].flow < 1)
+            if (level[v] + 1 != level[u])
                 continue;
             long long tr = dfs(u, min(pushed, edges[id].cap - edges[id].flow));
             if (tr == 0)
@@ -154,3 +154,7 @@ struct Dinic {
     }
 };
 ```
+
+## Practice Problems
+
+* [SPOJ: FASTFLOW](https://www.spoj.com/problems/FASTFLOW/)
