51.
. . . . . . . . is a family of combinatorial optimization problems in which a graph is partitioned into two or more parts with constraints.

52.
Which of the following graphs don't have chromatin number less than or equal to 2?

55.
What will be the worst case time complexity of finding the sum of elements in a given range of (l,r) in an array of size n when we use square root optimization?

57.
What will be output for the given code?
#include<bits/stdc++.h> 
using namespace std; 
string encrypter(string keyword) 
{ 
	string encoded = ""; 	
	bool arr[26] = {0}; 
	for (int i=0; i<keyword.size(); i++) 
	{ 
		if(keyword[i] >= 'A' && keyword[i] <= 'Z') 
		{ 		
			if (arr[keyword[i]-65] == 0) 
			{ 
				encoded += keyword[i]; 
				arr[keyword[i]-65] = 1; 
			} 
		} 
		else if (keyword[i] >= 'a' && keyword[i] <= 'z') 
		{ 
			if (arr[keyword[i]-97] == 0) 
			{ 
				encoded += keyword[i] - 32; 
				alpha[keyword[i]-97] = 1; 
			} 
		} 
	} 
	for (int i=0; i<26; i++) 
	{ 
		if(arr[i] == 0) 
		{ 
			arr[i]=1; 
			encoded += char(i + 65); 
		} 
	} 
	return encoded; 
} 
string ciphertxt(string msg, string encoded) 
{ 
	string cipher=""; 
	for (int i=0; i<msg.size(); i++) 
	{ 
		if (msg[i] >='a' && msg[i] <='z') 
		{ 
			int pos = msg[i] - 97; 
			cipher += encoded[pos]; 
		} 
		else if (msg[i] >='A' && msg[i] <='Z') 
		{ 
			int pos = msg[i] - 65; 
			cipher += encoded[pos]; 
		} 
		else
		{ 
			cipher += msg[i]; 
		} 
	} 
	return cipher; 
} 
int main() 
{ 
	string keyword; 
	keyword = "cipher"; 	
	string encoded = encrypter(keyword); 
	string message = "hello"; 
	cout  << ciphertxt(message,encoded) << endl; 
	return 0; 
}

58.
What is the set partition problem?

59.
Find the output of the following code.
#include<math.h> 
#include<iostream.h>
using namespace std;
void distance(float x, float y, float a, float b, float c) 
{ 
	float d = fabs((a * x + b * y + c)) / (sqrt(a * a + b * b)); 
	cout<<d;
	return; 
} 
int main() 
{ 
	float x = -2; 
	float y = -3; 
	float a = 5; 
	float b = -2; 
	float c = - 4; 
	distance(x, y, a, b, c); 
	return 0; 
}