void solve(int n, int m) { var binom = new BinomialCoefficient(n + m + 5); var dp = new ModInt[n + 3, m + 3]; dp[0, 0] = 1; for (int i = 0; i <= n; i++) { for (int j = 0; j <= m; j++) { if (j > 0) { dp[i + 1, j] += j * dp[i, j]; } dp[i, j + 1] += dp[i, j]; } } ModInt ans = 0; for (int i = 0; i <= n; i++) { var v = dp[i, m]; v *= binom[n + m, i + m]; v *= binom.fact[n - i]; ans += v; } ans *= binom.fact[m] * binom.fact[m]; ans *= binom.fact[n]; Console.WriteLine(ans); }
void solve() { int N = cin.nextint; var F = new ModInt[N + 1]; //?? F[0] = 1; for (int i = 1; i <= N; i++) { F[i] = F[i - 1] * i; } var ncr = new BinomialCoefficient(N); var OMEGA = new ModInt[N]; //????????? for (int i = 1; i < N; i++) { OMEGA[i] = OMEGA[i - 1] + F[N - i - 1] * ncr[N, N - i - 1] * F[i]; //WriteLine(" " + F[N - i - 1] * ncr[N, N - i - 1] + " " + OMEGA[i]); } var A = cin.scanlong; ModInt ans = 0; for (int i = 0; i < N; i++) { ans += F[N] * A[i]; //WriteLine(i + " " + (OMEGA[N - i - 1] + OMEGA[i])); ans += OMEGA[N - i - 1] * A[i]; ans += OMEGA[i] * A[i]; } WriteLine(ans); }
public static void TeoremCalculateThrowsException(int n, int k) { // Arrange // Act // Assert _ = Assert.Throws <ArgumentException>(() => BinomialCoefficient.Calculate(n, k)); }
public static void CalculateFromPairs(int n, int k, long expected) { // Arrange // Act var result = BinomialCoefficient.Calculate(n, k); // Assert Assert.AreEqual(expected, result); }
void solve() { int N = cin.nextint; int K = cin.nextint; var ncr = new BinomialCoefficient(N + K); if (K < N) { WriteLine(ncr[N + K - 1, K]); } else { WriteLine(ncr[N, K % N]); } }
void solve() { int N = cin.nextint; var G = new SortedDictionary <int, int>(); for (int i = 0; i < N; i++) { int t = cin.nextint; if (G.ContainsKey(t)) { G[t]++; } else { G[t] = 1; } } var B = new BinomialCoefficient(N); ModInt ans = 1; long sum = 0; long time = 0; foreach (var item in G) { for (int i = 0; i < item.Value; i++) { time += item.Key; sum += time; } ans *= B.fact[item.Value]; } WriteLine(sum); WriteLine(ans); }
public void Solve() { var n = ri; var m = ri; var sz = Enumerate(n, x => 1 << x); var all = sz.Sum(); var dp = new ModInt[1 << n]; dp[0] = 1; var comb = new BinomialCoefficient(all + 50); foreach (var x in Enumerate(m, x => ri).OrderByDescending(x => x)) { var next = new ModInt[1 << n]; for (int i = 0; i < 1 << n; i++) { var cnt = all - x + 2; for (int j = 0; j < n; j++) { if ((i >> j & 1) == 1) { cnt -= sz[j]; } } next[i] += dp[i]; for (int j = 0; j < n; j++) { if ((i >> j & 1) == 1) { continue; } if (cnt < sz[j]) { continue; } next[i | 1 << j] += dp[i] * comb[cnt - 1, sz[j] - 1] * comb.fact[sz[j]]; } } dp = next; } Debug.WriteLine(dp.AsJoinedString()); ModInt ans = 0; for (int i = 0; i < 1 << n; i++) { var cnt = n; var rem = 0; for (int j = 0; j < n; j++) { if ((i >> j & 1) == 0) { rem += sz[j]; cnt--; } } dp[i] *= comb.fact[rem]; Debug.WriteLine(dp[i]); ans += (cnt % 2 == 0) ? dp[i] : ModInt.Mod - dp[i].num; } ans *= ModInt.Pow(2, n); Console.WriteLine(ans); }
//Binomial Coefficient //Catalan value = C(2n, n)/n+1 public static long GetNumberWithBinomialCoefficient(int n) { return(BinomialCoefficient.BinominalCoefficient(2 * n, n) / (n + 1)); }
