ACM (UVa) : 10784

Diagonal

Data type:
Double

Algorithm:

Basic Formula: Number of diagonal in N-gon is (N * (N-3) ) / 2.

U are given the right portion of the equation, now u have to find the value of N.

Suppose, Given value X

N = ceil ( (3 + sqrt (9 + ( 8 * N))) /2); [ceil >>> under <math.h>]

This equation comes from:
( N * ( N-3 ) ) / 2 = X
> N^{2 –} 3*N – 2*X = 0

We know, X = (– b + sqrt (b² – 4 * a * c )) / 2 * a

In C/C++, u can print a double value like integer by using %0.lf.
For example, double X = 963.258;
printf(“%0.lf”, X);
output: 963

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