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pa:laboratoare:laborator-09 [2023/03/15 16:55] radu.nichita |
pa:laboratoare:laborator-09 [2026/01/21 12:53] (current) darius.neatu [Laborator 09: Drumuri minime în grafuri: surse / destinații multiple. (2/2)] |
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| ====== Laborator 09: Drumuri minime în grafuri: surse / destinații multiple. (2/2) ====== | ====== Laborator 09: Drumuri minime în grafuri: surse / destinații multiple. (2/2) ====== | ||
| + | {{:pa:new_pa:partners:adobe-logo.png?250 |}} | ||
| + | Adobe is a global technology leader with a mission to **change the world through personalized digital experiences**. For over four decades, Adobe has transformed how individuals, teams, businesses, and enterprises create, manage, and deliver content across every surface and channel. | ||
| - | {{:pa:new_pa:partners:adobe-logo.png?155 |}} | + | With **AI at the core**, tools like **Adobe Firefly** and AI-powered assistants make creativity faster, smarter, and more personalized—while keeping it safe and responsible. In **Adobe Experience Cloud**, AI powers real-time personalization, predictive insights, and automated customer journeys, helping brands deliver exceptional experiences at scale. At Adobe, **creativity meets productivity**, and AI is the catalyst for transformation. |
| - | \\ \\ \\ Changing the world through digital experiences is what Adobe’s all about. We give everyone - from emerging artists to global brands - everything they need to design and deliver exceptional digital experiences! We’re passionate about empowering people to create beautiful and powerful images, videos, and apps, and transform how companies interact with customers across every screen. | + | |
| ===== Obiective laborator ===== | ===== Obiective laborator ===== | ||
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| - | * $d_2$ (matricea dupa primul pas din algoritm; se modifică doar **d[4][3]**) | + | * $d_2$ (matricea dupa primul pas din algoritm; se modifică doar **d[4][3]** și **d[4][1]**) |
| |-|1|2|3|4| \\ | |-|1|2|3|4| \\ | ||
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| |2|4|0|2|+∞| \\ | |2|4|0|2|+∞| \\ | ||
| |3|+∞|+∞|0|2| \\ | |3|+∞|+∞|0|2| \\ | ||
| - | |4|+∞|-1|**1**|0| v | + | |4|**3**|-1|**1**|0| v |
| * $d_3$ (matricea dupa primul pas din algoritm; se modifică doar **d[1][4]** și **d[2][4]**) | * $d_3$ (matricea dupa primul pas din algoritm; se modifică doar **d[1][4]** și **d[2][4]**) | ||
| Line 145: | Line 146: | ||
| |2|4|0|2|**4**| \\ | |2|4|0|2|**4**| \\ | ||
| |3|+∞|+∞|0|2| \\ | |3|+∞|+∞|0|2| \\ | ||
| - | |4|+∞|-1|1|0| \\ | + | |4|3|-1|1|0| \\ |
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| |2|4|0|2|4| \\ | |2|4|0|2|4| \\ | ||
| |3|**5**|**1**|0|2| \\ | |3|**5**|**1**|0|2| \\ | ||
| - | |4|+∞|-1|1|0| \\ | + | |4|3|-1|1|0| \\ |
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| ==== Complexitate ==== | ==== Complexitate ==== | ||
| - | * **complexitate temporală**: $T = O(n^3)\ sau\ O(|E|^3)$ | + | * **complexitate temporală**: $T = O(n^3)\ sau\ O(|V|^3)$ |
| * **complexitate spațială** : $S = O(1)$ | * **complexitate spațială** : $S = O(1)$ | ||
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| Johnson(G=(nodes, adj)) { | Johnson(G=(nodes, adj)) { | ||
| // STEP 1: Compute adjustment distances h (using Bellmand-Ford). | // STEP 1: Compute adjustment distances h (using Bellmand-Ford). | ||
| - | has_cycle, h = ComputerH(G); | + | has_cycle, h = ComputeH(G); |
| if (has_cycle) { | if (has_cycle) { | ||
| return true, null, null; | return true, null, null; | ||
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| </note> | </note> | ||
| - | ==== Roy-Floyd ==== | + | ==== Task-1: Roy-Floyd ==== |
| Se dă un graf **orientat** cu **n** noduri. Graful are **costuri strict pozitive**. | Se dă un graf **orientat** cu **n** noduri. Graful are **costuri strict pozitive**. | ||
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| </note> | </note> | ||
| - | ==== Johnson ==== | + | ==== Task-2: Johnson ==== |
| Se dă un graf **orientat** cu **n** noduri. Graful are **costuri oarecare** (pot fi și negative). | Se dă un graf **orientat** cu **n** noduri. Graful are **costuri oarecare** (pot fi și negative). | ||
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| </note> | </note> | ||
| + | |||
| + | === Task-3: Orașul care poate accesa cele mai puține noduri (dându-se o distanță limită) === | ||
| + | Rezolvați problema [[ https://leetcode.com/problems/find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance/description/ | Find the City With the Smallest Number of Neighbors at a Threshold Distance ]] pe LeetCode. | ||
| + | |||
| ==== BONUS ==== | ==== BONUS ==== | ||
