// 1931. Painting a Grid With Three Different Colors #include "leetcode.h" /* * given two integers 'm' and 'n'. consider an 'm x n' grid where each cell is * initially white. you can painteach cell red, green, or blue. all cells must * be painted. return the number of ways to colour the grid with no two adjacent * cells having the same colour. */ class Solution { int memo[1000][1024] = {}; vector nei_memo[1024] = {}; int m, n, mod = 1e9 + 7; int dp(int c, int prev) { if (c == n) return 1; if (memo[c][prev]) return memo[c][prev]; int res = 0; for (int nei : neighbours(prev)) res = (res + dp(c + 1, nei)) % mod; return memo[c][prev] = res; } vector neighbours(int prev) { if (!nei_memo[prev].empty()) return nei_memo[prev]; dfs(0, prev, 0, nei_memo[prev]); return nei_memo[prev]; } void dfs(int r, int prev, int curr, vector &out) { if (r == m) { out.push_back(curr); return; } for (int i = 0; i <= 3; i++) if (get_colour(prev, r) != i && (!r || get_colour(curr, r - 1) != i)) dfs(r + 1, prev, set_colour(curr, r, i), out); } int get_colour(int mask, int pos) { return (mask >> (2 * pos)) & 3; } int set_colour(int mask, int pos, int colour) { return mask | (colour << (2 * pos)); } public: int colorTheGrid(int m, int n) { this->m = m; this->n = n; return dp(0, 0); } }; int main() { Solution obj; printf("%d\n", obj.colorTheGrid(1, 1)); // expect: 3 printf("%d\n", obj.colorTheGrid(1, 2)); // expect: 6 printf("%d\n", obj.colorTheGrid(5, 5)); // expect: 580986 }