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# Dijkstra’s Algorithm: The Shortest Path Algorithm

• Neelam Tyagi
• Dec 14, 2020
• Updated on: Feb 15, 2021

A Dutch computer scientist, Edsger Dijkstra, in 1959, proposed an algorithm that can be applied to a weighted graph. The graph can either be directed or undirected with the condition that the graph needs to embrace a non-negative value on its every edge. He named this algorithm “Dijkstra’s Algorithm” at his name.

Let’s dive right into the blog and we will learn

1. Introduction to Graphs

1. What is Dijkstra’s Algorithm?

2. How to Implement the Dijkstra's Algorithm?

3. Working Example of Dijkstra's Algorithm

4. Applications of Dijkstra’s Algorithm

In the series of blogs, we particularly focus on the detailed study, based on graphs, i.e., Group Theory and knowledge Graph, this blog will serve in building our knowledge base to the next level.

## Introduction to Graphs

In simple words, graphs are data structures that are used to depict connections amidst a couple of elements where these elements are called nodes (or vertex) that generally real-time objects, persons or entities and connections amid nodes are termed as edges. Also, two nodes only get connected if there is an edge between them.

"A graph is essentially an interrelationship of nodes/vertices connected by edges."

Generally, graphs are suited to real-world applications, such as graphs can be used to illustrate a transportation system/network, where nodes represent facilities that transfer or obtain products and edges show routes or subways that connect nodes.

Graphs can be divided into two parts;

• Undirected Graphs: For every couple of associated nodes, if an individual could move from one node to another in both directions, then the graph is termed as an undirected graph.

• Directed Graphs: For every couple of associated graphs, if an individual could move from one node to another in a specific (single) direction, then the graph is known as the directed graph. In this case, arrows are implemented rather than simple lines in order to represent directed edges.

### Weighted Graphs

The weight graphs are the graphs where edges of the graph have “a weight” or “cost” and also where weight could reflect distance, time, money or anything that displays the “association” amid a couple of nodes it links. These weights are an essential element under Dijkstra's Algorithm.

## What is Dijkstra’s Algorithm?

What if you are provided with a graph of nodes where every node is linked to several other nodes with varying distance. Now, if you begin from one of the nodes in the graph, what is the shortest path to every other node in the graph?

Well simply explained, an algorithm that is used for finding the shortest distance, or path, from starting node to target node in a weighted graph is known as Dijkstra’s Algorithm.

This algorithm makes a tree of the shortest path from the starting node, the source, to all other nodes (points) in the graph.

Dijkstra's algorithm makes use of weights of the edges for finding the path that minimizes the total distance (weight) among the source node and all other nodes. This algorithm is also known as the single-source shortest path algorithm.

(Also read: 7 Major Branches of Discrete Mathematics)

Dijkstra’s algorithm is the iterative algorithmic process to provide us with the shortest path from one specific starting node to all other nodes of a graph. It is different from the minimum spanning tree as the shortest distance among two vertices might not involve all the vertices of the graph.

It is important to note that Dijkstra’s algorithm is only applicable when all weights are positive because, during the execution, the weights of the edges are added to find the shortest path.

And therefore if any of the weights are introduced to be negative on the edges of the graph, the algorithm would never work properly. However, some algorithms like the Bellman-Ford Algorithm can be used in such cases.

It is also a known fact that breadth-first search(BFS) could be used for calculating the shortest path for an unweighted graph, or for a weighted graph that has the same cost at all its edges.

But if the weighted graph has unequal costs at all its edges, then BFS infers uniform-cost search. Now what?

Instead of extending nodes in order of their depth from the root, uniform-cost search develops the nodes in order of their costs from the root. And a variant of this algorithm is accepted as Dijkstra’s Algorithm.

Generally, Dijkstra’s algorithm works on the principle of relaxation where an approximation of the accurate distance is steadily displaced by more suitable values until the shortest distance is achieved.

Also, the estimated distance to every node is always an overvalue of the true distance and is generally substituted by the least of its previous value with the distance of a recently determined path.

It uses a priority queue to greedily choose the nearest node that has not been visited yet and executes the relaxation process on all of its edges. (From)

### Example Involved

For example, an individual wants to calculate the shortest distance between the source, A, and the destination, D, while calculating a subpath which is also the shortest path between its source and destination. Let’s see here how Dijkstra’s algorithm works;

It works on the fact that any subpath, let say a subpath B to D of the shortest path between vertices A and D is also the shortest path between vertices B and D, i.e., each subpath is the shortest path.

