PRACTICE QUESTION STRINGS
Duration: 2 min
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AI Summary
An AI-generated summary of this video lecture.
The video features a lecture solving a multiple-choice question regarding the number of substrings of all lengths for a character string of length n. The question displays four options: a) n!, b) n^2, c) n(n-1)/2 - 1, and d) n(n+1)/2 + 1. The instructor highlights the phrase "substrings (of all lengths inclusive)" to clarify the problem scope. He uses the string "GATE" as a concrete example, noting its length is n=4. He systematically lists the substrings: single characters (G, A, T, E), pairs (GA, AT, TE), triplets (GAT, ATE), and the full string (GATE). He counts these to arrive at a total of 11. He then substitutes n=4 into the formulas for options (c) and (d). Option (c) results in 5, while option (d) results in 11. Since his manual count matches option (d), he selects it as the correct answer.
Chapters
0:00 – 2:00 00:00-02:00
The instructor begins by reading the question: "The number of substrings (of all lengths inclusive) that can be formed from a character string of length n is". He uses a red pen to circle the key terms "substrings" and "of all lengths inclusive" on the screen. To solve this, he writes the example string "GATE" on the digital whiteboard. He breaks down the substrings of "GATE" into groups based on their length: length 1 includes G, A, T, E; length 2 includes GA, AT, TE; length 3 includes GAT, ATE; and length 4 is GATE. He writes "n=4" to denote the length of the example string. He then proceeds to evaluate the given options by substituting n=4. He calculates the value for option (c) n(n-1)/2 - 1, writing "4(3)/2 - 1" which equals 5. He circles the result "5". Next, he evaluates option (d) n(n+1)/2 + 1, writing "4(5)/2 + 1" which equals 11. He writes "11" next to his list of substrings, indicating that he has counted 11 substrings in total.
2:00 – 2:09 02:00-02:09
The instructor concludes the problem by finalizing his selection. He has circled the number "11" which corresponds to his manual count of substrings for the string "GATE". He then circles option (d) n(n+1)/2 + 1, confirming it as the correct formula based on the example. The final frame shows the circled option (d) and the calculated value 11, solidifying the connection between the example count and the algebraic expression.
The instructor demonstrates a problem-solving strategy for combinatorial string problems by using a concrete example to verify general formulas. By breaking down the string "GATE" into its constituent substrings and counting them to get 11, he establishes a baseline. He then validates this count against the provided algebraic options, finding that option (d) yields the same value (11) when n=4. This confirms option (d) as the correct answer in the context of this specific problem instance.