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- WELCOME TO A LESSON ON THE SORTED EDGES ALGORITHM THAT CAN BE USED TO TRY TO FIND THE OPTIMAL OR LOWEST COST HAMILTONIAN CIRCUIT. SO AS AN ALTERNATIVE OUR NEXT APPROACH WELL STEP BACK AND LOOK AT THE BIG PICTURE. WE DETERMINE A HAMILTONIAN CIRCUIT BY SELECTING EDGES WITH THE LEAST WEIGHT AND THEN FILL IN THE GAPS AS NEEDED. AND HERE ARE THE STEPS FOR THE SORTED EDGES ALGORITHM, ALSO KNOWN AS THE CHEAPEST LINK ALGORITHM. STEP ONE, WE SELECT THE CHEAPEST UNUSED EDGE IN THE GRAPH, STEP TWO, WE REPEAT STEP ONE ADDING THE CHEAPEST UNUSED EDGE TO THE CIRCUIT UNLESS A ADDING THE EDGE WOULD CREATE A CIRCUIT THAT DOESNT CONTAIN ALL VERTICES WHERE B ADDING THE EDGE WOULD GIVE A VERTEX DEGREE THREE. STEP THREE, REPEAT UNTIL A CIRCUIT CONTAINING ALL VERTICES IS FORMED. SO IN OUR PAST SEVERAL LESSONS, WE FOUND THE HAMILTONIAN CIRCUITS OF THE GIVEN GRAPH HERE WERE USING THE BRUTE FORCE ALGORITHM WE FOUND THE CIRCUIT, A, B, C, E, D, A, WITH A TOTAL WEIGHT OF 19 WHICH WE