Here, Dijkstra’s algorithm uses this property in the reverse direction, that means, while determining distance, we overestimate the distance of each vertex from the starting vertex then inspect each node and its neighbours for detecting the shortest subpath to those neighbours.

This way the algorithm deploys a greedy approach by searching for the next plausible solution and expects that the end result would be the appropriate solution for the entire problem.

## How to Implement the Dijkstra Algorithm?

Before proceeding the step by step process for implementing the algorithm, let us consider some essential characteristics of Dijkstra’s algorithm;

• Basically, the Dijkstra’s algorithm begins from the node to be selected, the source node, and it examines the entire graph to determine the shortest path among that node and all the other nodes in the graph.

• The algorithm maintains the track of the currently recognized shortest distance from each node to the source code and updates these values if it identifies another shortest path.

• Once the algorithm has determined the shortest path amid the source code to another node, the node is marked as “visited” and can be added to the path.

• This process is being continued till all the nodes in the graph have been added to the path, as this way, a path gets created that connects the source node to all the other nodes following the plausible shortest path to reach each node.

(Visit also: Types of Statistical Analysis)

#### Now explaining the step by step process of algorithm implementation;

1. The very first step is to mark all nodes as unvisited,

2. Mark the picked starting node with a current distance of 0 and the rest nodes with infinity,

3. Now, fix the starting node as the current node,

4. For the current node, analyse all of its unvisited neighbours and measure their distances by adding the current distance of the current node to the weight of the edge that connects the neighbour node and current node,

5. Compare the recently measured distance with the current distance assigned to the neighbouring node and make it as the new current distance of the neighbouring node,

6. After that, consider all of the unvisited neighbours of the current node, mark the current node as visited,

7. If the destination node has been marked visited then stop, an algorithm has ended, and

8. Else, choose the unvisited node that is marked with the least distance, fix it as the new current node, and repeat the process again from step 4.

## Working Example of Dijkstra's Algorithm

In the above section, you have gained the step by step process of Dijkstra’s algorithm, now let’s study the algorithm with an explained example.

We will calculate the shortest path between node C and the other nodes in the graph.

Example of Dijkstra's Algorithm

1. During the execution of the algorithm, each node will be marked with its minimum distance to node C as we have selected node C.

In this case, the minimum distance is 0 for node C. Also, for the rest of the nodes, as we don’t know this distance, they will be marked as infinity (∞), except node C (currently marked as red dot).

Graphical Representation of Node C as Current Node

1. Now the neighbours of node C will be checked, i.e, node A, B, and D. We start with B, here we will add the minimum distance of current node (0) with the weight of the edge (7) that linked the node C to node B and get 0+ 7= 7.

Now, this value will be compared with the minimum distance of B (infinity), the least value is the one that remains the minimum distance of B, like in this case, 7 is less than infinity, and marks the least value to node B.

Assign Node B a minimum distance value

1. Now, the same process is checked with neighbour A. We add 0 with 1 (weight of edge that connects node C to A), and get 1. Again, 1 is compared with the minimum distance of A (infinity), and marks the lowest value.

Assign Node A a minimum distance value

The same is repeated with node D, and marked 2 as lowest value at D.

Assign Node D a minimum distance value

Since, all the neighbours of node C have checked, so node C is marked as visited with a green check mark.

Marked Node C as visited

1. Now, we will select the new current node such that the node must be unvisited with the lowest minimum distance, or the node with the least number and no check mark. Here, node A is the unvisited with minimum distance 1, marked as current node with red dot.

Graphical Representation of Node A as Current Node

We repeat the algorithm, checking the neighbour of the current node while ignoring the visited node, so only node B will be checked.

For node B, we add 1 with 3 (weight of the edge connecting node A to B) and obtain 4. This value, 4, will be compared with the minimum distance of B, 7, and mark the lowest value at B as 4.

Assign Node B a minimum distance value

1. After this, node A marked as visited with a green check mark. The current node is selected as node D, it is unvisited and has a smallest recent distance. We repeat the algorithm and check for node B and E.

Graphical Representation of Node D as Current Node

For node B, we add 2 to 5, get 7 and compare it with the minimum distance value of B, since 7>4, so leave the smallest distance value at node B as 4.

For node E, we obtain 2+ 7= 9, and compare it with the minimum distance of E which is infinity, and mark the smallest value as node E as 9. The node D is marked as visited with a green check mark.

