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To calculate 3 order pattern lock

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#include <cstdio>
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#include <cstring>
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#define N 4
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#define DIGIT N*N
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#define THRESHOLD 4
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using namespace std;
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bool vis[DIGIT + 1];
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long long int dp[DIGIT + 1][1<<(DIGIT + 1)][DIGIT + 1];
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int ban_1[DIGIT + 1][DIGIT + 1] = {
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        {0,/*0*/ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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    //   0       1  2  3  4  5  6  7  8  9  10 11 12 13 14 15 16
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        {0,/*1*/ 0, 0, 2, 2, 0, 0, 0, 0, 5, 0, 6, 0, 5, 0, 0, 6},
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        {0,/*2*/ 0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 7, 0, 6, 0, 0},
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        {0,/*3*/ 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 7, 0, 0, 0, 7, 0},
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        {0,/*4*/ 2, 3, 0, 0, 0, 0, 0, 0, 0, 7, 0, 8, 7, 0, 0, 8},
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        {0,/*5*/ 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 9, 0,10, 0},
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        {0,/*6*/ 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0,10, 0,11},
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        {0,/*7*/ 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0,10, 0,11, 0},
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        {0,/*8*/ 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0,11, 0,12},
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        {0,/*9*/ 5, 0, 6, 0, 0, 0, 0, 0, 0, 0,10,10, 0, 0, 0, 0},
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        {0,/*10*/0, 6, 0, 7, 0, 0, 0, 0, 0, 0, 0,11, 0, 0, 0, 0},
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        {0,/*11*/6, 0, 7, 0, 0, 0, 0, 0,10, 0, 0, 0, 0, 0, 0, 0},
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        {0,/*12*/0, 7, 0, 8, 0, 0, 0, 0,10,11, 0, 0, 0, 0, 0, 0},
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        {0,/*13*/5, 0, 0, 7, 9, 0,10, 0, 0, 0, 0, 0, 0, 0,14,14},
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        {0,/*14*/0, 6, 0, 0, 0,10, 0,11, 0, 0, 0, 0, 0, 0, 0,15},
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        {0,/*15*/0, 0, 7, 0,10, 0,11, 0, 0, 0, 0, 0,14, 0, 0, 0},
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        {0,/*16*/6, 0, 0, 8, 0,11, 0,12, 0, 0, 0, 0,14,15, 0, 0}
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};
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int ban_2[DIGIT + 1][DIGIT + 1] = {
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        {0,/*0*/ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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    //   0       1  2  3  4  5  6  7  8  9  10 11 12 13 14 15 16
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        {0,/*1*/ 0, 0, 2, 3, 0, 0, 0, 0, 5, 0, 6, 0, 9, 0, 0,11},
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        {0,/*2*/ 0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 7, 0,10, 0, 0},
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        {0,/*3*/ 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 7, 0, 0, 0,11, 0},
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        {0,/*4*/ 3, 3, 0, 0, 0, 0, 0, 0, 0, 7, 0, 8,10, 0, 0,12},
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        {0,/*5*/ 0, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 9, 0,10, 0},
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        {0,/*6*/ 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0,10, 0,11},
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        {0,/*7*/ 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0,10, 0,11, 0},
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        {0,/*8*/ 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0,11, 0,12},
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        {0,/*9*/ 5, 0, 6, 0, 0, 0, 0, 0, 0, 0,10,11, 0, 0, 0, 0},
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        {0,/*10*/0, 6, 0, 7, 0, 0, 0, 0, 0, 0, 0,11, 0, 0, 0, 0},
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        {0,/*11*/6, 0, 7, 0, 0, 0, 0, 0,10, 0, 0, 0, 0, 0, 0, 0},
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        {0,/*12*/0, 7, 0, 8, 0, 0, 0, 0,11,11, 0, 0, 0, 0, 0, 0},
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        {0,/*13*/9, 0, 0,10, 9, 0,10, 0, 0, 0, 0, 0, 0, 0,14,15},
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        {0,/*14*/0,10, 0, 0, 0,10, 0,11, 0, 0, 0, 0, 0, 0, 0,15},
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        {0,/*15*/0, 0,11, 0,10, 0,11, 0, 0, 0, 0, 0,14, 0, 0, 0},
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        {0,/*16*/11,0, 0,12, 0,11, 0,12, 0, 0, 0, 0,15,15, 0, 0}
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};
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long long int dfs(int len, int pre, int status, bool is_zero) {
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    if(len <= 0) return 1;
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    if(!is_zero && dp[len][status][pre] != -1)
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        return dp[len][status][pre];
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    long long int sum = 0;
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    for(int i = 0; i <= DIGIT; i++) {
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        if(vis[i]) continue;
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        if(is_zero) {
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            if(!i) {
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                if(len > THRESHOLD)
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                    sum += dfs(len - 1, 0, 0, true);
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            }
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            else {
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                vis[i] = true;
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                sum += dfs(len - 1, i, 1<<i, false);
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                vis[i] = false;
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            }
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        }
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        else if(i) {
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            if(!ban_1[pre][i] || (vis[ban_1[pre][i]] && vis[ban_2[pre][i]])) {
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                vis[i] = true;
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                sum += dfs(len - 1, i, (1<<i) + status, false);
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                vis[i] = false;
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            }
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        }
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    }
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    if(!is_zero)
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        dp[len][status][pre] = sum;
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    return sum;
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}
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int main() {
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    memset(vis, false, sizeof(vis));
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    memset(dp, -1, sizeof(dp));
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    printf("%lld\n", dfs(DIGIT, 0, 0, true));
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    return 0;
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}
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