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#include "difference_of_squares.h"
#include <math.h>
/*
Returns the sum of squares upto nth Natural number.
The difference in squares increases by a incrementing (by 2) step.
Sequence:
1 4 9 16 25 36 49 64 81 100
4 - 1 = 3
9 - 4 = 5 (3 + 2 = 5)
16 - 9 = 7 (5 + 2 = 7)
step is our incrementing step, we increment it by 2 in every
iteration and add it to previous square to get the current term.
*/
unsigned int sum_of_squares(unsigned int number) {
unsigned int sum = 1;
unsigned int step = 1;
unsigned int prev_sq = 1;
for (; number > 1; number--) {
step += 2;
prev_sq += step;
sum += prev_sq;
}
return sum;
}
unsigned int square_of_sum(unsigned int number) {
unsigned int sum = 0;
for (; number > 0; number--)
sum += number;
return pow(sum, 2);
}
unsigned int difference_of_squares(unsigned int number) {
return square_of_sum(number) - sum_of_squares(number);
}
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