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- 18:09, 28 October 2020 Solution Wiki, The Algorithm Design Manual, 3rd Edition (hist) [2,007 bytes] Algowikiadmin (talk | contribs) (Created page with " The Wiki is an experiment, a grass-roots effort to create an answer key to aid self-study with the third edition of Steven Skiena's ''The Algorithm Design Manual''. Students...")
- 14:12, 21 September 2020 8.29 (hist) [238 bytes] Algowikiadmin (talk | contribs) (Created page with "1. Find maximum matching. Bipartite matching is described in the book. General matching would require Edmonds Blossom algorithm. 2. Include an arbitrary edge for every uncover...")
- 14:12, 21 September 2020 8.27 (hist) [438 bytes] Algowikiadmin (talk | contribs) (Created page with "The problem reduces to Floyd - Warshall algorithm if you take logs of all currency-exchange rates, as if a * b = c then ln(a) + ln(b) = ln(c). In computational finance people...")
- 14:11, 21 September 2020 8.25 (hist) [561 bytes] Algowikiadmin (talk | contribs) (Created page with "Step 1: Perform topological sorting of the graph (we can do it as Graph is acyclic). This is O(n + m) Step 2: Go through vertices in topological order. Initially all vertic...")
- 14:10, 21 September 2020 8.23 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:09, 21 September 2020 8.21 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:09, 21 September 2020 8.19 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:09, 21 September 2020 8.17 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:09, 21 September 2020 8.15 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:07, 21 September 2020 8.13 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:07, 21 September 2020 8.11 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:07, 21 September 2020 8.9 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:07, 21 September 2020 8.7 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:06, 21 September 2020 8.5 (hist) [252 bytes] Algowikiadmin (talk | contribs) (Created page with "In both algorithms, an edge can only ever be picked once, so they will both eventually terminate regardless of negative edge weights. I also suspect that they still generate...")
- 14:06, 21 September 2020 8.3 (hist) [252 bytes] Algowikiadmin (talk | contribs) (Created page with "No. Counter example provided below: G(V,E,W) = ((A,B,C,D),({A,B},{B,C},{C,D},{D,A}),(1,2,3,4)) Minimum spanning tree has a weight of 6 with edges {A,B},{B,C},{C,D}. In the...")
- 14:04, 21 September 2020 8.1 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 8")
- 14:02, 21 September 2020 9.33 (hist) [2,114 bytes] Algowikiadmin (talk | contribs) (Created page with "We avoid sums and products and throw away parts of the sample space we don't need. At the same time, we want to be efficient in our use of the space. Conceptually we create a...")
- 14:02, 21 September 2020 9.31 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:02, 21 September 2020 9.29 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:01, 21 September 2020 9.27 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:01, 21 September 2020 9.25 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:01, 21 September 2020 9.23 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:01, 21 September 2020 9.21 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:00, 21 September 2020 9.19 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:00, 21 September 2020 9.17 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:00, 21 September 2020 9.15 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:00, 21 September 2020 9.13 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 14:00, 21 September 2020 9.11 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 13:52, 21 September 2020 9.9 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 13:52, 21 September 2020 9.7 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 13:52, 21 September 2020 9.5 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 13:51, 21 September 2020 9.3 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 9")
- 13:51, 21 September 2020 9.1 (hist) [1,837 bytes] Algowikiadmin (talk | contribs) (Created page with "== Algorithm == Given <code>a</code>, the input array, and <code>curr</code>, the derangement built up so far: # If <code>curr</code> represents a complete solution, print i...")
- 13:49, 21 September 2020 10.39 (hist) [3,139 bytes] Algowikiadmin (talk | contribs) (Created page with "== A Python Solution - O(1) == <PRE> import sys n = int(sys.argv[1]) OUT_TMP = "Min # of coins for covering %d: %d, coins used: %s" COINS = tuple(sorted((3, 4, 9, 20, 22, 23)...")
