排列组合递推公式以及代码

A(n, m) = A(n - 1, m - 1) + A(n - m, m) {n在下，m在上，下同}

UESTC 1721

static final int MOD = 1000000007;
static final int MAXN = 2005;

int A[][];

void solve() {
A = new int[MAXN][MAXN];
for (int i = 1; i < MAXN; i++) {
A[i][1] = A[i][i] = 1;
}
for (int i = 3; i < MAXN; i++) {
for (int j = 2; j < i; j++) {
A[i][j] = (A[i - 1][j - 1] + A[i - j][j]) % MOD;
}
}
}

 

C(n, m) = C(n - 1, m - 1) + C(n - 1, m)

HDU 2032

static final int MAXN = 35;
    int C[][];
    
    void solve() {
        C = new int[MAXN][MAXN];
        for (int i = 1; i < MAXN; i++) {
            C[i][1] = C[i][i] = 1;
        }
        for (int i = 3; i < MAXN; i++) {
            for (int j = 2; j < i; j++) {
                C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
            }
        }
    }


注意：组合排列数会很大，注意变量的范围（可求余）