c34026b101
note: done using ```sh git grep -l "2010-2024 Google" | xargs sed -i 's/2010-2024 Google/2010-2025 Google/' ```
56 lines
1.6 KiB
C++
56 lines
1.6 KiB
C++
// Copyright 2010-2025 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#if defined(_MSC_VER)
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#define _USE_MATH_DEFINES
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#include <cmath>
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#endif
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#include "ortools/base/logging.h"
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#include "ortools/base/mathutil.h"
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namespace operations_research {
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// The formula is extracted from the following page
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// http://en.wikipedia.org/w/index.php?title=Stirling%27s_approximation
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double MathUtil::Stirling(double n) {
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static const double kLog2Pi = log(2 * M_PI);
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const double logN = log(n);
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return (n * logN - n + 0.5 * (kLog2Pi + logN) // 0.5 * log(2 * M_PI * n)
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+ 1 / (12 * n) - 1 / (360 * n * n * n));
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}
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double MathUtil::LogCombinations(int n, int k) {
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CHECK_GE(n, k);
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CHECK_GT(n, 0);
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CHECK_GE(k, 0);
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// use symmetry to pick the shorter calculation
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if (k > n / 2) {
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k = n - k;
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}
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// If we have more than 30 logarithms to calculate, we'll use
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// Stirling's approximation for log(n!).
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if (k > 15) {
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return Stirling(n) - Stirling(k) - Stirling(n - k);
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} else {
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double result = 0;
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for (int i = 1; i <= k; i++) {
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result += log(n - k + i) - log(i);
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}
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return result;
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}
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}
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} // namespace operations_research
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