Algorithm/state-compress-dp/main.cpp

#include <iostream>
#include <vector>

using namespace std;

int m, n;
int obstacle[101];
int dp[101][1025];

const int MOD_FACTOR = 100000007;

vector<int> state;

void init_state() {
    state.push_back(0);
    for (int i = 0; i < (1 << n); i++) {
        if (!(i & i << 1)) {
            state.push_back(i);
        }
    }
}

void calculate() {
    for (int j = 1; j < state.size(); j++) {
        if (!(state[j] & obstacle[1])) { // Check overlap
            dp[1][j] = 1;
        }
    }
    for (int i = 2; i <= m; i++) {
        for (int j = 1; j < state.size(); j++) {
            if (!(state[j] & obstacle[i])) { // Check obstacle overlap
                for (int k = 1; k < state.size(); k++) {
                    if (!(state[j] & state[k])) { // Check overlap
                        dp[i][j] = (dp[i][j] + dp[i - 1][k]) % MOD_FACTOR;
                    }
                }
            }
        }
    }

}

int main() {
    cin >> m >> n;
    for (int i = 1; i <= m; i++) {
        obstacle[i] = 0;
        int num;
        for (int j = 1; j <= n; j++) {
            cin >> num;
            if (num == 0) {
                obstacle[i] += (1 << (n - j));
            }
        }
    }

    init_state();
    calculate();
    int ans = 0;
    for (int j = 1; j < state.size(); j++) {
        ans = (ans + dp[m][j]) % MOD_FACTOR;
    }
    cout << ans - 1 << endl;
    return 0;
}