# fn()allPairsShortestPathFinds shortest paths between all pairs of vertices in a graph.

Defined in ```void allPairsShortestPath(graph, weight, distance, predecessor); ```

## Parameters

 `graph` A Directed Graph. A property map with edge weights. Edge weights may be negative. A Matrix with distances. Entry (i,j) in this matrix indicates the distance from vertex i to vertex j. A Matrix with predecessors. Entry (i,j) in this matrix indicates the predecessor of j on a shortest path from vertex i to vertex j. You can use _printAllPairsShortestPath(graph, predecessor, i, j) to print the shortest path from i to j.

## Detailed Description

### Example

```#include <iostream>
#include <seqan/graph_algorithms.h>

using namespace seqan;

int main()
{
typedef Graph<Directed<> > TGraph;
typedef VertexDescriptor<TGraph>::Type TVertexDescriptor;
typedef EdgeDescriptor<TGraph>::Type TEdgeDescriptor;
typedef Size<TGraph>::Type TSize;

// Create a graph with 9 directed edges (0,1), (0,2), ...
TSize numEdges = 9;
TVertexDescriptor edges[] = {0,1, 0,2, 0,4, 1,3, 1,4, 2,1, 3,0, 3,2, 4,3};
TGraph g;
addEdges(g, edges, numEdges);
// Print graph.
std::cout << g << std::endl;

// Create a property map with edge weights.  Note that we can use negative
// weights since the edges are directed and there are no cycles.
int weights[] = {3, 8, -4, 1, 7, 4, 2, -5, 6};
String<int> weightMap;
assignEdgeMap(g,weightMap, weights);

// Compute all-pairs shortest path.
String<int> distMat;
String<TVertexDescriptor> predMat;
allPairsShortestPath(g, weightMap, distMat, predMat);

// Print the result to stdout.
unsigned int len = static_cast<unsigned>(std::sqrt((double)length(distMat)));
for (TSize row = 0; row < len; ++row)
for (TSize col = 0; col < len; ++col)
{
std::cout << row << "," << col << " (Distance="
<< getValue(distMat, row * len + col) << "): ";
_printAllPairsShortestPath(g, predMat, row, col);
std::cout << "\n";
}

return 0;
}
```
```Adjacency list:
0 -> 4,2,1,
1 -> 4,3,
2 -> 1,
3 -> 2,0,
4 -> 3,
Edge list:
Source: 0,Target: 4 (Id: 2)
Source: 0,Target: 2 (Id: 1)
Source: 0,Target: 1 (Id: 0)
Source: 1,Target: 4 (Id: 4)
Source: 1,Target: 3 (Id: 3)
Source: 2,Target: 1 (Id: 5)
Source: 3,Target: 2 (Id: 7)
Source: 3,Target: 0 (Id: 6)
Source: 4,Target: 3 (Id: 8)

0,0 (Distance=0): 0
0,1 (Distance=1): 0,4,3,2,1
0,2 (Distance=-3): 0,4,3,2
0,3 (Distance=2): 0,4,3
0,4 (Distance=-4): 0,4
1,0 (Distance=3): 1,3,0
1,1 (Distance=0): 1
1,2 (Distance=-4): 1,3,2
1,3 (Distance=1): 1,3
1,4 (Distance=-1): 1,3,0,4
2,0 (Distance=7): 2,1,3,0
2,1 (Distance=4): 2,1
2,2 (Distance=0): 2
2,3 (Distance=5): 2,1,3
2,4 (Distance=3): 2,1,3,0,4
3,0 (Distance=2): 3,0
3,1 (Distance=-1): 3,2,1
3,2 (Distance=-5): 3,2
3,3 (Distance=0): 3
3,4 (Distance=-2): 3,0,4
4,0 (Distance=8): 4,3,0
4,1 (Distance=5): 4,3,2,1
4,2 (Distance=1): 4,3,2
4,3 (Distance=6): 4,3
4,4 (Distance=0): 4
```