Marked Node D as visited

1. The current node is set as node B, here we need to check only node E as it is unvisited and the node D is visited. We obtain 4+ 1=5, compare it with the minimum distance of the node.

As 9 > 5, leave the smallest value at node node E as 5.

We mark D as visited node with a green check mark, and node E is set as the current node.

Marked Node B as visited

1. Since it doesn’t have any unvisited neighbours, so there is not any requirement to check anything. Node E is marked as a visited node with a green mark.

Marked Node E as visited

So, we are done as no unvisited node is left. The minimum distance of each node is now representing the minimum distance of that node from node C.

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## Applications of Dijkstra’s Algorithm

Before learning any algorithm, we should know the fundamental purpose of using an algorithm that could help us in real-world applications. Such as, for Dijkstra’s algorithm, we are trying to find the solutions to least path based problems.

For example, if a person wants to travel from city A to city B where both cities are connected with various routes. Which route commonly he/ she should choose?

Undoubtedly, we would adopt the route through which we could reach the destination with the least possible time, distance and even cost.

Further, with the discussion, it has various real-world use cases, some of the applications are the following:

• For map applications, it is hugely deployed in measuring the least possible distance and check direction amidst two geographical regions like Google Maps, discovering map locations pointing to the vertices of a graph, calculating traffic and delay-timing, etc.

• For telephone networks, this is also extensively implemented in the conducting of data in networking and telecommunication domains for decreasing the obstacle taken place for transmission.

• Wherever addressing the need for shortest path explications either in the domain of robotics, transport, embedded systems, laboratory or production plants, etc, this algorithm is applied.

• Besides that, other applications are road conditions, road closures and construction, and IP routing to detect Open Shortest Path First.

#### Discussing some advantages of Dijkstra’s algorithm;

1. One of the main advantages of it is its little complexity which is almost linear.

2. It can be used to calculate the shortest path between a single node to all other nodes and a single source node to a single destination node by stopping the algorithm once the shortest distance is achieved for the destination node.

3. It only works for directed-, weighted graphs and all edges should have non-negative values.

#### Despite various applications and advantages, Dijkstra’s algorithm has disadvantages also, such as;

1. It does an obscured exploration that consumes a lot of time while processing,

2. It is unable to handle negative edges,

3. As it heads to the acyclic graph, so can’t achieve the accurate shortest path, and

4. Also, there is a need to maintain tracking of vertices, have been visited.

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## Conclusion

Among many, we have discussed the Dijkstra algorithm used for finding the shortest path, however, one of the obstacles while implementing the algorithm on the internet is to provide a full representation of the graph to execute the algorithm as an individual router has a complete outline for all the routers on the internet. We have seen

• Graphs are used to display connections between objects, entities or people, they have the main elements: Nodes and edges.

• Dijkstra’s algorithm enables determining the shortest path amid one selected node and each other node in a graph.

• And finally, the steps involved in deploying Dijkstra’s algorithm.

(Must check:Statistical Data Analysis)

I hope you really enjoyed reading this blog and found it useful, for other similar blogs and continuous learning follow us regularly.

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Good day everyone on this site reading this testimony, I have been playing the lottery for the past 8years, and had not been able to win I was so upset and worried all day and night looking for who will help me to win the lottery, because buying the ticket not winning losing money get me angry, i was almost giving up until no other option going browsing online when I found a website It was there I came across a comment on the blogs about a powerful spell caster called Dr Kachi who helps so many people to achieve their goals with the lucky winning numbers to win the lotteries. I contacted him also and told him I want to win a lottery, Dr Kachi cast the winning numbers for me which I used to play and when I took the ticket and checked the winning numbers online. When I realized I’d matched all five numbers I was not at first believe, I thought my eyes were playing tricks on me, it was when i getting the message, I won the jackpot \$128,166.00 million dollars, I'm a proud winners I want you, my friends who are passing through to win lottery games, contact drkachispellcast@gmail.com his WhatsApp number:+1 (570) 775-3362 visit his website: https://drkachispellcast.wixsite.com/my-site .

