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• String searching
  ...e number of matches found for the needle in the haystack), which is linear time. ...ear-time algorithm, as it will use <math>O(m + n_1 + m + n_2 + ...)</math> time, which is the same as <math>O(n_1 + n_2 + ...)</math> since the needle is n
  16 KB (2,766 words) - 19:54, 6 April 2011
• Knuth–Morris–Pratt algorithm
  ...Together with linear time preprocessing of the needle, this gives a linear time algorithm overall. ...'', occupies linear space, and, as we shall see, can be computed in linear time. It contains ''all'' the information we need in order to execute the "smart
  18 KB (3,295 words) - 22:01, 11 December 2011
• Rabin–Karp algorithm
  ...thm, which simply assumes all probable matches are correct, guaranteeing a linear runtime but with a small probability of false positives. ...al to the length of the needle. (In general, equality comparisons may take time proportional to the amount of data being compared. Hence, a CPU can often c
  9 KB (1,664 words) - 16:33, 29 May 2011
• Sliding range minimum query
  ...pecial case is important because it can be solved in linear time (that is, linear in the size of the array plus the number of query intervals) and requires n ...'remove'' in logarithmic time and ''query'' in constant time. This gives a time bound of <math>O(N \log N + Q)</math> where <math>N</math> is the size of t
  5 KB (938 words) - 21:33, 4 April 2021
• Map
  ..., ''Search'', ''Delete'', and ''Change'' have a worst-case time complexity linear in the size of the list, as they may have to examine all of its elements, w [[Skip list]]s are not often used in practice, but offer the same time complexity guarantees as BBSTs and are efficient with space as well.
  13 KB (2,270 words) - 18:16, 25 February 2012
• All nearest smaller values
  ...we do a linear scan on each element, we get a trivial <math>O(n^2)</math> time solution to ANSV. However, it turns out that there is a simple linear time (<math>O(n)</math>) solution to ANSV, which is clearly asymptotically optim
  4 KB (826 words) - 14:12, 2 January 2018
• Range minimum query
  ...range given and selecting the minimum element, which can take up to linear time. The problem is interesting because we often desire to answer a large numbe This problem can be solved in linear time in the special case in which the intervals are guaranteed to be given in su
  14 KB (2,606 words) - 16:46, 24 April 2014
• Lowest common ancestor
  ...s approach will actually perform quite well (around <math>O(\log N)</math> time per query, where <math>N</math> is the size of the tree). ...> time (that is, linear)<ref>Gabow, H. N.; Tarjan, R. E. (1983), "A linear-time algorithm for a special case of disjoint set union", ''Proceedings of the 1
  11 KB (2,023 words) - 23:03, 5 April 2016
• Cartesian tree
  The naive method described above may take up to <math>O(N^2)</math> time, since it requires scanning the sequence to find its minimum, then scanning This is true just before the loop runs for the first time (<math>m = 0</math>), because we will have a singleton tree that contains j
  17 KB (3,062 words) - 18:02, 13 June 2016
• Prefix sum array and difference array
  We see that the difference array can be computed in [[linear time]] from the original array, and is shorter than the original array by one el ..., 18, 18, 25]</math>. Computing the prefix sum array can be done in linear time as well, and the prefix sum array is longer than the original array by one
  25 KB (4,594 words) - 23:35, 19 December 2023
• Hidden constant factor
  When the time or space required for an [[algorithm]] is expressed in terms of the input s ...always design a faster machine, which would make our algorithms take less time to run, but that wouldn't reflect the efficiency of the algorithm itself; a
  4 KB (675 words) - 08:49, 18 February 2012
• Asymptotic analysis
  ...refers to the fact that this form of analysis neglects the exact amount of time or memory that the algorithm uses on specific cases, but is concerned only ...mn, the execution time of Alice's program in the second, and the execution time of Bob's program in the third:
  47 KB (8,394 words) - 02:12, 10 October 2012
• Binary search
  ...bisection strategy'', or ''binary search'', is a vast improvement over the linear search. ...ments of the array are simple scalar variables that take <math>O(1)</math> time to compare. However, because the array is sorted, we can do better than thi
  21 KB (3,719 words) - 05:17, 19 March 2017
• Binomial heap
  ...ath>m</math> and <math>n</math> can be merged in <math>O(\log(m+n))</math> time). ...wo tree, again of size <math>2^{k-1}</math>. This procedure takes constant time.
  15 KB (2,633 words) - 06:16, 10 October 2012
• Shunting yard algorithm
  ...o right. It also constructs the postfix notation from left to right. Every time an operand is encountered, it is immediately transferred to the output stre ...contribution to the running time.) The space requirement is also obviously linear.
  15 KB (2,569 words) - 19:07, 21 October 2015
• Maximum subvector sum
  ...'''61'''.</ref> In algorithmic programming competitions, Kadane's [[linear time]] algorithm for this problem is often useful as a building block within a m ...ef name="bentley"/> describes four algorithms for this problem, of running time <math>O(n^3)</math>, <math>O(n^2)</math>, <math>O(n\log n)</math>, and <mat
  9 KB (1,454 words) - 06:09, 3 May 2012