- 13:49, 21 September 2020 10.41 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:48, 21 September 2020 10.37 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:44, 21 September 2020 10.35 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:44, 21 September 2020 10.33 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:44, 21 September 2020 10.31 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:44, 21 September 2020 10.29 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:44, 21 September 2020 10.27 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:40, 21 September 2020 10.23 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:40, 21 September 2020 10.21 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:39, 21 September 2020 10.19 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 13:39, 21 September 2020 10.17 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 01:31, 21 September 2020 10.15 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 01:17, 21 September 2020 10.11 (hist) [534 bytes] Algowikiadmin (talk | contribs) (Created page with "Answer to both a) and b) is no. Knapsack problem is NP-complete. ---- (a) Yes, this is a special case of the Knapsack problem where the value of each item is the same (desc...")
- 01:17, 21 September 2020 10.13 (hist) [2,566 bytes] Algowikiadmin (talk | contribs) (Created page with "==== 1 ==== # 20 x 1 # 1 x 6 + 14 x 1 # 2 x 6 + 8 x 1 # 3 x 6 + 2 x 1 # 1 x 10 + 10 x 1 # 1 x 10 + 1 x 6 + 4 x 1 # 2 x 10 ==== 2 ==== More generally: # there is always o...")
- 01:16, 21 September 2020 10.9 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 01:16, 21 September 2020 10.7 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 01:15, 21 September 2020 10.1 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 01:15, 21 September 2020 10.5 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 01:15, 21 September 2020 10.3 (hist) [24 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 10")
- 01:13, 21 September 2020 7.43 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:13, 21 September 2020 7.41 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:13, 21 September 2020 7.39 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:12, 21 September 2020 7.37 (hist) [3,727 bytes] Algowikiadmin (talk | contribs) (Created page with "Proof by induction. A tournament with 2 vertices (1,2) has a Hamiltonian path. 1 -> 2 or vice versa Now suppose our tournament with n vertices has a Hamiltonian path 1,..,n....")
- 01:11, 21 September 2020 7.35 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:11, 21 September 2020 7.33 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:11, 21 September 2020 7.31 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:11, 21 September 2020 7.29 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:11, 21 September 2020 7.27 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:09, 21 September 2020 7.25 (hist) [334 bytes] Algowikiadmin (talk | contribs) (Created page with "Use the BFS starting from the vertex v. For every node keep track of the level from the vertex v. When w is encountered for the first time the level of w is the length of the...")
- 01:07, 21 September 2020 7.23 (hist) [1,381 bytes] Algowikiadmin (talk | contribs) (Created page with " for any node in the tree, there are two possibilities # either the diameter is contained in one of the subtrees # or the node itself is at the top of the longest path in the...")
- 01:06, 21 September 2020 7.21 (hist) [2,464 bytes] Algowikiadmin (talk | contribs) (Created page with "(a) Compare every possible set of three vertices and test if there is an edge between the three. (b) One may be tempted to use DFS to find cycle of length 3, by maintaining a...")
- 01:05, 21 September 2020 7.19 (hist) [232 bytes] Algowikiadmin (talk | contribs) (Created page with "# This translates to the question of labeling the tree with two colors, because this way each edge's vertices are colored differently. The larger group of colors is the sought...")
- 01:04, 21 September 2020 7.17 (hist) [1,498 bytes] Algowikiadmin (talk | contribs) (Created page with "1) We can determine that leafs should never be included into the cover. Therefore all leaves should be unmarked, which means that all of their parents should be marked. Now we...")
- 01:03, 21 September 2020 7.15 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:03, 21 September 2020 7.13 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:02, 21 September 2020 7.11 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:02, 21 September 2020 7.9 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:01, 21 September 2020 7.7 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 7")
- 01:01, 21 September 2020 7.5 (hist) [1,169 bytes] Algowikiadmin (talk | contribs) (Created page with "Graphs with max degree 2, can be bipartite (even number of edges) or tripartite (odd number of edges) ----- Consider a triangle (3 edges, 3 vertices): it's not bipartite eve...")
- 01:00, 21 September 2020 7.3 (hist) [325 bytes] Algowikiadmin (talk | contribs) (Created page with "Induction proof: Base case: Tree composed of just two nodes: x(root) and y. There is only one way x -> y Assuming there is an unique path between x and y, we add a new leaf...")
