2021-12-10 Daily-Challenge

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In: DailyChallenge

Today I have done leetcode's December LeetCoding Challenge with cpp.

December LeetCoding Challenge 10

Description

Domino and Tromino Tiling

You have two types of tiles: a 2 x 1 domino shape and a tromino shape. You may rotate these shapes.

img

Given an integer n, return the number of ways to tile an 2 x n board. Since the answer may be very large, return it modulo 109 + 7.

In a tiling, every square must be covered by a tile. Two tilings are different if and only if there are two 4-directionally adjacent cells on the board such that exactly one of the tilings has both squares occupied by a tile.

Example 1:

img

Input: n = 3
Output: 5
Explanation: The five different ways are show above.

Example 2:

Input: n = 1
Output: 1

Constraints:

  • 1 <= n <= 1000

Solution

auto speedup = [](){
  cin.tie(nullptr);
  cout.tie(nullptr);
  ios::sync_with_stdio(false);
  return 0;
}();
const int MOD = 1e9 + 7;
constexpr auto table = []{
  array<int, 1001> table{1, 1, 2};
  for(int i = 3; i < 1001; ++i) {
    table[i] = 2 * table[i - 1] % MOD + table[i - 3];
    table[i] %= MOD;
  }
  return table;
}();

class Solution {
public:
  int numTilings(int n) {
    return table[n];
  }
};

// Accepted
// 39/39 cases passed (0 ms)
// Your runtime beats 100 % of cpp submissions
// Your memory usage beats 60.67 % of cpp submissions (6.1 MB)
Algorithm