static void Main(string[] args) { // StringProblems //Test calls for Reverse string string input = "jacob"; Console.WriteLine(input + "<=>" + new string(SimpleProblem.ReverseString(input.ToCharArray()))); input = "jake"; Console.WriteLine(input + "<=>" + new string(SimpleProblem.ReverseString(input.ToCharArray()))); input = ""; Console.WriteLine(input + "<=>" + new string(SimpleProblem.ReverseString(input.ToCharArray()))); input = "jdshjdh@#$%^&)"; Console.WriteLine(input + "<=>" + new string(SimpleProblem.ReverseString(input.ToCharArray()))); ReplaceSpaces.TestReplaceSpacesInplace(); Anagrams.TestIsAnagramAlgo(); StringRotation.TestIsThisRotatedString(); RemoveDuplicates.TestRemoveDuplicatesFromString(); StringToLongConverter.TestStringToLong(); RegexMatching.TestMatch(); SumOfTwoNumbersInArray.TestSumOfTwoNumbersInArray(); SumOfThreeNumbersInArray.TestSumOfThreeNumbersInArray(); PairInSortedArrayClosestToAParticularValue.TestPairInSortedArrayClosestToAParticularValue(); PalindromeInStringPermutation.TestPalindromeInStringPermutation(); EditDistanceBetweenStrings.TestEditDistanceBetweenStrings(); AnagramIsPalindrome.TestAnagramIsPalindrome(); GreatestPalindrome.TestGreatestPalindrome(); ReverseStringWithoutVowels.TestReverseStringWithoutVowels(); LongestSubstringWithKDistinctChars.TestLongestSubstringWithKDistinctChars(); // Pattern Matching NativePatternMatching.TestNativePatternMatching(); KMPPatternMatching.TestKMPPatternMatching(); BoyerMoorePatternMatching.TestPatternMatching(); RabinKarp.TestRabinKarp(); //Console.ReadLine(); //Array Problems ArrayOfNumsIncrement.TestIncrementArrayOfNumbers(); MajorityElement.TestFindMajorityElement(); Merge2SortedArrays.TestMergeSortedArrays(); MaxDistanceInArray.TestMaxDistanceInArray(); MovingAverage.TestMovingAverage(); TotalAverage.TestTotalAverage(); ArrayWithGreaterElementToRight.TestArrayWithGreaterElementToRight(); WaterCollectedInPuddleShownByHistogram.TestWaterCollectedInPuddleShownByHistogram(); CountOfPairsWhichSumUpToGivenSum.TestCountOfPairsWhichSumUpToGivenSum(); //Median.TestGetMedianOf2SortedArray(); // Sorting Problems SelectionSort.TestSorting(); BubbleSort.TestSorting(); InsertionSort.TestSorting(); ShellSort.TestSorting(); MergeSort.TestMergeSort(); QuickSort.TestQuickSort(); HeapSortTester.TestHeapSort(); CountingSort.TestSorting(); RadixSort.TestRadixSort(); DutchNationalFlag.TestDutchNationalFlag(); SortedSquares.TestSortedSquares(); // Matrix Problem Rotate_Matrix_90_degree.TestRotateMatrix(); Matrix_Column_Rows_0.TestMakeRowColZero1(); Matrix_Column_Rows_0.TestMakeRowColZero2(); RotateMatrix180.TestRotateMatrix180(); SumOfMatrixElementsFormedByRectangleWithCoordinates.TestSumOfMatrixElements(); SortedArrayFromSortedMatrix.TestSortedArrayFromSortedMatrix(); SearchWordInMatrix.TestSearchWordInMatrix(); MaxOnesInRow.TestMaxOnesInRow(); MatrixAsTriangle.TestMatrixAsTriangle(); MinRangeInMatrix.TestMinRangeInMatrix(); PrintMatrixAsSnake.TestPrintMatrixAsSnake(); PrintMatrixInSpiral.TestPrintMatrixInSpiral(); MaxSqAreaInBinaryMatrix.TestMaxRectAreaInBinaryMatrix(); TicTacToeWinner.TestTicTacToeWinner(); WaterfallCreation.TestWaterfallCreation(); // Linked