From 69ff07860ebc196122b83bec3a85d74d5a3e7a92 Mon Sep 17 00:00:00 2001
From: jackfiled <xcrenchangjun@outlook.com>
Date: Sun, 18 May 2025 14:14:12 +0800
Subject: [PATCH] 20250518 finished.

---
 src/problem/mod.rs                            |  2 +
 ...ting_a_grid_with_three_different_colors.rs | 91 +++++++++++++++++++
 2 files changed, 93 insertions(+)
 create mode 100644 src/problem/p1931_painting_a_grid_with_three_different_colors.rs

diff --git a/src/problem/mod.rs b/src/problem/mod.rs
index 75dc885..64ce830 100644
--- a/src/problem/mod.rs
+++ b/src/problem/mod.rs
@@ -660,3 +660,5 @@ mod p2900_longest_unequal_adjacent_groups_subsequence_i;
 mod p2901_longest_unequal_adjacent_groups_subsequence_ii;
 
 mod p75_sort_colors;
+
+mod p1931_painting_a_grid_with_three_different_colors;
diff --git a/src/problem/p1931_painting_a_grid_with_three_different_colors.rs b/src/problem/p1931_painting_a_grid_with_three_different_colors.rs
new file mode 100644
index 0000000..4367c96
--- /dev/null
+++ b/src/problem/p1931_painting_a_grid_with_three_different_colors.rs
@@ -0,0 +1,91 @@
+/**
+ * [1931] Painting a Grid With Three Different Colors
+ */
+pub struct Solution {}
+
+// submission codes start here
+use std::collections::HashMap;
+
+const MOD: i32 = 1_000_000_007;
+
+impl Solution {
+    pub fn color_the_grid(m: i32, n: i32) -> i32 {
+        let mut mask_count = 3_usize.pow(m as u32);
+        // 存储一行的所有合法涂色方式
+        // key表示mask
+        // value表示实际的涂色数组
+        let mut valid_masks = HashMap::new();
+
+        for mask in 0..mask_count {
+            let mut color = vec![];
+            let mut m_mask = mask;
+
+            for _ in 0..m {
+                color.push(m_mask % 3);
+                m_mask = m_mask / 3;
+            }
+
+            if color.iter().skip(1).zip(color.iter()).all(|(x, y)| x != y) {
+                valid_masks.insert(mask, color);
+            }
+        }
+
+        // 预处理相邻行的合法表示
+        let mut adjacent_valid_masks = HashMap::new();
+
+        for (&mask1, color1) in valid_masks.iter() {
+            for (&mask2, color2) in valid_masks.iter() {
+                if color1.iter().zip(color2.iter()).all(|(x, y)| x != y) {
+                    let entry = adjacent_valid_masks.entry(mask1).or_insert(vec![]);
+                    entry.push(mask2)
+                }
+            }
+        }
+
+        // 滚动的DP数组
+        let mut dp = vec![0; mask_count];
+
+        // 初始化为第一行
+        for &mask in valid_masks.keys() {
+            dp[mask] = 1;
+        }
+
+        for _ in 1..n {
+            let mut next_dp = vec![0; mask_count];
+
+            for &next_mask in valid_masks.keys() {
+                for &mask in adjacent_valid_masks.get(&next_mask).unwrap() {
+                    next_dp[next_mask] += dp[mask];
+
+                    if next_dp[next_mask] >= MOD {
+                        next_dp[next_mask] -= MOD;
+                    }
+                }
+            }
+
+            dp = next_dp;
+        }
+
+        dp.into_iter().fold(0, |sum, i| {
+            if sum + i >= MOD {
+                sum + i - MOD
+            } else {
+                sum + i
+            }
+        })
+    }
+}
+
+// submission codes end
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_1931() {
+        assert_eq!(3, Solution::color_the_grid(1, 1));
+        assert_eq!(6, Solution::color_the_grid(1, 2));
+        assert_eq!(580986, Solution::color_the_grid(5, 5));
+    }
+}