Arup has to make many practice questions for his Computer Science 1 students. Since many ofthe questions deal with arrays, he has to generate arrays for his students. Since he doesn’t want togive them difficult practice problems, he always guarantees that the arrays have unique values. Namely, no value will appear twice in any of his arrays.Unfortunately, Arup is too lazy to generate arrays!About 20 years ago when he started teachingComputer Science 1, he made one really long array to reuse but this long array may have duplicatevalues. When he makes problems, he simply grabs a contiguous subsequence of this long array tobe the array to be used for a problem but he needs to make sure the contiguous subsequence doesnot contain duplicates. If the long array has terms a[0], a[1], …, a[n-1], a contiguous subsequenceof the long array is any sequence of j-i+1 terms a[i], a[i+1], …, a[j] where 0 ≤ i ≤ j ≤ n – 1.
Arup has to make many practice questions for his Computer Science 1 students. Since many of the questions deal with arrays, he has to generate arrays for his students. Since he doesn’t want to give them difficult practice problems, he always guarantees that the arrays (given to the students) have unique values. Namely, no value will appear twice in any of his arrays. Unfortunately, Arup is too lazy to generate arrays! About 20 years ago when he started teaching Computer Science 1, he made one really long array to reuse but this long array may have duplicate values. When he makes problems, he simply grabs a contiguous subsequence of this long array to be the array to be used for a problem but he needs to make sure the contiguous subsequence does not contain duplicates. If the long array has terms a[0], a[1], …, a[n-1], a contiguous subsequence of the long array is any sequence of j-i+1 terms a[i], a[i+1], …, a[j] where 0 ≤ i ≤ j ≤ n – 1. Given an array of n integers, determine how many contiguous subsequences of the array do not contain any repeated values. Note that two subsequences with the same contents are considered different (i.e., both counted in the total) if they start at different locations of the original long array.
