askrene: add graph algorithms module

Changelog-EXPERIMENTAL: askrene: add graph algorithms module

Signed-off-by: Lagrang3 <lagrang3@protonmail.com>

plugins/askrene/algorithm.h

@@ -0,0 +1,36 @@
+#ifndef LIGHTNING_PLUGINS_ASKRENE_ALGORITHM_H
+#define LIGHTNING_PLUGINS_ASKRENE_ALGORITHM_H
+
+/* Implementation of network algorithms: shortests path, minimum cost flow, etc.
+ */
+
+#include "config.h"
+#include <plugins/askrene/graph.h>
+
+/* Search any path from source to destination using Breadth First Search.
+ *
+ * input:
+ * @ctx: tal allocator,
+ * @graph: graph of the network,
+ * @source: source node,
+ * @destination: destination node,
+ * @capacity: arcs capacity
+ * @cap_threshold: an arc i is traversable if capacity[i]>=cap_threshold
+ *
+ * output:
+ * @prev: prev[i] is the arc that leads to node i for an optimal solution, it
+ * @return: true if the destination node was reached.
+ *
+ * precondition:
+ * |capacity|=graph_max_num_arcs
+ * |prev|=graph_max_num_nodes
+ *
+ * The destination is only used as a stopping condition, if destination is
+ * passed with an invalid idx then the algorithm will produce a discovery tree
+ * of all reacheable nodes from the source.
+ * */
+bool BFS_path(const tal_t *ctx, const struct graph *graph,
+	      const struct node source, const struct node destination,
+	      const s64 *capacity, const s64 cap_threshold, struct arc *prev);
+
+#endif /* LIGHTNING_PLUGINS_ASKRENE_ALGORITHM_H */