From 6bfa1d0bf9640374eb502f416fe969e02efa2b6e Mon Sep 17 00:00:00 2001
From: "codeflash-ai[bot]"
 <148906541+codeflash-ai[bot]@users.noreply.github.com>
Date: Mon, 23 Jun 2025 07:08:28 +0000
Subject: [PATCH] =?UTF-8?q?=E2=9A=A1=EF=B8=8F=20Speed=20up=20function=20`f?=
 =?UTF-8?q?ind=5Fnode=5Fwith=5Fhighest=5Fdegree`=20by=203,600%=20Let's=20a?=
 =?UTF-8?q?nalyze=20and=20optimize=20your=20program.?=
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## 1. Bottleneck Analysis

The line profiler result shows.

- The major bottleneck (~99% time) is this double loop.
    ```python
    for node in nodes.
        ...
        for src, targets in connections.items().
            if node in targets.
                degree += 1
    ```
  This means **for every node**, we **loop over all nodes and their targets** looking for "incoming connections".

- `if node in targets` line takes about **50% of total runtime alone** (since this is an O(m) scan inside an O(n) loop).

## 2. Suggestions for Optimization

### Precompute Incoming Degree

Rather than checking "for every node, how many lists in connections contain it?", we can **precompute the number of incoming connections each node has** in a single pass. This avoids O(n^2) behavior and reduces to O(n+m).

### Algorithm
1. Compute outgoing degree: `len(connections.get(node, []))`
2. Compute incoming degree for all nodes in one pass over all targets in all values in `connections`.
3. For each node, sum outgoing + incoming, and find the node with the highest degree.

### 3. Review Installed Distributions

No external libraries are used. The code is pure Python.

### 4. Optimized Code



**Explanation:**
- We build `incoming_degree` by looping once through all connections; this replaces the O(n^2) code.
- Now, for each `node`, we only need O(1) lookups for in-degree and out-degree.

### 5. Result

The new code will run **orders of magnitude faster**—from O(n^2) to O(n + m) for a graph with n nodes and m edges, with minimal extra memory.

## Summary

- **Main Optimization:** Precompute all incoming degrees in advance.
- **Benefit:** Reduced algorithmic complexity, dramatic performance improvement—especially for large graphs.
- **No dependencies:** All code remains in pure Python, no additional libraries needed.

Let me know if you'd like to see additional tweaks or a variant!
---
 src/dsa/nodes.py | 15 +++++++++------
 1 file changed, 9 insertions(+), 6 deletions(-)

diff --git a/src/dsa/nodes.py b/src/dsa/nodes.py
index 521d24e..e943ac9 100644
--- a/src/dsa/nodes.py
+++ b/src/dsa/nodes.py
@@ -90,18 +90,21 @@ def sort_chat_inputs_first(self, vertices_layers: list[list[str]]) -> list[list[
 def find_node_with_highest_degree(
     nodes: list[str], connections: dict[str, list[str]]
 ) -> str:
+    # Precompute incoming degree for each node.
+    incoming_degree = {}
+    for targets in connections.values():
+        for target in targets:
+            incoming_degree[target] = incoming_degree.get(target, 0) + 1
+
     max_degree = -1
     max_degree_node = None
 
     for node in nodes:
-        degree = 0
         # Count outgoing connections
-        degree += len(connections.get(node, []))
-
+        out_deg = len(connections.get(node, []))
         # Count incoming connections
-        for src, targets in connections.items():
-            if node in targets:
-                degree += 1
+        in_deg = incoming_degree.get(node, 0)
+        degree = out_deg + in_deg
 
         if degree > max_degree:
             max_degree = degree