Jun 10, 2022

Jun 15, 2022

• #### drmahlanguhome

Jun 15, 2022

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Jun 15, 2022

• #### drmahlanguhome

Jun 15, 2022

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• #### drmahlanguhome

Jun 15, 2022

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• #### drmahlanguhome

Jun 15, 2022

My work is a mixture of African traditional spiritualism, psychic powers, rituals, native healing, spell casting, all of which are designed to take care of whatever adversity you may face.my solutions are tailor designed depending on the nature of your problem or adversity-Healing Am well qualified, having honed my skills from experiences and tradition passed down through the centuries from my forefathers. I deal with occult, spiritual and the paranormal. I do email, phone and private readings and consultations to enable you take control of the situation. Are you looking for the best on line help? Through the use of my lifelong practices in native healing techniques, dreaming and trance work, I am able to reach within to an individual’s eternal soul, unblocking the paths and tunnels to one’s own innate healing abilities allowing one’s life force to burn brightly once again, enlivening peace, abundance, joy, and creativity. Native healing works on all facets of the person – past, present and future – restoring and opening the natural lines for personal success in mind, body and spirit,E-mail: drmahlanguhome@gmail.com, whats-app: +27787390989. website :https://www.drmahlangu-home.com/ Welcome To Astrologer Dr - in London, Best/Top & World Famous Africa Astrologer in London, UK: Unit 11 st George walk Park Street Croydon high street London CRO 1YH MOB-+27787390989 For any questions or any problem you can WATSAPP. The details for - +27787390989 You can Talk Directly To Astrologer Dr ,You can Ask Two Questions Completely Free. world Africa Famous Psychic. Gold medallist.. Reading,Spiritual healer in London,UK. E-mail: drmahlanguhome@gmail.com, whats-app: +27787390989. website :https://www.drmahlangu-home.com/ Famous & Genuine Africa Astrology

Jun 15, 2022

• #### righteva05

Jun 16, 2022

ARE YOU IN NEED OF HELP TO SOLVE YOUR INFERTILITY PROBLEM OR GET PREGNANT? contact Dr. LUCAS Miracle Center on this email (miraculouscentre@gmail.com) I'm Wright Eva from the USA, I have been trying to get pregnant for 6 years and I needed help! I have been to different hospitals and Doctors. The doctors always say that my husband and I are fine and I don't know where else to turn. Until one day an old friend introduced me to this great spell caster who helped her to get her lost husband back with a love spell and also made her pregnant, So I decided to contact this spell caster Dr. Lucas on his email (miraculouscentre@gmail.com) after interaction with him he instructed me on what to do, after then i should have sex with the my husband or any man I love in this world, And i did so, within the next one months i went for a check up and my doctor confirmed that i am 2 weeks pregnant with two babies. I am so happy!! If you also need help to get pregnant or need your ex back then contact his email address: miraculouscentre@gmail.com My Blog: https://righteva05.blogspot.com

• #### righteva05

Jun 16, 2022

ARE YOU IN NEED OF HELP TO SOLVE YOUR INFERTILITY PROBLEM OR GET PREGNANT? contact Dr. LUCAS Miracle Center on this email (miraculouscentre@gmail.com) I'm Wright Eva from the USA, I have been trying to get pregnant for 6 years and I needed help! I have been to different hospitals and Doctors. The doctors always say that my husband and I are fine and I don't know where else to turn. Until one day an old friend introduced me to this great spell caster who helped her to get her lost husband back with a love spell and also made her pregnant, So I decided to contact this spell caster Dr. Lucas on his email (miraculouscentre@gmail.com) after interaction with him he instructed me on what to do, after then i should have sex with the my husband or any man I love in this world, And i did so, within the next one months i went for a check up and my doctor confirmed that i am 2 weeks pregnant with two babies. I am so happy!! If you also need help to get pregnant or need your ex back then contact his email address: miraculouscentre@gmail.com My Blog: https://righteva05.blogspot.com

• #### Patrick Williams

Jun 17, 2022

Good day everyone on this site reading this testimony, I have been playing the lottery for the past 8years, and had not been able to win I was so upset and worried all day and night looking for who will help me to win the lottery, because buying the ticket not winning losing money get me angry, i was almost giving up until no other option going browsing online when I found a website It was there I came across a comment on the blogs about a powerful spell caster called Dr Kachi who helps so many people to achieve their goals with the lucky winning numbers to win the lotteries. I contacted him also and told him I want to win a lottery, Dr Kachi cast the winning numbers for me which I used to play and when I took the ticket and checked the winning numbers online. When I realized I’d matched all five numbers I was not at first believe, I thought my eyes were playing tricks on me, it was when i getting the message, I won the jackpot \$128,166.00 million dollars, I'm a proud winners I want you, my friends who are passing through to win lottery games, contact drkachispellcast@gmail.com his WhatsApp number:+1 (570) 775-3362 visit his website: https://drkachispellcast.wixsite.com/my-site

• #### emiratetrustloan

Jun 18, 2022

Learn from my mistakes. My ex broke up with me and I did the begging and pleading routine that didn’t work at all. I kept in contact with her because I was afraid of losing her forever. I will send text messages and try calling. Most of the time she either ignore or replied with vague messages. I really want her and my kids back, I begged her with everything, I made promises to her, but she refused. I explained my problem to my friend and he suggested that I should contact a spell caster that could help me cast a love-spell to bring her back, I had no choice than to give it a trail. I messaged the spell caster called Dr Unity, and he assured me there was no problem and that everything will be ok. He cast the spell and surprisingly 11 hours later my wife called me. I was so surprised, I answered the call and all she said was that she was so sorry for everything that had happened. she also said she loved me so much. I was so very happy and that was how we started talking that made us come back together happily again. thanks to Dr unity . if you need ex-Lover back or your wife/husband moved to someone else, do not cry anymore, contact Dr.Unity for help now.. Here his contact...WhatsApp: +2348055361568 . Email: Unityspelltemple@gmail.com , website:http://unityspelltemple.website2.me

• #### emiratetrustloan

Jun 23, 2022

Hey everyone, Get Your Ex Lover Back Quickly & Permanently. My name is Maria. My husband left me for a younger woman and I was devastated. It was as if she had him under an evil spell, Gonzales turned against me overnight without any warning. It happened this year, I was desperate for him to return because we had built a lot together and it would break the kids hearts. I used every single spell casting website that I could find with no results. Then i saw a particular testimony about Dr. Unity and it really gave me hope because it was similar to my case. I contacted him and he explained everything to me on what i should do. He started working with me in April and as a result from all of his wonderful works, Gonzales is here right now beside me which is a dream come true. I’m so happy and privileged to have met Dr Unity. Thank you! If you have similar issues, kindly contact Dr. Unity and be rest assured to get help. Here his contact. WhatsApp him at: +2348055361568 , Email him at: Unityspelltemple@gmail.com , His website:http://unityspelltemple.website2.me

• #### Sakshi Singh

Jun 23, 2022

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• #### ALBERT MIKE

Jun 23, 2022

HELLO EVERYONE I WAS BROWSING THE INTERNET AND I SAW A LOT OF WRONG QUOTE CONCERNING THE ILLUMINATI SOCIETY, I FELT BAD ABOUT IT, I WANT TO LET YOU KNOW FEW THINGS ABOUT THE ILLUMINATI SOCIETY. FIRST, I JOIN THE ILLUMINATI SOCIETY THROUGH THE HELP OF AN AGENT SOMEONE INTRODUCED ME TO ONLINE, AFTER YEARS OF DETERMINATION TO BE A MEMBER. BEING A MEMBER OF THE ILLUMINATI YOUR WEALTH IS GUARANTEE, YOU WILL BE PROTECTED, FAME, POWER INFLUENCE E.T.C ALL THESE THEY WILL GIVE YOU. ONE THING I WANT TO CORRECT IS THAT THE ILLUMINATI DON'T PAY MEMBER ANY SALARY, IF YOU ARE NEWLY INITIATED THEY WILL GIVE YOU THE SEED OF WEALTH AND BLESS YOU WITH WISDOM, POWER, INFLUENCE E.T.C YOU NEED TO BE SUCCESSFUL THE SEED OF WEALTH IS THE ONLY MONEY THE ILLUMINATI SOCIETY GIVE TO THEIR MEMBER, WITH THIS YOU CAN START ANYTHING WITH THE MONEY AND YOU WILL BE SUCCESSFUL. ANOTHER THING IS THAT THE SOCIETY HAVE SPECIAL BLESSING FOR POLITICIANS AND SUPER STARS. BEING AN ILLUMINATI MEMBER IS A PERSONAL DECISION, THE SOCIETY DON'T FORCE OR BEG PEOPLE TO JOIN THEM. I JOINED BECAUSE I WANT TO, NO BODY FORCE ME AND AM VERY HAPPY TO BE A MEMBER TODAY BECAUSE THEY HAVE CONTRIBUTED GREATLY TO MY LIFE BY MAKING ME ONE OF THE LEADING BUSINESS MAN IN THE WORLD. IF YOU ARE INTERESTED IN JOINING THE ILLUMINATI SOCIETY CALL/WHATSAPP Mr BERRY WARD on +1 (832) 789-0695 email grandmasterilluminati29@gmail.com HE WAS THE ONE THAT HELP ME AND I PROMISE I WILL FOREVER BE GRATEFUL

