如何判断一组点是否构成三角形？求更Pythonic的实现方案

Hey there! Let's break down your problem of determining if three points in a triangular number grid form a triangle, plus optimize your code to be more Pythonic.

Simplified Approach to Check for a Triangle #

First, I assume you're working with a triangular number array—where the nth row has n numbers, starting at (n-1)*n//2 + 1 and ending at n*(n+1)//2. For three points to form a triangle, they just need to not be collinear. Collinearity here falls into three cases:

• All three points are on the same row (same row number n)
• All three lie on a left-slanting diagonal (where n - k is constant; k is the position in the row, starting at 1 from the left)
• All three lie on a right-slanting diagonal (where n + k is constant)

So the straightforward steps are:

1. Convert each value v to its corresponding (n, k) coordinate in the grid
2. Check if the three coordinates meet any of the collinearity conditions above
3. If none are met, the points form a triangle

Pythonic Implementation #

Your original code uses sympy for solving equations, which is overkill and slow. We can replace that with direct math to compute coordinates, then use clean Pythonic checks:

import math

def get_grid_coords(value):
    # Calculate row number n: satisfies (n-1)*n//2 < value <= n*(n+1)//2
    sqrt_term = math.sqrt(8 * value - 7)
    row = math.ceil((sqrt_term - 1) / 2)
    # Calculate position k in the row
    pos = value - (row - 1) * row // 2
    return (row, pos)

def forms_triangle(values):
    if len(values) != 3:
        return False  # We're only handling 3-point checks here
    coords = [get_grid_coords(v) for v in values]
    
    # Check if all share the same row
    rows = {row for row, pos in coords}
    if len(rows) == 1:
        return False
    
    # Check left-slanting diagonal (row - pos is constant)
    left_diags = {row - pos for row, pos in coords}
    if len(left_diags) == 1:
        return False
    
    # Check right-slanting diagonal (row + pos is constant)
    right_diags = {row + pos for row, pos in coords}
    if len(right_diags) == 1:
        return False
    
    # No collinearity = valid triangle
    return True

# Test with your example values
vals = [8, 17, 19]
print(forms_triangle(vals))  # Will return True/False based on actual collinearity

Why This Is Better Than Your Original Code #

1. No more equation solving: We use a mathematical formula to compute the row directly, avoiding loops and symbolic computation—way faster.
2. Clean collinearity checks: Using sets to check if all coordinates share a row/diagonal is concise and readable, which is very Pythonic.
3. Modular functions: Breaking the logic into small, reusable functions makes the code easier to debug and extend later.

Your original stepsb and stepsf variables are equivalent to pos-1 and row-pos respectively, but we don't need them explicitly here since we can use the row and pos values directly to check diagonals.

内容的提问来源于stack exchange，提问作者Roy Ancri