From 7a7590d872e63280bb768c5a8776575b7f09fa63 Mon Sep 17 00:00:00 2001
From: Fuchen Shi <152240393+fuchenshi@users.noreply.github.com>
Date: Tue, 21 Jan 2025 23:23:56 +0800
Subject: [PATCH] fix: incorrect descriptions of the P = NP problem (#8084)

---
 .../content/p--np@0btHNkzWL1w_-pUgU_k2y.md                | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/src/data/roadmaps/computer-science/content/p--np@0btHNkzWL1w_-pUgU_k2y.md b/src/data/roadmaps/computer-science/content/p--np@0btHNkzWL1w_-pUgU_k2y.md
index 8c893f44b..274b0a158 100644
--- a/src/data/roadmaps/computer-science/content/p--np@0btHNkzWL1w_-pUgU_k2y.md
+++ b/src/data/roadmaps/computer-science/content/p--np@0btHNkzWL1w_-pUgU_k2y.md
@@ -1,6 +1,12 @@
 # P = NP
 
-The P = NP problem is one of the most famous problems in computer science. It asks if the problem of determining if a given input belongs to a certain class of problems is as hard as the problem of solving the given input. In other words, it asks if the problem of determining if a given input belongs to a certain class of problems is as hard as the problem of determining if a given input belongs to a certain class of problems. This problem is also known as the Halting Problem.
+The P = NP problem is one of the most famous problems in computer science. It asks whether a problem that can be solved in polynomial time on a non-deterministic machine (i.e., the problem is in NP) can also be solved in polynomial time on a deterministic machine (i.e., the problem is in P).
+
+If you can find a polynomial-time solution to an NP-complete problem, then all problems in NP can be solved in polynomial time. This shows that P = NP.
+
+If you can prove for any single NP-complete problem that it is only solvable in exponential time, then all NP-complete problems are only solvable in exponential time. This shows that P ≠ NP.
+
+So far, we don't know whether P = NP or P ≠ NP.
 
 Visit the following resources to learn more: