Run Dijkstra’s algorithm on the following graph. How many times does each vertex’s key decrease? Recall that D [ v ] is the key of vertex v v ; it represents the algorithm’s current best‑known estimate of the shortest‑path distance from the source s to v v . (Decrease from infinity counts as decrease) The a decreases [Fill in the blank] times. The b decreases [Fill in the blank] times. The c decreases [Fill in the blank] times. The d decreases [Fill in the blank] times

Dijkstra’s relaxation updates (decreases) occur whenever we find a strictly smaller tentative distance. Use these directed edges and weights read from the diagram: s->a = 2, s->b = 9, a->c = 2, a->d = 20, c->b = 1, c->d = 8, b->d = 2. Initial keys: d[s]=0, d[a]=d[b]=d[c]=d[d]=∞. 1) Relax edges out of s: - relax s->a: d[a] becomes 2 (∞ -> 2). Count: a: 1. - relax s->b: d[b] becomes 9 (∞ -> 9). Count: b: 1. Current keys: a=2, b=9, c=∞, d=∞. 2) Extract minimum: a (key 2). Relax edges from a: - relax a->c: d[c] becomes 2 + 2 = 4 (∞ -> 4). Count: c: 1. - relax a->d: d[d] becomes 2 + 20 = 22 (∞ -> 22). Count: d: 1. Current keys: c=4, b=9, d=22. 3) Extract minimum: c (key 4). Relax edges from c: - relax c->b: d[b] becomes 4 + 1 = 5 (9 -> 5). This is a decrease for b. Count: b: 2. - relax c->d: d[d] becomes 4 + 8 = 12 (22 -> 12). This is a decrease for d. Count: d: 2. Current keys: b=5, d=12. 4) Extract minimum: b (key 5). Relax edges from b: - relax b->d: d[d] becomes 5 + 2 = 7 (12 -> 7). This is another decrease for d. Count: d: 3. No other relaxations improve keys. 5) Extract d (key 7). No further improvements. Summary of decreases: - a: decreased once (∞ -> 2). - b: decreased twice (∞ -> 9, then 9 -> 5). - c: decreased once (∞ -> 4). - d: decreased three times (∞ -> 22, 22 -> 12, 12 -> 7). Why other counts are wrong: any smaller count for b would ignore the update via c (4+1=5); any smaller count for d would ignore successive improvements via a then c then b. These stepwise relaxations yield exactly the counts above. Final answer confirmed: a = 1, b = 2, c = 1, d = 3.

Run Dijkstra’s algorithm on the following graph. How many times does each vertex’s key decrease? Recall that <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>D</mi><mo stretchy="false">[</mo><mi>v</mi><mo stretchy="false">]</mo></mrow></math> is the key of vertex v<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>v</mi></mrow></math>; it represents the algorithm’s current best‑known estimate of the shortest‑path distance from the source <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>s</mi></mrow></math> to v<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>v</mi></mrow></math>. (Decrease from infinity counts as decrease) The a decreases [Fill in the blank] times. The b decreases [Fill in the blank] times. The c decreases [Fill in the blank] times. The d decreases [Fill in the blank] times 多项填空题

登录即可查看完整答案

我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

类似问题

What is the time complexity of Dijkstra's algorithm using a priority queue (min-heap) implemented with a binary heap?

Why is Dijkstra's algorithm not suitable for graphs with negative weight edges?

Question textApply Dijkstra's algorithm to find the shortest path from node 1 to all other nodes in the following directed graph. The numbers on the arcs represent costs , with data provided again below for completeness. Node 1: Node 2: Node 3: Node 4: Node 5: Node 6: Node 7: Node 8: Enter the shortest distance from node 1 to each node: Node 3: Answer 1 Question 3[input] predecessor = Answer 2 Question 3[input] Node 4: Answer 3 Question 3[input] Node 5: Answer 4 Question 3[input] If the problem of finding a shortest path from node 1 to node 3 was solved as a linear program with arc flow variables , then:The reduced cost of would be Answer 5 Question 3[input] If is the optimal value of the dual variables for the flow conservation constraints, then Answer 6 Question 3[input]

Dijkstra's Link State Algorithm Consider the incomplete 6-node network shown below, with given link costs; where links x and y are unknown Consider the completed table below, which calculates the shortest distance to all nodes from U: Nodes d, (p) d, (p) d, (p) d, (p) d, (p) U V W X Y Z shortest distance from node U 0 4, X 3, U 1, U 5, X 6, W For link x (link from node X, to node Y) , what is the cost associated with this link? [Fill in the blank] For link y (link from node U to node W) , what is the cost associated with this link?[Fill in the blank]

希望你的学习变得更简单

加入我们，立即解锁海量真题与独家解析，让复习快人一步！

类似问题

What is the time complexity of Dijkstra's algorithm using a priority queue (min-heap) implemented with a binary heap?

Why is Dijkstra's algorithm not suitable for graphs with negative weight edges?

狄克斯特拉算法在社交网络中用于判定： Dijkstra’s Algorithm is used in social network for determining

Which of the following properties of a weighted graph G will prevent the use of Dijkstra's algorithm for finding shortest paths in G?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单