C: Improve difference-of-squares

Use sum of series instead of calculating it.

1 files changed, 4 insertions, 28 deletions

diff --git a/c/difference-of-squares/src/difference_of_squares.c b/c/difference-of-squares/src/difference_of_squares.c
index 8a422eb..27311ec 100644
--- a/c/difference-of-squares/src/difference_of_squares.c
+++ b/c/difference-of-squares/src/difference_of_squares.c
@@ -1,38 +1,14 @@
 #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.
-*/
+// Returns the sum of squares upto nth Natural number.
 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;
+    return (number * (number + 1) * (2 * number + 1)) / 6;
 }
 
+// Returns the square of sum upto nth Natural number.
 unsigned int square_of_sum(unsigned int number) {
-    unsigned int sum = 0;
-    for (; number > 0; number--)
-        sum += number;
-    return pow(sum, 2);
+    return pow((number * (1 + number)) / 2, 2);
 }
 
 unsigned int difference_of_squares(unsigned int number) {