Add O(1) optimized solution for Project Euler Problem 6

project_euler/problem_6/o(1)sol.c

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+// Project Euler Problem 6
+// Find the difference between the sum of the squares of the first n natural
+// numbers and the square of the sum of the first n natural numbers.
+//
+// Formula used:
+// Sum of squares = n(n+1)(2n+1)/6
+// Square of sum  = (n(n+1)/2)^2
+//
+// Example:
+// Input : 100
+// Output: 25164150
+
+#include <stdio.h>
+
+// Function to compute sum of squares using formula
+long long sum_of_square(int n)
+{
+    return (long long)n * (n + 1) * (2 * n + 1) / 6;
+}
+
+// Function to compute square of sum using formula
+long long square_of_sum(int n)
+{
+    long long sum = (long long)n * (n + 1) / 2;
+    return sum * sum;
+}
+
+int main()
+{
+    int n;
+    scanf("%d", &n);
+
+    long long answer = square_of_sum(n) - sum_of_square(n);
+    printf("%lld\n", answer);
+
+    return 0;
+}
+//this calculates in o(1) ,enter the n till which u want to find. for our case (in question) its 100