By Anil K. Jain
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Extra info for Algorithms for Clustering Data
Q-1] and x is not present in these already searched columns. j] that contains x followed by making this region smaller till x is found. Initial bounded searcheable region is represented by : i = 0 p = m - 1 q = 0 j = n - 1 Looking at bounds of the rectangle, there are 4 ways to march towards contracting it: if a[i,j] < x then since the row is ordered i ← i + 1, because if a[i,j] > x, then all the entries of that row is also greater than x. , in ith row. if a[p,q] > x p ← p - 1 if a[p,q] < x q ← q + 1 if a[i,j] > x j ← j - 1 These conditions are also known as guards.
It came out as a result of numerous requests received from coders across the Globe, primarily from Google aspirants. Author has a vast collection of algorithmic problems since 20 years including experience in preparing computer science students for participation in programming contests like TopCoder, ACM ICPC and others. 2 Proof Bibliography * List of Algorithms 1 Partitioning a sequence 2 Quicksort to sort a sequence 3 Randomized Partition Algorithm 4 Randomized Quicksort Algorithm 5 Selecting a c-approximate median of X with O(n) complexity 6 Back-Tracking 7 Finding Misplaced Nuts and Bolts 8 Saddleback Search Algorithm 9 Saddleback Search Algorithm in practice 10 Saddleback Search Algorithm : Find First Occurrence 11 Saddleback Search Algorithm : Find All Occurrences 12 Saddleback Count Algorithm : Initial Approach 13 Saddleback Count : Correct Algorithm 14 Kadane’s 1D Algorithm 15 Kadane’s 1D Algorithm : Find Indices 16 Maximum sub-array sum using prefix array 17 K-Maximum sub-array sum using prefix array 18 Exhaustive Search Algorithm 19 Exhaustive Search Algorithm : Improved 20 Row Based 2D Binary Search 21 Searching in a 2D Array 22 Searching in a 2D Array : Another Program 23 Searching in a 2D Array : Another Program(Simplified) 24 Maximum of a sequence 25 Generic Kth Select Minimum 26 Partitioning a sequence 27 Randomized Partition Algorithm 28 Randomized Quicksort Algorithm 29 Randomized Kth Min Select Algorithm 30 Iterative Version of Quick Select Algorithm 31 Searching in a possibly empty 2D Array 32 Celebrity Algorithm 33 Celebrity Algorithm Brute Force 34 Celebrity Algorithm Optimized 35 Switches And Bulbs Problem 36 Interpolation Search Algorithm 37 Find Majority Simple Algorithm 38 Find Majority Algorithm Revisited 39 Find Majority Algorithm Simplified 40 Find Majority Algorithm Final 41 The Plateau Problem 42 The Plateau Problem Revisited 43 All Zeros Program 44 The Non-Crooks Program 45 Find Median of two sorted array 46 Median Search List of listings 1 Partitioning in C++ 2 STL style implementation of partition 3 std::partition 4 quicksort in C++ 5 STL style implementation of quicksort 6 Implementing quicksort 7 randomized partition in C++ 8 randomized quicksort in C++ 9 Saddleback search in C++11 10 Using Saddleback Search 11 Saddleback Search : First Occurrence 12 Using Saddleback Search : First Occurrence 13 Saddleback Find All 14 Using Saddleback Find All 15 Another Usage of Saddleback Find All 16 Continue Using Saddleback Find All 17 Saddleback Count : Initial Approach 18 Using Saddleback Count 19 Using Saddleback Count : Count of 6 should be 6 20 Implementing Saddleback Count 21 Using Saddleback Count 22 another Usage of Saddleback Count 23 Simple n-ary tree 24 Compute LCA : C++ : Stack Based 25 Compute LCA : C++ : Level Based 26 Implementing Kadane’s Algorithm 27 Implementing Kadane’s Algorithm 28 Implementing Kadane’s Algorithm : Finding Indices 29 Using Kadane’s Algorithm : Finding Indices 30 Finding sum closest to zero 31 C++ Implementation : Find the next higher permutation 32 next_permutation 33 reversing a sequence 34 C++ Implementation of prev_permutation 35 Usage of previous permutation 36 Implementation of C++ Binary Search 37 Implementation of C++ Lower Bound 38 Custom Implementation of Binary Search 39 Usage of Custom Implementation of Binary Search 40 Simple Implementation : Levenshtein edit distance 41 Improved Implementation : Levenshtein edit distance 42 Boost Implementation : Levenshtein edit distance 43 searching 2D Array 44 Search for 6 : yields a : 2 2 45 C++11 Version : Searching 2D Array 46 Usage : C++11 Version : Searching 2D Array 47 Finding Maximum in an integer array 48 Finding First Maximum in an integer array 49 Finding First Maximum Satisfying Predicate 50 Finding First Minimum in an integer array 51 Ordering Equivalence 52 caption=Finding Last Maximum in an integer array 53 Finding Last Minimum in an integer array 54 Another Ordering Equivalence 55 C++ Implementation of first min and first max 56 first_min_last_max_element 57 Generic Kth Select Minimum 58 Randomized version of Kth Select Minimum 59 Searching 2D Array 60 Search for 6 : yields a 2 2 61 Finding Celebrity Program 62 Interpolation Search 63 generate efficient permutation * Chapter 1 Matching Nuts and Bolts Optimally Problem1 (G.
T(n) = T(n - 1) + T(0) + Θ(n) = T(n - 1) + Θ(n) = Θ(n2) Best case partition will result into almost equal size subsequences every time. T(n) = 2T(n∕2) + Θ(n) = Θ(nlog n) quicksort’s average case is closer to the best case than to the worst case. 4 Randomized Quicksort So far we have assumed that all input permutations are equally likely which is true always, hence we add randomization to quicksort. e. chosing element at random, to achieve this. So instead of picking the last element a[r] as pivot, it is picked up randomly from the sequence.
Algorithms for Clustering Data by Anil K. Jain