"""
pyth.py

Find (a,b,c) such that 

  a < b < c
  a + b + c = N           =>    c = N - a - b
  a*a + b*b = c*c

In class playing around ...

"""

N = 100

for a in range(1, N+1):                    # 100 times
    for b in range(1, N+1):                # 100*100 
        for c in range(1, N+1):            # 100*100*100 
            if a < b < c and a + b + c == N and a*a + b*b == c*c:
                print(" a,b,c is ", a, b,c)

# -----------------------------------------------------------------

#  a :    1   2   3   4   5 
#    b  1 .   *   *   *   *
#       2 .   .   *   *   *
#       3 .   .   .   *   *
#       4 .   .   .   .   *
#       5 .   .   .   .   .

for a in range(1, N+1):                      # check all options
    for b in range(a+1, N+1):                # "BRUTE FORCE"
        c = N - a - b
        if c > a and c > b:
            if a*a + b*b == c*c:
                print("a, b, c is ", a, b, c)

# --- even better -----------------------
                
# since b > a      ,  so b < N/2
# since c > b > a  ,  so a < N/3 

for a in range(1, N//3):
    for b in range(a+1, N//2):
        c = N - a - b
        if c > b and a*a + b*b == c*c:
            print(a,b,c)
            

def is_pyth(a, b, c):
    """ True if a, b, c form a pythagorean triple """
    return a*a + b*b == c*c

assert is_pyth(3, 4, 5), "valid pyth"
assert not is_pyth(1, 2, 3), "invalid pyth"

def search(n):
    """ search for a,b,c up to n """
    pass
    # ... we didn't finish this.