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Diffstat (limited to 'painting_grid_three_colour.cpp')
-rw-r--r-- | painting_grid_three_colour.cpp | 58 |
1 files changed, 58 insertions, 0 deletions
diff --git a/painting_grid_three_colour.cpp b/painting_grid_three_colour.cpp new file mode 100644 index 0000000..11fb014 --- /dev/null +++ b/painting_grid_three_colour.cpp @@ -0,0 +1,58 @@ +// 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<int> 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<int> 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<int> &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 +} |