list Problems DeleteLinkedListNode.TestDeleteFirstNode(); DeleteDuplicatesFromLinkedList.TestDeleteDuplicates(); NthLastElementOfLinkedList.TestNthLastNodeOfLinkedList(); DeleteNodeWithDirectReference.TestDeleteNode(); AddNumbers.TestAddNumbersRepresentedByLinkedList(); CopyLinkedListWithRandomNode.TestGetCopiedLinkedListWithRandomNode(); CommonElementInTwoLinkedList.TestCommonElement(); ReverseAdjacentNodesInLinkedList.TestReverseAdjacentNodes(); MergeSortedLinkedList.TestMerge(); CycleInLinkedList.TestStartOfCycleInLinkedList(); MedianForCircularLinkedList.TestGetMedian(); ReverseLinkedList.TestReverseLinkedList(); SortedCircularLinkedList.TestCircularLinkedList(); // stack and queue problem ThreeStackWithOneArray.TestThreeStackWithOneArray(); StackWithMinElement.TestStackWithMinElement(); StackOfPlates.TestStackOfPlates(); SortAStack.TestSortAStackAscending(); WellFormedExpression.TestWellFormedExpression(); QueueVia2Stack.TestQueueVia2Stack(); LRUCache.TestLRUCache(); EvaluatePrefixNotation.TestGetPrefixNotationResult(); EvaluateInflixNotation.TestGetInflixNotationResults(); EvaluatePostfixNotation.TestGetPostfixNotationResult(); TestCircularQueue.TestCircularQueueWithDifferentCases(); LargestAreaInHistogram.TestLargestAreaInHistogram(); TextEditerWithUndo.TestTextEditerWithUndo(); //Recursion Problem TowerOfHanoi.TestTowerOfHanoi(); MaxSumOfConsecutiveNums.TestMaxSumOfConsecutiveNums(); // Back tracking problems Sudoku.TestSudokuSolver(); HamiltonianCycle.TestHamiltonianCycle(); GraphColoringWithMColors.TestGraphColoringWithMColors(); MakeLargestIsland.TestMakeLargestIsland(); //Misc Problem MinNumOfCoins.TestMinNumOfCoins(); IsPrime.TestCheckPrime(); SquareRoot.TestCalculateSquareRoot(); CreditCardCheck.TestLuhnAlgo(); ExcelFirstRowConversion.TestCovertExcelColumnToLong(); Skyline.TestSkyline(); SumOfSquaresWithoutMultiplication.TestSumOfSquares(); MergeIntervals.TestMergeIntervals(); WidthOfCalendar.TestWidthOfCalendar(); JosephusProblem.TestJosephusProblem(); // Permutation and Combination problem ShuffleAList.TestFisherYatesAlgo(); CombinationsOfBinaryString.TestCombinationsOfBinaryString(); AllCombinationsOfString.TestAllCombinationsOfString(); AllPermutationsOfString.TestAllPermutationsOfString(); PhoneNumberToWords.TestPhoneNumberToWords(); AllNumbersInRangeWithDifferentDigits.TestAllNumbersInRangeWithDifferentDigits(); DivideSetIntoTwoEqualSetsWithMinSumDiff.TestDivideSetIntoTwoEqualSetsWithMinSumDiff(); PowerSet.TestPowerSet(); AllCombinationsOfParenthesis.TestAllCombinationsOfParenthesis(); GoodDiceRoll.TestGoodDiceRoll(); PermutationsOfValidTime.TestPermutationsOfValidTime(); // Tree Problems TreeFromExpression.TestCreateTreeFromExpression(); TestBinarySearchTree.TestDifferentOperationsOnBST(); AncestorOfTwoNodesInBST.TestAncestorOfTwoNodesInBST(); CheckBTisBST.TestCheckBTisBST(); MaxSumOnTreeBranch.TestMaxSum(); WalkTheTree.TestWalkTheTree(); SkewedBSTToCompleteBST.TestConvertSkewedBSTToCompleteBST(); CheckIfTheTreeIsBalanced.TestIsTreeBalanced(); LinkedListOfTreeNodesAtEachDepth.TestCreateLinkedListOfTreeNodesAtEachDepth(); PrintBinaryTreeNodeAtEachLevel.TestPrintBinaryTreeNodeAtEachLevel(); PrintBinaryTreeNodeAtEachLevelSpirally.TestPrintBinaryTreeNodeAtEachLevelSpirally(); TreeSubtreeOfAnother.TestMatchTree(); AncestorOfTwoNodesInBT.TestGetAncestorOfTwoNodesInBT(); AncestorOfMultiNodesInBT.TestAncestorOfMultiNodesInBT(); LinkedListFromLeavesOfBT.TestLinkedListFromLeavesOfBT(); ExteriorOfBT.TestPrintExteriorOfBT(); DepthOfTree.TestGetDepthOfTree(); TreeToColumns.TestTreeToColumns(); KthSmallestElementFromBST.TestKthSmallestElementFromBST(); MakeBSTFromPreOrder.TestMakeBSTFromPreOrder(); MirrorATree.TestMirrorATree(); CloneABTWithRandPointer.TestCloneABTWithRandPointer(); TreeWithInorderAndPreorder.TestTreeWithInorderAndPreorder(); TreeWithInorderAndPostorder.TestTreeWithInorderAndPostorder(); TreePathSumsToValue.TestTreePathSumsToValue(); AllPathInNArayTree.TestAllPathInNArayTree(); SerializeDeserializeBinaryTree.TestSerializeDeserializeBinaryTree(); SerializeDeserializeAnNaryTree.TestSerializeDeserializeAnNaryTree(); AncestorOfTwoNodesInNaryTree.TestAncestorOfTwoNodesInNaryTree(); AbsOfMaxAndSecondMaxDepthInBT.TestGetAbsOfMaxAndSecondMaxDepthInBT(); // Trie problems CreateAndSearchSimpleTrie.TestCreateAndSearchSimpleTrie(); // ToDo: have a problem of suffix trees ShortestPrefix.TestGetShortestPrefixNotPresentInStringSet(); // Dynamic Programming problems LongestCommonSubsequence.TestGetLongestCommonSubsequence(); LongestPalindromeSubString.TestGetLongestPalindromeSubString(); LongestPalindromicSubsequence.TestGetLongestPalindromicSubsequence(); MaximumAs.TestGetMaximumAs(); MinNumberOfJumps.TestGetMinimumNumberOfJumps(); LongestCommonSubString.TestGetLongestCommonSubString(); KnapSackProblem.TestGetTheMaximumValueWithLimitedWeight(); TreeCuttingProblem.TestGetTreeCuttingToMaximizeProfits(); WordBreaking.TestBreakTheWords(); DistanceOfWords.TestDistanceOfWords(); LongestIncreasingSubSequence.TestLongestIncreasingSubSequence(); MinCostPath.TestMinCostPath(); DifferentWaysForCoinChange.TestDifferentWaysForCoinChange(); MatrixMultiplication.TestMatrixMultiplication(); BinomialCoefficient.TestBinomialCoefficient(); BoxStacking.TestBoxStacking(); WordWrapping.TestWordWrapping(); MaxSubMatrixWithAllOnes.TestMaxSubMatrixWithAllOnes(); LongestSubStringWithEqualSum.TestLongestSubStringWithEqualSum(); PartitionArrayIntoEqualSumSets.TestPartitionArrayIntoEqualSumSets(); MaxSumRectangle.TestMaxSumRectangle(); RegularExpressionMatch.TestRegularExpressionMatch(); NumRepresentedByPerfectSquares.TestNumRepresentedByPerfectSquares(); LongestCommonSubsequenceInSameString.TestLongestCommonSubsequenceInSameString(); StringDecodeAsAlphabets.TestStringDecodeAsAlphabets(); BalloonBursting.TestBalloonBursting(); TravellingSalesmanProblem.TestTravellingSalesmanProblem(); MaxSumWithoutAdjacentElements.TestMaxSumWithoutAdjacentElements(); MaxPathThroughMatrix.TestMaxPathThroughMatrix(); BrickLaying.TestBrickLaying(); JobSchedullingWithConstraints.TestJobSchedullingWithConstraints(); EggDropMinTrials.TestEggDropMinTrials(); // Graph Problems