• #### ALBERT MIKE

Jun 23, 2022

HELLO EVERYONE I WAS BROWSING THE INTERNET AND I SAW A LOT OF WRONG QUOTE CONCERNING THE ILLUMINATI SOCIETY, I FELT BAD ABOUT IT, I WANT TO LET YOU KNOW FEW THINGS ABOUT THE ILLUMINATI SOCIETY. FIRST, I JOIN THE ILLUMINATI SOCIETY THROUGH THE HELP OF AN AGENT SOMEONE INTRODUCED ME TO ONLINE, AFTER YEARS OF DETERMINATION TO BE A MEMBER. BEING A MEMBER OF THE ILLUMINATI YOUR WEALTH IS GUARANTEE, YOU WILL BE PROTECTED, FAME, POWER INFLUENCE E.T.C ALL THESE THEY WILL GIVE YOU. ONE THING I WANT TO CORRECT IS THAT THE ILLUMINATI DON'T PAY MEMBER ANY SALARY, IF YOU ARE NEWLY INITIATED THEY WILL GIVE YOU THE SEED OF WEALTH AND BLESS YOU WITH WISDOM, POWER, INFLUENCE E.T.C YOU NEED TO BE SUCCESSFUL THE SEED OF WEALTH IS THE ONLY MONEY THE ILLUMINATI SOCIETY GIVE TO THEIR MEMBER, WITH THIS YOU CAN START ANYTHING WITH THE MONEY AND YOU WILL BE SUCCESSFUL. ANOTHER THING IS THAT THE SOCIETY HAVE SPECIAL BLESSING FOR POLITICIANS AND SUPER STARS. BEING AN ILLUMINATI MEMBER IS A PERSONAL DECISION, THE SOCIETY DON'T FORCE OR BEG PEOPLE TO JOIN THEM. I JOINED BECAUSE I WANT TO, NO BODY FORCE ME AND AM VERY HAPPY TO BE A MEMBER TODAY BECAUSE THEY HAVE CONTRIBUTED GREATLY TO MY LIFE BY MAKING ME ONE OF THE LEADING BUSINESS MAN IN THE WORLD. IF YOU ARE INTERESTED IN JOINING THE ILLUMINATI SOCIETY CALL/WHATSAPP Mr BERRY WARD on +1 (832) 789-0695 email grandmasterilluminati29@gmail.com HE WAS THE ONE THAT HELP ME AND I PROMISE I WILL FOREVER BE GRATEFUL

• #### margareatwood22

Jun 24, 2022

Hello everyone, I want to use this medium to thank a great spell caster called Dr Grceondu for transforming my life financially, i have been playing lottery game for long but have never won any reasonable amount, I contacted Dr Graceondu after i red about him on the internet on how he help a lady with a lottery winning numbers and the lady won a very big amount of money, so i contacted him and He instructed me on what to do which i did and he told me to give him some time to pray, on the second day he sent me some numbers and he said i should go and play them, so i went to play the numbers he gave me, after two day the result came out, and i went to check and to my greatest surprise my name came out as one of the winners i won \$45 million, i still cant believe what happened to me that i am now a millionaire over night, i just want to say a very big thank you to Dr Graceondu i have never seen a powerful man like him, I will advice everyone out there to contact Dr Graceondu if you want to win big in your lottery game. You can reach him via his email, drgraceondu12@gmail.com or WhatsApp him +15204677763, you can also visit his Website. https://drgraceonduadodo.com

• #### chardon084

Jun 24, 2022

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• #### lisaamy09

Jun 24, 2022

Sir, thank you so much for your genuine spell, my lover is back!!! I am very happy to recommend Dr. Zaba to everybody that truly needs help to fix his or her broken relationship. When I found Dr. Zaba I was in desperate need of bringing my ex lover back. He left me for another woman. It happened so fast and I hSad no say in the situation at all. He just dumped me after 3 years without any explanation. I contacted Dr. Zaba through his website and he cast a love spell to help us get back together. Shortly after he did the spell, my boyfriend started testing me again and felt horrible for what he just put me through. He said that I was the most important person in his life and he knows that now. Email now for urgent help. write him on whatsApp: + 1 (631) 320-5873 Zaba24hoursspell1@gmail.com OR Zaba24hoursspell@yahoo.com Read more on his website: https://zaba24hoursspell1.wixsite.com/zabaspell Facebook Page: https://web.facebook.com/Zaba24hoursspell1/

