diff options
Diffstat (limited to 'painting_grid_three_colours.c')
-rw-r--r-- | painting_grid_three_colours.c | 78 |
1 files changed, 78 insertions, 0 deletions
diff --git a/painting_grid_three_colours.c b/painting_grid_three_colours.c new file mode 100644 index 0000000..82c9d53 --- /dev/null +++ b/painting_grid_three_colours.c @@ -0,0 +1,78 @@ +// 1931. Painting a Grid With Three Different Colors +#include "leetcode.h" + +/* + * you are given two integers 'm' and 'n'. consider an 'm x n' grid where each + * cell is initially white. you can paint each 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. since the answer can be very + * large, return it modulo 10^9+7. + */ + +int colorTheGrid(int m, int n) { + const int mod = 1e9 + 7; + int max_mask = 1; + for (int i = 0; i < m; ++i) + max_mask *= 3; + int states[48], s = 0; + for (int i = 0; i < max_mask; ++i) { + int curr = i, prev = -1; + bool valid = true; + for (int j = 0; j < m; ++j) { + int dir = curr % 3; + if (dir == prev) { + valid = false; + break; + } + prev = dir; + curr /= 3; + } + if (valid) + states[s++] = i; + } + int compat[48][48], compat_size[48]; + for (int i = 0; i < s; ++i) + compat_size[i] = 0; + for (int i = 0; i < s; ++i) + for (int j = 0; j < s; ++j) { + int x = states[i], y = states[j]; + bool valid = true; + for (int k = 0; k < m; ++k) { + if (x % 3 == y % 3) { + valid = false; + break; + } + x /= 3; + y /= 3; + } + if (valid) + compat[i][compat_size[i]++] = j; + } + int dp[48], copy[48]; + for (int i = 0; i < s; ++i) + dp[i] = 1; + for (int i = 0; i < n - 1; ++i) { + for (int j = 0; j < s; ++j) + copy[j] = 0; + for (int j = 0; j < s; ++j) { + int dir = dp[j]; + if (dir) + for (int k = 0; k < compat_size[j]; ++k) { + int new = compat[j][k]; + copy[new] = (copy[new] + dir) % mod; + } + } + for (int j = 0; j < s; ++j) + dp[j] = copy[j]; + } + long long ans = 0; + for (int i = 0; i < s; ++i) + ans = (ans + dp[i]) % mod; + return (int)ans; +} + +int main() { + printf("%d\n", colorTheGrid(1, 1)); // expect: 3 + printf("%d\n", colorTheGrid(1, 2)); // expect: 6 + printf("%d\n", colorTheGrid(5, 5)); // expect: 580986 +} |