Miscellaneous On Data Structures - Study Mode

[#806] Calculating the chromatic index of a graph is a . . . . . . . .
Correct Answer

(C) NP complete problem

[#807] What is the formula used for encryption of data using affine cipher(a,b are constants and x is the numerical equivalent of a letter to be encrypted)?
Correct Answer

(B) (ax+b)%26

[#808] What is testing of a complete bipartite subgraph in a bipartite graph problem called?
Correct Answer

(D) NP-Complete Problem

[#809] What will be the plain text corresponding to cipher text "KEPWSN" if running key cipher is used with keyword as "DATASTRUCTURE"?
Correct Answer

(A) GEWWAU

Explanation

Solution: Running Key Cipher: In a running key cipher, the plaintext is encrypted by combining it with a keyword. The keyword is repeated as needed to match the length of the plaintext. Given: Ciphertext: "KEPWSN" Keyword: "DATASTRUCTURE" Steps to Decrypt Using Running Key Cipher: Step 1: Convert the keyword "DATASTRUCTURE" and the ciphertext "KEPWSN" to their numeric values. Keyword: D=4, A=0, T=19, A=0, S=18, T=19, R=18 Ciphertext: K=10, E=4, P=15, W=22, S=18, N=13 Step 2: Align the numeric values of the keyword with the ciphertext: Ciphertext: K=10, E=4, P=15, W=22, S=18, N=13 Keyword: D=4, A=0, T=19, A=0, S=18, T=19 Step 3: Subtract the keyword values from the ciphertext values and take modulo 26 to get the plaintext values: For K - D: (10 - 4) mod 26 = 6 = G For E - A: (4 - 0) mod 26 = 4 = E For P - T: (15 - 19) mod 26 = 22 = W For W - A: (22 - 0) mod 26 = 22 = W For S - S: (18 - 18) mod 26 = 0 = A For N - T: (13 - 19) mod 26 = 20 = U Conclusion: The decrypted plaintext from the ciphertext "KEPWSN" using the Running Key cipher with the keyword "DATASTRUCTURE" is "GEWWAU". Therefore, the correct answer is Option A: GEWWAU.

[#810] Which of the following operation will give a vector that is perpendicular to both vectors a and b?
Correct Answer

(D) both a x b and b x a