feature: friends pairing problem sol added

Author: Debashis08

include/0005_DynamicProgramming/0009_FriendsPairingProblem.h

@@ -0,0 +1,46 @@
+#pragma once
+
+#include<vector>
+using namespace std;
+
+/*
+Pattern 1
+Linear Recurrence
+
+Description
+Given n friends, each one can remain single or can be paired up with some other friend. Each friend can be paired only once. Find out the total number of ways in which friends can remain single or can be paired up.
+
+Examples:
+
+Input  : n = 3
+Output : 4
+Explanation:
+{1}, {2}, {3} : all single
+{1}, {2, 3} : 2 and 3 paired but 1 is single.
+{1, 2}, {3} : 1 and 2 are paired but 3 is single.
+{1, 3}, {2} : 1 and 3 are paired but 2 is single.
+Note that {1, 2} and {2, 1} are considered same.
+
+Mathematical Explanation:
+The problem is simplified version of how many ways we can divide n elements into multiple groups.
+(here group size will be max of 2 elements).
+In case of n = 3, we have only 2 ways to make a group:
+	1) all elements are individual(1,1,1)
+	2) a pair and individual (2,1)
+In case of n = 4, we have 3 ways to form a group:
+	1) all elements are individual (1,1,1,1)
+	2) 2 individuals and one pair (2,1,1)
+	3) 2 separate pairs (2,2)
+*/
+
+namespace FriendsPairingProblem
+{
+	class DynamicProgramming
+	{
+	private:
+		int CountFriendsPairingsRecursiveHelper(int n);
+	public:
+		int RecursiveCountFriendsPairings(int n);
+		int DpCountFriendsPairings(int n);
+	};
+}

source/0005_DynamicProgramming/0009_FriendsPairingProblem.cc

@@ -0,0 +1,39 @@
+#include "../../include/0005_DynamicProgramming/0009_FriendsPairingProblem.h"
+
+namespace FriendsPairingProblem
+{
+	// Dynamic Programming Private Member Methods.
+	int DynamicProgramming::CountFriendsPairingsRecursiveHelper(int n)
+	{
+		if (n <= 1)
+		{
+			return 1;
+		}
+		int result = 0;
+		result += this->CountFriendsPairingsRecursiveHelper(n - 1);
+		result += (n - 1) * this->CountFriendsPairingsRecursiveHelper(n - 2);
+
+		return result;
+	}
+
+	// Dynamic Programming Public Member Methods.
+	int DynamicProgramming::RecursiveCountFriendsPairings(int n)
+	{
+		return this->CountFriendsPairingsRecursiveHelper(n);
+	}
+
+	int DynamicProgramming::DpCountFriendsPairings(int n)
+	{
+		vector<int> dp(n + 1, 0);
+		dp[0] = 0;
+		dp[1] = 1;
+		dp[2] = 2;
+
+		for (int i = 3; i <= n; i++)
+		{
+			dp[i] = dp[i - 1] + (i - 1) * dp[i - 2];
+		}
+
+		return dp[n];
+	}
+}

source/0005_DynamicProgramming/CMakeLists.txt

@@ -8,7 +8,7 @@ set(0005DYNAMICPROGRAMMING_SOURCES
     0006_HouseRobber2.cc
     0007_DecodeWays.cc
     0008_TilingProblem.cc
-
+    0009_FriendsPairingProblem.cc
 )
 
 # Create a library target

test/0005_DynamicProgramming/0009_FriendsPairingProblemTest.cc

@@ -0,0 +1,91 @@
+#include <gtest/gtest.h>
+#include "../../include/0005_DynamicProgramming/0009_FriendsPairingProblem.h"
+
+namespace FriendsPairingProblem
+{
+	TEST(FriendsPairingProblemDynamicProgrammingTest, RecursiveCountFriendsPairingsTest1)
+	{
+		// Arrange
+		DynamicProgramming dp;
+		int numberOfFriends = 3;
+		int expectedPairings = 4;
+		
+		// Act
+		int actualPairings = dp.RecursiveCountFriendsPairings(numberOfFriends);
+
+		// Assert
+		ASSERT_EQ(expectedPairings, actualPairings);
+		EXPECT_EQ(dp.RecursiveCountFriendsPairings(4), 10);
+		EXPECT_EQ(dp.RecursiveCountFriendsPairings(5), 26);
+	}
+
+	TEST(FriendsPairingProblemDynamicProgrammingTest, RecursiveCountFriendsPairingsTest2)
+	{
+		// Arrange
+		DynamicProgramming dp;
+		int numberOfFriends = 4;
+		int expectedPairings = 10;
+
+		// Act
+		int actualPairings = dp.RecursiveCountFriendsPairings(numberOfFriends);
+
+		// Assert
+		ASSERT_EQ(expectedPairings, actualPairings);
+	}
+
+	TEST(FriendsPairingProblemDynamicProgrammingTest, RecursiveCountFriendsPairingsTest3)
+	{
+		// Arrange
+		DynamicProgramming dp;
+		int numberOfFriends = 5;
+		int expectedPairings = 26;
+
+		// Act
+		int actualPairings = dp.RecursiveCountFriendsPairings(numberOfFriends);
+
+		// Assert
+		ASSERT_EQ(expectedPairings, actualPairings);
+	}
+
+	TEST(FriendsPairingProblemDynamicProgrammingTest, DpCountFriendsPairingsTest1)
+	{
+		// Arrange
+		DynamicProgramming dp;
+		int numberOfFriends = 3;
+		int expectedPairings = 4;
+
+		// Act
+		int actualPairings = dp.RecursiveCountFriendsPairings(numberOfFriends);
+
+		// Assert
+		ASSERT_EQ(expectedPairings, actualPairings);
+	}
+
+	TEST(FriendsPairingProblemDynamicProgrammingTest, DpCountFriendsPairingsTest2)
+	{
+		// Arrange
+		DynamicProgramming dp;
+		int numberOfFriends = 4;
+		int expectedPairings = 10;
+
+		// Act
+		int actualPairings = dp.RecursiveCountFriendsPairings(numberOfFriends);
+
+		// Assert
+		ASSERT_EQ(expectedPairings, actualPairings);
+	}
+
+	TEST(FriendsPairingProblemDynamicProgrammingTest, DpCountFriendsPairingsTest3)
+	{
+		// Arrange
+		DynamicProgramming dp;
+		int numberOfFriends = 5;
+		int expectedPairings = 26;
+
+		// Act
+		int actualPairings = dp.RecursiveCountFriendsPairings(numberOfFriends);
+
+		// Assert
+		ASSERT_EQ(expectedPairings, actualPairings);
+	}
+}

test/0005_DynamicProgramming/CMakeLists.txt

@@ -22,6 +22,7 @@ add_executable(
   0006_HouseRobber2Test.cc
   0007_DecodeWaysTest.cc
   0008_TilingProblemTest.cc
+  0009_FriendsPairingProblemTest.cc
 
 )