Solution.ts

function colorTheGrid(m: number, n: number): number {
    const f1 = (x: number): boolean => {
        let last = -1;
        for (let i = 0; i < m; ++i) {
            if (x % 3 === last) {
                return false;
            }
            last = x % 3;
            x = Math.floor(x / 3);
        }
        return true;
    };
    const f2 = (x: number, y: number): boolean => {
        for (let i = 0; i < m; ++i) {
            if (x % 3 === y % 3) {
                return false;
            }
            x = Math.floor(x / 3);
            y = Math.floor(y / 3);
        }
        return true;
    };
    const mx = 3 ** m;
    const valid = new Set<number>();
    const f: number[] = Array(mx).fill(0);
    for (let i = 0; i < mx; ++i) {
        if (f1(i)) {
            valid.add(i);
            f[i] = 1;
        }
    }
    const d: Map<number, number[]> = new Map();
    for (const i of valid) {
        for (const j of valid) {
            if (f2(i, j)) {
                d.set(i, (d.get(i) || []).concat(j));
            }
        }
    }
    const mod = 10 ** 9 + 7;
    for (let k = 1; k < n; ++k) {
        const g: number[] = Array(mx).fill(0);
        for (const i of valid) {
            for (const j of d.get(i) || []) {
                g[i] = (g[i] + f[j]) % mod;
            }
        }
        f.splice(0, f.length, ...g);
    }
    let ans = 0;
    for (const x of f) {
        ans = (ans + x) % mod;
    }
    return ans;
}