HDU 5151 Sit sit sit

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
typedef long long LL;
const int mod = 1000000007;
int n, col[105];
int f[105][105];
int fact[105], inv[105];
void ModAdd(int & x, int y) {
    x += y;
    if(x >= mod) x -= mod;
}
int C(int x, int y) {
    return (LL)fact[y] * inv[x] % mod * inv[y - x] % mod;
}
int power(int x, int y) {
    int res = 1;
    while(y) {
        if(y & 1) res = (LL) res * x % mod;
        x = (LL) x * x % mod;
        y >>= 1;
    }
    return res;
}
int DP(int l, int r) {
    int lcol = col[l - 1], rcol = col[r + 1];
    if(l == r) {
        if(lcol == -1 || rcol == -1) return 1;
        if(lcol != rcol) return 0;
        return 1;
    }
    int & res = f[l][r];
    if(res != -1) return res;
    res = 0;
    ModAdd(res, DP(l + 1, r));
    ModAdd(res, DP(l, r - 1));
    for(int i = l + 1; i < r; i++) {
        ModAdd(res, 
        (LL)DP(l, i - 1) * DP(i + 1, r) % mod * C(i - l, r - l) % mod);
    }
    return res;
}
int main() {
    fact[0] = 1;
    for(int i = 1; i <= 100; i++) 
    fact[i] = (LL) fact[i - 1] * i % mod;
    inv[100] = power(fact[100], mod - 2);
    for(int i = 99; i >= 0; i--) 
    inv[i] = (LL) inv[i + 1] * (i + 1) % mod;
    while(scanf("%d", &n) != EOF) {
        for(int i = 1; i <= n; i++) scanf("%d", &col[i]);
        memset(f, -1, sizeof(f));
        col[0] = col[n + 1] = -1;
        printf("%d\n", DP(1, n));
    }
    return 0;
}