Floyd Warshall All Pairs Shortest Paths in Python

from bisect import bisect_left

# Floyd Warshall All Pairs Shortest Paths in Python
#
# PURPOSE
# Floyd-Warshall computes distances between every pair by gradually allowing more
# intermediate vertices. The ordering of the three loops expresses the dynamic programming
# recurrence.
#
# METHOD
# For each intermediate k, try improving every i-to-j path through k. Skip unreachable
# halves before adding distances. After pass k, paths may use only intermediates up to k.
#
# COMPLEXITY
# O(n cubed) time and O(1) auxiliary space beyond the caller-owned n squared distance
# matrix.
#
# CONTRACT
# Mutates flattened distance matrix. Diagonal starts at 0; missing edges use 1,000,000,000.
# Negative edges allowed. Finite path sums must fit and remain strictly between -INF and
# INF. Returns -1 if any negative cycle exists, otherwise 0.
# 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: 0.
# Expected distance after call: [0, 4, 6, 1000000000, 0, 2, 1000000000, 1000000000, 0].
# 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 floyd_warshall(distance: list[int], n: int) -> int:
    alg_require(isinstance(distance, list) and len(distance) <= 1000000)
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(len(distance) == n * n)
    k: int = 0
    i: int = 0
    j: int = 0
    while k < n:
        i = 0
        while i < n:
            j = 0
            while j < n:
                if distance[i * n + k] != 1000000000 and distance[k * n + j] != 1000000000:
                    distance[i * n + j] = min(distance[i * n + j], distance[i * n + k] + distance[k * n + j])
                j += 1
            i += 1
        k += 1
    i = 0
    while i < n:
        if distance[i * n + i] < 0:
            return -1
        i += 1
    return 0

distance = [0, 4, 10, 1000000000, 0, 2, 1000000000, 1000000000, 0]
n = 3
result = floyd_warshall(distance, n)
print(result)
print(distance)
# Expected distance: [0, 4, 6, 1000000000, 0, 2, 1000000000, 1000000000, 0]