# Python – Find the maximum number of triangles with given points on three lines

Given three parallel straight lines l1, l2 and l3 lying in the same plane. Total numbers of m, n and k points lie on the line l1, l2, l3 respectively. This article aims to find the maximum number of triangles formed with vertices at these points.

Examples:

Input : m = 14, n = 34, k = 114
Output : 448708.0

Input : m = 95, n = 77, k = 94
Output : 2755951.0

Approach-

1. Total number of triangle = 2. Number of triangle that is not valid traingle from l1 plane = 3. Number of triangle that is not valid traingle from l2 plane = 4. Number of triangle that is not valid traingle from l3 plane = 5. so number of valid Triangle = Below is the Python code implementation of the approach.

 `# Pyton code implementation ` `import` `math ` `def` `nooftriangle(m, n, k): ` `     `  `    ``# r1 = (m + n + k)C3 ` `    ``r1 ``=` `math.factorial(m ``+` `n ``+` `k) ``/` `( ` `            ``math.factorial(``3``) ``*` `math.factorial(m ``+` `n ``+` `k ``-` `3``)) ` `    ``# r2 = mC3 ` `    ``r2 ``=` `math.factorial(m) ``/` `(math.factorial(``3``) ``*` `math.factorial(m ``-` `3``)) ` `     `  `    ``# r3 = nC3 ` `    ``r3 ``=` `math.factorial(n) ``/` `(math.factorial(``3``) ``*` `math.factorial(n ``-` `3``)) ` `     `  `    ``#r4 = kC3 ` `    ``r4 ``=` `math.factorial(k) ``/` `(math.factorial(``3``) ``*` `math.factorial(k ``-` `3``)) ` `     `  `    ``result ``=` `r1 ``-` `r2 ``-` `r3 ``-` `r4 ` `    ``return``(result)  ` `     `  `# Driver code ` `m ``=` `17` `n ``=` `16` `k ``=` `11` `print``(``"Number of traingles : "``, nooftriangle(m, n, k)) ` `     `

Output:

`Number of traingles :  11839.0`

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