Conquering dynamic programming and graph algorithms requires recognizing underlying problem states and sub-problem optimal substructures.

Dijkstra Algorithm Template in Python

import heapq

def shortest_path(graph, start_node, n):
    distances = {i: float('inf') for i in range(1, n + 1)}
    distances[start_node] = 0
    pq = [(0, start_node)]
    
    while pq:
        curr_dist, u = heapq.heappop(pq)
        
        if curr_dist > distances[u]:
            continue
            
        for v, weight in graph[u]:
            if distances[u] + weight < distances[v]:
                distances[v] = distances[u] + weight
                heapq.heappush(pq, (distances[v], v))
                
    return distances