combinations.c

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/* -*- C -*- */
/*
 * Copyright (c) 2016-2020 Seagate Technology LLC and/or its Affiliates
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * For any questions about this software or licensing,
 * please email opensource@seagate.com or cortx-questions@seagate.com.
 *
 */


#define M0_TRACE_SUBSYSTEM M0_TRACE_SUBSYS_LIB
#include "lib/trace.h"

M0_INTERNAL uint64_t m0_fact(uint64_t n)
{
        M0_PRE(n > 0);

        return n == 1 || n == 0 ? 1 : n * m0_fact(n - 1);
}

M0_INTERNAL uint32_t m0_ncr(uint64_t n, uint64_t r)
{
        uint64_t i;
        uint64_t m = n;

        M0_PRE(n >= r);

        if (r == 0)
                return 1;
        for (i = 1; i < r; i++)
                m *= n - i;
        return m / m0_fact(r);
}

M0_INTERNAL int m0_combination_index(int N, int K, int *x)
{
        int m;
        int q;
        int n;
        int r;
        int idx = 0;

        M0_ENTRY("N:%d K=%d", N, K);
        M0_PRE(0 < K && K <= N);
        M0_PRE(m0_forall(i, K, x[i] < N));

        for (q = 0; q < x[0]; q++) {
                n = N - (q + 1);
                r = K - 1;
                idx += m0_ncr(n, r);
        }
        for (m = 1; m < K; m++) {
                for (q = 0; q < (x[m] - x[m - 1] - 1); q++) {
                        n = N - (x[m - 1] + 1) - (q + 1);
                        r = K - m - 1;
                        idx += m0_ncr(n, r);
                }
        }
        return M0_RC(idx);
}

M0_INTERNAL void m0_combination_inverse(int cid, int N, int K, int *x)
{
        int m;
        int q;
        int n;
        int r;
        int idx = 0;
        int old_idx = 0;
        int i = 0;
        int j;

        M0_ENTRY("N:%d K=%d cid:%d \n", N, K, cid);
        M0_PRE(0 < K && K <= N);

        for (q = 0; idx < cid + 1; q++) {
                old_idx = idx;
                n = N - (q + 1);
                r = K - 1;
                idx += m0_ncr(n, r);
        }
        idx = old_idx;
        x[i++] = q - 1;

        for (m = 1; m < K; m++) {
                for (q = 0; idx < cid + 1; q++) {
                        old_idx = idx;
                        n = N - (x[i - 1] + 1) - (q + 1);
                        r = K - m - 1;
                        idx += m0_ncr(n, r);
                }
                if (idx >= cid + 1)
                        idx = old_idx;
                x[i] = x[i - 1] + q;
                i++;
        }

        M0_LOG(M0_DEBUG, "Combinations");
        for (j = 0; j < i; j++)
                M0_LOG(M0_DEBUG, "%d \t", x[j]);
        M0_LEAVE();
}

#undef M0_TRACE_SUBSYSTEM

/*
 *  Local variables:
 *  c-indentation-style: "K&R"
 *  c-basic-offset: 8
 *  tab-width: 8
 *  fill-column: 80
 *  scroll-step: 1
 *  End:
 */