ShortestPath.TestGetShortestPathBetween2Vertex(); CycleInDirectedGraph.TestIsCycleInDirectedGraph(); CycleInUnDirectedGraph.TestIsCycleInUnDirectedGraph(); SolveAMaze.TestSolveAMaze(); AllPathsGivenStartEndVertex.TestGetAllPathsInGraphFromStartVertexToEndVertex(); AllPaths.TestGetAllPathsInGraphFromStartVertex(); ColorVertices.TestColorVerticesWithDifferentColor(); CheckBipartiteGraph.TestCheckBipartiteGraph(); TransformOneWordToAnother.TestGetTransformation(); ConstraintsVerification.TestConstraintsVerification(); ExtendedContactsInSocialNetwork.TestComputeExtendedContacts(); CourseScheduling.TestCourseScheduling(); SnakeAndLadder.TestSnakeAndLadder(); IsGraphATree.TestIsGraphATree(); ReverseGraph.TestReverseGraph(); StronglyConnectedGraph.TestStronglyConnectedGraph(); ConnectedComponents.TestConnectedComponents(); ContinentalDivide.TestContinentalDivide(); CloneGraph.TestCloneGraph(); Wordament.TestWordament(); // ShortestPathAlgo FloydWarshall.TestFloydWarshall(); DijkstraAlgorithm.TestDijkstraAlgorithm(); BellmanFord.TestBellmanFord(); TravelFromLeftToRightInMatrix.TestTravelFromLeftToRightInMatrix(); HeuristicSearch.TestHeuristicSearch(); AStar.TestAStar(); ShortestPathWhenObstaclesRemoved.TestShortestPathWhenObstaclesRemoved(); ShortestDistanceFromRoomsToGates.TestShortestDistanceFromRoomsToGates(); //MaxFlow FordFulkersonEdmondKarp.TestFordFulkersonEdmondKarp(); MinCut.TestMinCut(); MaximumBipartiteMatching.TestMaximumBipartiteMatching(); //Minimum Spanning Tree KruskalAlgorithm.TestKruskalAlgorithm(); PrimsAlgorithm.TestPrimsAlgorithm(); //Heap problems BasicMaxHeap.TestMaxHeap(); BasicMinHeap.TestMinHeap(); TestMinHeapMap.DoTest(); TestPriorityQueue.Run(); MedianForAStreamOfNumbers.TestMedianForAStreamOfNumbers(); //DisjointSets TestingDisjointSet.Run(); //TestWeightedDisjointSetsWithPathCompression.Run(); // this runs slow, hence commenting it //Geometry ClosestPairOfPoints.TestClosestPairOfPoints(); RectangleIntersection.TestRectangleIntersection(); LineSegmentIntersection.TestLineSegmentIntersection(); ConvexHull.TestConvexHull(); KClosestPointToOrigin.TestKClosestPointToOrigin(); //Greedy Algorithm HuffmanCoding.TestHuffmanCoding(); //Randomized Algorithm RandomGeneration.TestRandomGeneration(); // Bit Algorithms IntHaveOppositeSigns.TestIntHaveOppositeSigns(); Parity.TestParity(); //Math Problem ZerosInFactorial.TestZerosInFactorial(); GetAllPrimeFactors.TestGetAllPrimeFactors(); NumberOfFactors.TestNumberOfFactors(); AllFactors.TestAllFactors(); MultiplyLongNumbers.TestMultiplyLongNumbers(); NextLargestPermutation.TestNextLargestPermutation(); AllPrimesTillN.TestAllPrimesTillN(); PascalsTriangle.TestPascalsTriangle(); SubtractLongNumbers.TestSubtractLongNumbers(); //Search problems SearchInSortedRotatedArray.TestSearchInSortedRotatedArray(); KClosestElementInArray.TestKClosestElementInArray(); SearchInSortedMatrix.TestSearchInSortedMatrix(); BinarySearchUnbounded.TestBinarySearchUnbounded(); LinkedListSublistSearch.TestLinkedListSublistSearch(); NoOfOccuranceInSortedArray.TestNoOfOccuranceInSortedArray(); GetSmallestInSortedRotatedArray.TestGetSmallestInSortedRotatedArray(); //Distributed algorithms KWayMerge.TestKWayMerge(); Console.ReadLine(); }
private float basisFunction(int i, float time) { int n = model.ControlPoints.Count - 1; return(BinomialCoefficient.С(n, i) * Mathf.Pow(time, i) * Mathf.Pow(1 - time, n - i)); }