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Question 1: Find duplicate numbers in the array.
All numbers in an array of length N are within the range of 0-n-1. Some numbers in the array are repeated, but I don’t know how many numbers are repeated. I don’t know how many times the number is repeated. Please find any repeated number in the array.
Solution 1: Sort this array. It is very easy to find duplicate numbers from the sorted array. Just scan the sorted array from beginning to end. Sorting an array of length N requires O(nLogn) time.
Solution 2: Use a hash table to solve the problem. Scan each number in the array from beginning to end. Each time a number is scanned, determine whether the number is in the hash table. This The time of the algorithm is O(N), but its time efficiency comes at the expense of a hash table of size O(N).
Solution 3: We rearrange the array and scan each number in the array from beginning to end. When the number with subscript i is scanned, compare the value of this number (m) Is it equal to i? If it is equal, the value of m is paid to i. If it is not equal, compare it with the value corresponding to the m subscript until all repeated values are found.
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