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| 1 | +class Solution(object): |
| 2 | + def colorTheGrid(self, m, n): |
| 3 | + """ |
| 4 | + :type m: int |
| 5 | + :type n: int |
| 6 | + :rtype: int |
| 7 | + """ |
| 8 | + MOD = 10 ** 9 + 7 |
| 9 | + |
| 10 | + # Step 1: Generate all valid column colorings (no vertical conflicts) |
| 11 | + def generate_states(pos, prev_color, state): |
| 12 | + if pos == m: |
| 13 | + states.append(tuple(state)) |
| 14 | + return |
| 15 | + for color in range(3): |
| 16 | + if color != prev_color: |
| 17 | + state[pos] = color |
| 18 | + generate_states(pos + 1, color, state) |
| 19 | + |
| 20 | + states = [] |
| 21 | + generate_states(0, -1, [0] * m) |
| 22 | + index_map = {state: i for i, state in enumerate(states)} |
| 23 | + |
| 24 | + # Step 2: Precompute valid transitions (no horizontal conflicts) |
| 25 | + size = len(states) |
| 26 | + transitions = [[] for _ in range(size)] |
| 27 | + for i, a in enumerate(states): |
| 28 | + for j, b in enumerate(states): |
| 29 | + if all(x != y for x, y in zip(a, b)): |
| 30 | + transitions[i].append(j) |
| 31 | + |
| 32 | + # Step 3: DP initialization |
| 33 | + dp = [1] * size |
| 34 | + |
| 35 | + # Step 4: DP iteration for each column |
| 36 | + for _ in range(1, n): |
| 37 | + new_dp = [0] * size |
| 38 | + for i in range(size): |
| 39 | + for j in transitions[i]: |
| 40 | + new_dp[j] = (new_dp[j] + dp[i]) % MOD |
| 41 | + dp = new_dp |
| 42 | + |
| 43 | + # Step 5: Return total number of valid colorings |
| 44 | + return sum(dp) % MOD |
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