This is the proof for Dijkstra's algorithm, also known as the single source shortest path algorithm.
Prerequisite:
https://youtu.be/d6ZFqjH63vo
Code:
To be added soon (Comment below to contribute)
References:
http://www.geeksforgeeks.org/greedy-algorithms-set-6-dijkstras-shortest-path-algorithm/
https://web.engr.oregonstate.edu/~glencora/wiki/uploads/dijkstra-proof.pdf
http://math.mit.edu/~rothvoss/18.304.3PM/Presentations/1-Melissa.pdf