docker_space/frontier_cs_8/construct2.py

#!/usr/bin/env python3
"""
Trace modified chain to understand why it's infinite, then fix it.
"""

P = 998244353

def evaluate_verbose(n, instructions, max_depth=50):
    dp = {}
    vis = set()
    depth = [0]

    def solve(i, x, indent=0):
        prefix = "  " * indent
        if (i, x) in dp:
            return dp[(i, x)]
        if (i, x) in vis:
            print(f"{prefix}CYCLE at ({i}, {x})")
            return None
        vis.add((i, x))
        if indent > max_depth:
            print(f"{prefix}MAX DEPTH at ({i}, {x})")
            return None

        inst = instructions[i]
        if inst[0] == 'POP':
            _, pop_c, g1, push_c, g2 = inst
            if x == pop_c:
                print(f"{prefix}solve({i},{x}): POP match, goto {g1}. cost=1")
                dp[(i, x)] = (g1, 1)
            else:
                print(f"{prefix}solve({i},{x}): POP miss (need {pop_c}), push {push_c} goto {g2}")
                r = solve(g2, push_c, indent+1)
                if r is None: return None
                j, u = r
                print(f"{prefix}  resolve returned to instr {j}, cost {u}")
                r2 = solve(j, x, indent+1)
                if r2 is None: return None
                k, v = r2
                print(f"{prefix}  continue from {j} with {x}: -> {k}, cost {v}")
                dp[(i, x)] = (k, (u + v + 1) % P)
        else:
            _, push_c, g2 = inst
            if x == 0:
                print(f"{prefix}solve({i},{x}): HALT. cost=1")
                dp[(i, x)] = (-1, 1)
            else:
                print(f"{prefix}solve({i},{x}): HALT non-empty, push {push_c} goto {g2}")
                r = solve(g2, push_c, indent+1)
                if r is None: return None
                j, u = r
                print(f"{prefix}  resolve returned to instr {j}, cost {u}")
                r2 = solve(j, x, indent+1)
                if r2 is None: return None
                k, v = r2
                dp[(i, x)] = (k, (u + v + 1) % P)

        return dp[(i, x)]

    r = solve(0, 0)
    if r is None: return -1
    return r[1]

# Test: d=3, modified POP 0 pushes char 4 instead of 1
# HALT pushes 1 goto 0
d = 3
instrs = [
    ('POP', 1, 1, 4, 0),  # POP 0: pop 1, goto 1, push 4, goto 0
    ('POP', 2, 2, 2, 0),  # POP 1: pop 2, goto 2, push 2, goto 0
    ('POP', 3, 3, 3, 0),  # POP 2: pop 3, goto 3, push 3, goto 0
    ('HALT', 1, 0),        # HALT 3: push 1, goto 0
]
print("=== Modified chain d=3, POP 0 pushes 4 ===")
T = evaluate_verbose(4, instrs)
print(f"T = {T}")