From 12ac1a81fd4728031cf9151196999edc1cadde7d Mon Sep 17 00:00:00 2001
From: chayan das <dasshuvo817@gmail.com>
Date: Sun, 18 May 2025 23:45:54 +0530
Subject: [PATCH] Create 1931. Painting a Grid With Three Different Colors

---
 ...ainting a Grid With Three Different Colors | 59 +++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 1931. Painting a Grid With Three Different Colors

diff --git a/1931. Painting a Grid With Three Different Colors b/1931. Painting a Grid With Three Different Colors
new file mode 100644
index 0000000..cb70fad
--- /dev/null
+++ b/1931. Painting a Grid With Three Different Colors	
@@ -0,0 +1,59 @@
+class Solution {
+public:
+    int md = 1e9+7;
+    bool isValid(int mask,int m){
+        int prev = -1;
+        for(int i=0;i<m;i++){
+            int cur = mask%3;
+            mask/=3;
+            if(prev==cur) return false;
+            prev = cur;
+        }
+        return true;
+    }
+    bool isCompatible(int a,int b,int m){
+        for(int i=0;i<m;i++){
+            if(a%3==b%3) return false;
+            a/=3;b/=3;
+        }
+        return true;
+    }
+    int colorTheGrid(int m, int n) {
+        int limit = pow(3,m);
+        vector<int> validMasks;
+        for(int i=0;i<limit;i++){
+            if(isValid(i,m)){
+                validMasks.push_back(i);
+            }
+        }
+        map<int,vector<int>> adj;
+        for(auto a : validMasks){
+            for(auto b : validMasks){
+                if(isCompatible(a,b,m)){
+                    adj[a].push_back(b);
+                }
+            }
+        }
+        map<int,int> dp;
+        for(auto mask : validMasks){
+            dp[mask] = 1;
+        }
+
+        for(int i=1;i<n;i++){
+            map<int,int> updatedDP;
+            for(auto &[mask,count] : dp){
+                for(auto nei : adj[mask]){
+                    updatedDP[nei] = (updatedDP[nei] + count)%md; 
+                }
+            }
+            dp = updatedDP;
+        }
+
+        int ans = 0;
+        for(auto &[x,val] : dp) ans = (ans + val)%md;
+
+        return ans; 
+
+    }
+
+};