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how to make barcode in c#.net Figure 410 Singleedge extensions of known shortest paths in Software
Figure 410 Singleedge extensions of known shortest paths Generate QRCode In None Using Barcode printer for Software Control to generate, create QR Code ISO/IEC18004 image in Software applications. QR Code ISO/IEC18004 Decoder In None Using Barcode reader for Software Control to read, scan read, scan image in Software applications. Known region R
QR Code ISO/IEC18004 Printer In Visual C#.NET Using Barcode creator for .NET Control to generate, create QR Code ISO/IEC18004 image in .NET applications. Draw QRCode In .NET Using Barcode creation for ASP.NET Control to generate, create QR Code image in ASP.NET applications. An alternative derivation
Generate QRCode In Visual Studio .NET Using Barcode printer for VS .NET Control to generate, create QR Code image in Visual Studio .NET applications. Denso QR Bar Code Drawer In VB.NET Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in Visual Studio .NET applications. Here s a plan for computing shortest paths: expand outward from the starting point s, steadily growing the region of the graph to which distances and shortest paths are known This growth should be orderly, rst incorporating the closest nodes and then moving on to those further away More precisely, when the known region is some subset of vertices R that includes s, the next addition to it should be the node outside R that is closest to s Let us call this node v; the question is: how do we identify it To answer, consider u, the node just before v in the shortest path from s to v: Data Matrix ECC200 Printer In None Using Barcode generator for Software Control to generate, create DataMatrix image in Software applications. EAN13 Supplement 5 Creator In None Using Barcode drawer for Software Control to generate, create EAN13 image in Software applications. Since we are assuming that all edge lengths are positive, u must be closer to s than v is This means that u is in R otherwise it would contradict v s status as the closest node to s outside R So, the shortest path from s to v is simply a known shortest path extended by a single edge But there will typically be many singleedge extensions of the currently known shortest paths (Figure 410); which of these identi es v The answer is, the shortest of these extended paths Because, if an even shorter singleedgeextended path existed, this would once more contradict v s status as the node outside R closest to s So, it s easy to nd v: it is the node outside R for which the smallest value of distance(s, u) + l(u, v) is attained, as u ranges over R In other words, try all singleedge extensions of the currently known shortest paths, nd the shortest such extended path, and proclaim its endpoint to be the next node of R We now have an algorithm for growing R by looking at extensions of the current set of shortest paths Some extra ef ciency comes from noticing that on any given iteration, the only new extensions are those involving the node most recently added to region R All other extensions will have been assessed previously and do not need to be recomputed In the following pseudocode, dist(v) is the length of the currently shortest singleedgeextended path leading to v; it is for nodes not adjacent to R 113 Draw Bar Code In None Using Barcode creation for Software Control to generate, create bar code image in Software applications. USS Code 128 Generator In None Using Barcode drawer for Software Control to generate, create ANSI/AIM Code 128 image in Software applications. Make EAN 128 In None Using Barcode drawer for Software Control to generate, create GTIN  128 image in Software applications. Encode Bar Code In None Using Barcode encoder for Software Control to generate, create bar code image in Software applications. Encode 4State Customer Barcode In None Using Barcode drawer for Software Control to generate, create Intelligent Mail image in Software applications. Barcode Generation In Java Using Barcode maker for BIRT reports Control to generate, create bar code image in Eclipse BIRT applications. ! "# ! DE H I FG
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Matrix 2D Barcode Generation In .NET Framework Using Barcode encoder for ASP.NET Control to generate, create 2D Barcode image in ASP.NET applications. Paint Code128 In VB.NET Using Barcode maker for .NET Control to generate, create Code 128 Code Set A image in .NET applications. Initialize dist(s) to 0, other dist( ) values to R = { } (the known region ) while R = V : Pick the node v R with smallest dist( ) Add v to R for all edges (v, z) E: if dist(z) > dist(v) + l(v, z): dist(z) = dist(v) + l(v, z) Incorporating priority queue operations gives us back Dijkstra s algorithm (Figure 48) To justify this algorithm formally, we would use a proof by induction, as with breadth rst search Here s an appropriate inductive hypothesis At the end of each iteration of the while loop, the following conditions hold: (1) there is a value d such that all nodes in R are at distance d from s and all nodes outside R are at distance d from s, and (2) for every node u, the value dist(u) is the length of the shortest path from s to u whose intermediate nodes are constrained to be in R (if no such path exists, the value is ) Making Code 128 Code Set A In None Using Barcode drawer for Online Control to generate, create Code128 image in Online applications. Paint Universal Product Code Version A In None Using Barcode creator for Word Control to generate, create Universal Product Code version A image in Word applications. The base case is straightforward (with d = 0), and the details of the inductive step can be lled in from the preceding discussion Running time
At the level of abstraction of Figure 48, Dijkstra s algorithm is structurally identical to breadth rst search However, it is slower because the priority queue primitives are computationally more demanding than the constanttime eject s and inject s of BFS Since makequeue takes at most as long as V  insert operations, we get a total of V  deletemin and V  + E insert/decreasekey operations The time needed for these varies by implementation; for instance, a binary heap gives an overall running time of O((V  + E) log V )

