add divSum (sum of floor linear)

1 files changed, 9 insertions, 0 deletions

diff --git a/content/math/divSum.cpp b/content/math/divSum.cpp
new file mode 100644
index 0000000..dc4bc4d
--- /dev/null
+++ b/content/math/divSum.cpp
@@ -0,0 +1,9 @@
+// Calculates the sum of (a*i+b)/m for i=0..(n-1) in O(log(n))
+// Note that b should not be negative!
+ll divSum(ll n, ll m, ll a, ll b){
+	if(m == 0) return 0;
+	ll ans = a/m * n*(n-1) / 2 + b/m * n;
+	a %= m, b %= m;
+	ll y = (a*(n-1)+b)/m;
+	return ans + y*(n-1) - divSum(y, a, m, m-b-1);
+}
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