• #### Natasha Thompson

Jun 25, 2022

My name is Natasha Thompson from the USA/Texas.. Am so overwhelmed with gratitude to let the world know how Dr Kachi, the great spell caster changed my life for good. It all started when I lost my job and I was down financially and emotionally because I couldn’t be able provide for my two kids and staying home all day Jobless it’s not easy until I was checking on the internet when I saw a series of testimonies hearing people winning the Powerball lottery, I didn’t believed, but being poor no job you have no option. I gave it a try and I contacted Dr Kachi who told me what i have to do before I can become a big lottery winner and I accepted. He made special prayers for me in his temple and gave me the required numbers to play the lottery game and when I used the numbers to play it, I won a massive \$344.6 million Powerball jackpot. I was so happy and I choose to review my winning in any platform, I would love other people to seek help from Dr Kachi through WhatsApp/number :+1 (570) 775-3362 or email drkachispellcast@gmail.com by his website: https://drkachispellcast.wixsite.com/my-site

Jun 25, 2022

Jun 26, 2022

Jun 26, 2022

• #### emiratetrustloan

Jun 26, 2022

hey I'm glad to telling everyone here how i got my ex husband back. I'm Maria from USA. My husband left me for a younger woman and I was devastated. It was as if she had him under an evil spell, Gonzales turned against me overnight without any warning. It happened this year, I was desperate for him to return because we had built a lot together and it would break the kids hearts. I used every single spell casting website that I could find with no results. Then i saw a particular testimony about Dr. Unity and it really gave me hope because it was similar to my case. I contacted him and he explained everything to me on what i should do. He started working with me in April and as a result from all of his wonderful works, Gonzales is here right now beside me which is a dream come true. I’m so happy and privileged to have met Dr Unity. Thank you! If you have similar issues, kindly contact Dr. Unity and be rest assured to get help. Here his contact. WhatsApp him at: +2348055361568 , Email him at: Unityspelltemple@gmail.com , His website:http://unityspelltemple.website2.me

• #### Natasha Thompson

Jun 26, 2022

My name is Natasha Thompson from the USA/Texas.. Am so overwhelmed with gratitude to let the world know how Dr Kachi, the great spell caster changed my life for good. It all started when I lost my job and I was down financially and emotionally because I couldn’t be able provide for my two kids and staying home all day Jobless it’s not easy until I was checking on the internet when I saw a series of testimonies hearing people winning the Powerball lottery, I didn’t believed, but being poor no job you have no option. I gave it a try and I contacted Dr Kachi who told me what i have to do before I can become a big lottery winner and I accepted. He made special prayers for me in his temple and gave me the required numbers to play the lottery game and when I used the numbers to play it, I won a massive \$344.6 million Powerball jackpot. I was so happy and I choose to review my winning in any platform, I would love other people to seek help from Dr Kachi through WhatsApp/number :+1 (570) 775-3362 or email drkachispellcast@gmail.com by his website: https://drkachispellcast.wixsite.com/my-site

• #### bethanynash01

Jun 27, 2022

"HOW I GOT MY HUSBAND BACK" Infuse your life with action Don't wait for it to happen Make it happen. Make your own future. Make your own hope. Make your own love. And whatever your beliefs, We may encounter many defeats but we must not be defeated Either I will find a way, or I will make one these were the words that kept me going after my husband was snatched away from me until i met True Love spell caster, he is Just and Blessed with The Spell Power Of love life, Power to grant our heart desires granted. Cause my wish have come through, I am aback with the loml and i am so happy and proud that i made this Decision. Reach out to TrueLoveSpellcaster1@gmail.com +1(520) 346-0286. Who Promised to help me regain joy and happiness in 48 hours and am grateful to him that i not disappointed he kept his word and today i live happily with my husband. Contact True Love Spell Cater on (TrueLoveSpellCater1@gmail.com) or whatsApp +1(520) 346-0286. its a life changing experience, I have experienced it, Its your turn, do not Miss it.

