Dijkstra Shortest Path in Python

from bisect import bisect_left

# Dijkstra Shortest Path in Python
#
# PURPOSE
# Dijkstra repeatedly settles the unsettled vertex with smallest tentative distance.
# Nonnegative edge weights ensure that distance can never improve later.
#
# METHOD
# Initialize source distance zero. Select the unused minimum-distance vertex by scanning,
# stop if none is reachable, and relax all its outgoing edges.
#
# COMPLEXITY
# O(n squared) time and O(n) auxiliary space for this dense-graph matrix version. A heap
# plus adjacency lists gives a different bound.
#
# CONTRACT
# Flattened n by n weight matrix; -1 means no edge, other weights >= 0. n >= 1. Every finite
# path must be < 1,000,000,000; additions must fit. Returns -1 if unreachable.
# Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
# counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
# Sorted order, correct tree topology, and caller-owned data-structure invariants are
# preconditions; checking them on every query would change query complexity.
# Scalar and shape checks are included. Value-range checks are included where needed to
# prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
# workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
# uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
# partly updated after arithmetic failure. These are single-threaded, in-memory
# implementations.
#
# LANGUAGE DETAILS
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 6.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def dijkstra(graph: list[int], n: int, source: int, target: int) -> int:
    alg_require(isinstance(graph, (list, tuple)) and len(graph) <= 1000000)
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(type(source) is int and -2147483648 <= source <= 2147483647)
    alg_require(type(target) is int and -2147483648 <= target <= 2147483647)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(graph) == n * n)
    alg_require(n >= 1 and source >= 0 and (source < n))
    alg_require(target >= 0 and target < n)
    alg_require(n >= 1)
    for value in graph:
        alg_require(value >= -1 and value < 1000000000)
    distance: list[int] = [0] * alg_size(n)
    used: list[int] = [0] * alg_size(n)
    i: int = 0
    v: int = 0
    u: int = 0
    best: int = 0
    while i < n:
        distance[i] = 1000000000
        i += 1
    distance[source] = 0
    i = 0
    while i < n:
        u = -1
        best = 1000000000
        v = 0
        while v < n:
            if used[v] == 0 and distance[v] < best:
                best = distance[v]
                u = v
            v += 1
        if u == -1:
            break
        used[u] = 1
        v = 0
        while v < n:
            if graph[u * n + v] >= 0:
                distance[v] = min(distance[v], distance[u] + graph[u * n + v])
            v += 1
        i += 1
    if distance[target] == 1000000000:
        return -1
    return distance[target]

graph = [0, 4, 10, -1, 0, 2, -1, -1, 0]
n = 3
source = 0
target = 2
result = dijkstra(graph, n, source, target)
print(result)