Programs for IT Unified State Exam (Game Theory)

1prom.py

# 1 heap
# Prohibition of repetition of the opponent's move

def f(s,p,c,m):
    if s>64: return c%2==m%2
    if c==m: return 0
    
    h=[]
    if p!='+1': h+=[f(s+1,'+1',c+1,m)]
    if p!='+2': h+=[f(s+1,'+2',c+1,m)]
    if p!='*2': h+=[f(s+1,'*2',c+1,m)]

    return any(h) if (c+1)%2==m%2 else all(h)

for s in range(1, 65):
    for m in range(1,10):
        if f(s,0,m):
            print(s, m)
            break

1wal.py

# 1 heap
# "With a loss" condition

def f(s,c,m):
    if 32<=s<64: return c%2==m%2
    if s>64: return c%2!=m%2
    if c==m: return 0
    
    h=[f(s+1,c+1,m), f(s+2,c+1,m), f(s*3,c+1,m)]
    return any(h) if (c+1)%2==m%2 else all(h)

for s in range(1, 65):
    for m in range(1,10):
        if f(s,0,m):
            print(s, m)
            break

1wr.py

# 1 heap
# Without restrictions

def f(s,c,m):
    if s>64: return c%2==m%2
    if c==m: return 0

    h=[f(s+1,c+1,m), f(s+2,c+1,m), f(s*3,c+1,m)]
    return any(h) if (c+1)%2==m%2 else all(h)

for s in range(1, 65):
    for m in range(1,10):
        if f(s,0,m):
            print(s, m)
            break

2wr.py

# 2 heaps
# Without restrictions

def f(a,b,c,m):
    if s>64: return c%2==m%2
    if c==m: return 0

    h=[f(a+1,b,c+1,m), f(a,b+1,c+1,m), f(a+2,b,c+1,m), f(a,b+2,c+1,m)]
    return any(h) if (c+1)%2==m%2 else all(h)

for a in range(1, 65):
    for m in range(1,10):
        if f(a,10,0,m):
            print(s, m)
            break

shortlink.md

https://is.gd/M8wJ1e