• #### jenkinscooper750

Jun 28, 2022

BITCOIN RECOVERY IS REAL!!! ( MorrisGray830 At gmail Dot Com, is the man for the job ) This man is dedicated to his work and you can trust him more than yourself. I contacted him a year and a half Ago and he didn't succeed. when i got ripped of \$491,000 worth of bitcoins by scammers, I tried several recovery programs with no success too. I kept on. And now after so much time Mr Morris Gray contacted me with a success, and the reward he took was small because obviously he is doing this because he wants to help idiots like me who fell for crypto scam, and love his job. Of course he could have taken all the coins and not tell me , I was not syncing this wallet for a year, but he didn't. He is the MAN guys , He is! If you have been a victim of crypto scam before you can trust Morris Gray 10000000%. I thought there were no such good genuine guys anymore on earth, but Mr Morris Gray brought my trust to humanity again. GOD bless you sir...you can reach him via ( MORRIS GRAY 830 at Gmaill dot com ) or Whatsapp +1 (607)698-0239..

• #### bethanynash01

Jun 29, 2022

"HOW I GOT MY HUSBAND BACK" Infuse your life with action Don't wait for it to happen Make it happen. Make your own future. Make your own hope. Make your own love. And whatever your beliefs, We may encounter many defeats but we must not be defeated Either I will find a way, or I will make one these were the words that kept me going after my husband was snatched away from me until i met True Love spell caster, he is Just and Blessed with The Spell Power Of love life, Power to grant our heart desires granted. Cause my wish have come through, I am aback with the loml and i am so happy and proud that i made this Decision. Reach out to TrueLoveSpellcaster1@gmail.com +1(520) 346-0286. Who Promised to help me regain joy and happiness in 48 hours and am grateful to him that i not disappointed he kept his word and today i live happily with my husband. Contact True Love Spell Cater on (TrueLoveSpellCater1@gmail.com) or whatsApp +1(520) 346-0286. its a life changing experience, I have experienced it, Its your turn, do not Miss it.

• #### Alex Stephen

Jun 30, 2022

worked for me! It worked just like I thought it would. It was easy enough and I just want others to know when something works. My husband and I have been married for about 4 yrs now. We were happily married with a 2yrs old son. 3 months ago, I started to notice some strange behavior from him and a few weeks later I found out that my husband is seeing someone. He started coming home late from work, he hardly cares about me or the kids anymore, Sometimes he goes out and doesn't even come back home for about 2-3 days. I did all I could to rectify this problem but all to no avail. I became very worried and needed help. As I was browsing through the internet one day, I came across a website that suggested that Dr Unity can help solve marital problems, restore broken relationships and so on. So, I felt I should try him out. I contacted him and told him my problems and he told me what to do and I did it and he did a spell for me. 28 hours later, my husband came to me and apologized for the wrongs he did and promised never to do it again. Ever since then, everything has returned back to normal. My family and I are living together happily again.. All thanks to Dr Unity. If you have any problem contact him and I guarantee you that he will help you. Here’s his contact: WhatsApp him at: +2348055361568 , Email him at: Unityspelltemple@gmail.com , His website:http://unityspelltemple.website2.me

• #### emiratetrustloan

Jul 01, 2022

How to Win Your Wife/husband back Quickly & Permanently - I suggest you read this. My name is Maria. My husband left me for a younger woman and I was devastated. It was as if she had him under an evil spell, Gonzales turned against me overnight without any warning. It happened this year, I was desperate for him to return because we had built a lot together and it would break the kids hearts. I used every single spell casting website that I could find with no results. Then i saw a particular testimony about Dr. Unity and it really gave me hope because it was similar to my case. I contacted him and he explained everything to me on what i should do. He started working with me in April and as a result from all of his wonderful works, Gonzales is here right now beside me which is a dream come true. I’m so happy and privileged to have met Dr Unity. Thank you! If you have similar issues, kindly contact Dr. Unity and be rest assured to get help. Here his contact. WhatsApp him at: +2348055361568 , Email him at: Unityspelltemple@gmail.com , His website:http://unityspelltemple.website2.me

• #### lisaamy09

Jul 01, 2022

I am so overwhelmed and grateful to you and the magic you have done that make me win millions of dollars in lottery. I would like to say,-Thank you. I was on the edge of losing my house and so many things around me, so I asked a spell from you, so that I will be able to save my house and come up with payment options. He help me with his magic spell and i win 500,000.00 \$ all thinks goes to dr.zaba for what him has just done for me. Sure enough,-what I asked for. You have proven over and over again, that you are the best spell caster. any body out there that is reading this my testimony,you have to hurry and get in touch with the spell caster,so that he can help you to win the lottery. email Zaba24hoursspell1@gmail.com OR Zaba24hoursspell@yahoo.com or his web sit https://zaba24hoursspell1.wixsite.com/zabaspell WhatsApp: + 1 (631)320-5873. Shally Mily From United State. Thanks again for your wonderful help