- 00:59, 21 September 2020 7.1 (hist) [241 bytes] Algowikiadmin (talk | contribs) (Created page with "(a) BFS: * Graph G1: A, B, D, I, C, E, G, J, F, H * Graph G2: A, B, E, C, F, I, D, G, J, M, H, K, N, L, O, P (b) DFS: * Graph G1: A, B, C, E, D, G, H, F, J, I * Graph G2: A,...")
- 00:58, 21 September 2020 6.11 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 6")
- 00:58, 21 September 2020 6.9 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 6")
- 00:58, 21 September 2020 6.7 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 6")
- 00:58, 21 September 2020 6.5 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 6")
- 00:58, 21 September 2020 6.1 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 6")
- 00:57, 21 September 2020 6.3 (hist) [1,666 bytes] Algowikiadmin (talk | contribs) (Created page with "1) Starting from left to right, the number of inversions for 1st number is n-1 for 2nd number is n-2 ... .. ....nth number is n-n = 0 Total number of inversions is...")
- 00:56, 21 September 2020 5.15 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 5")
- 00:56, 21 September 2020 5.13 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 5")
- 00:56, 21 September 2020 5.11 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 5")
- 00:56, 21 September 2020 5.9 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 5")
- 00:56, 21 September 2020 5.7 (hist) [729 bytes] Algowikiadmin (talk | contribs) (Created page with "<math>O(n+m)</math> is necessary and sufficient. Lower bound comes from potentially independent values along second diagonal -- upper bound comes from observing that we can el...")
- 00:55, 21 September 2020 5.5 (hist) [520 bytes] Algowikiadmin (talk | contribs) (Created page with "Apply binary search to find out transition point <pre> Assume set indexes are zero based FindIndex(A): 1. low = 0, high =1 2. mid = (low + high)/2 3. if(A[mid] >...")
- 00:54, 21 September 2020 5.3 (hist) [391 bytes] Algowikiadmin (talk | contribs) (Created page with "(1) Do a binary search within the range of <math>1-n</math>. You guess the right number within O(log n) questions. (2) If you don't know n start with a random number <math>2^...")
- 00:53, 21 September 2020 5.1 (hist) [888 bytes] Algowikiadmin (talk | contribs) (Created page with "'''Part -1''' Since set is sorted the max element will lie at position <pre> Since set is sorted the max element will lie at position Max = Set[k] where k != 0 Set[n...")
- 18:36, 20 September 2020 4.51 (hist) [802 bytes] Algowikiadmin (talk | contribs) (Created page with "If we are allowed to maintain a second stack on the side, this should be possible. The main stack is a regular stack that can be implemented using an array and an index to the...")
- 18:36, 20 September 2020 4.53 (hist) [2,780 bytes] Algowikiadmin (talk | contribs) (Created page with "If we are allowed to maintain a second stack on the side, this should be possible. The main stack is a regular stack that can be implemented using an array and an index to the...")
- 18:35, 20 September 2020 4.49 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 4")
- 18:34, 20 September 2020 4.47 (hist) [475 bytes] Algowikiadmin (talk | contribs) (Created page with " For a known set of integer numbers ( assume Nr-1, Nr-2 ... Nr-k) the best is to use a non-comparison based sort algorithm like radix sort with O(n) You have an array that cr...")
- 18:33, 20 September 2020 4.45 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 4")
- 18:32, 20 September 2020 4.43 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 4")
- 18:32, 20 September 2020 4.41 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 4")
- 18:31, 20 September 2020 4.39 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 4")
- 18:30, 20 September 2020 4.37 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 4")
- 18:30, 20 September 2020 4.35 (hist) [668 bytes] Algowikiadmin (talk | contribs) (Created page with "It's not clear to me if the first <math>n - \sqrt n</math> element being sorted means that the remaining <math>\sqrt n</math> elements are all bigger or not, but let's suppose...")
- 18:30, 20 September 2020 4.33 (hist) [23 bytes] Algowikiadmin (talk | contribs) (Created page with " Back to Chapter 4")