From 13bac9590e85c37debbadb852094eff6a9ad59f2 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Wed, 20 Mar 2019 16:38:07 -0300
Subject: [PATCH] Add sqrt decomposition
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/structure/sqrt_decomposition.cpp | 62 +++++++++++++++++++++
1 file changed, 62 insertions(+)
create mode 100644 algorithms/structure/sqrt_decomposition.cpp
diff --git a/algorithms/structure/sqrt_decomposition.cpp b/algorithms/structure/sqrt_decomposition.cpp
new file mode 100644
index 0000000..92e58ce
--- /dev/null
+++ b/algorithms/structure/sqrt_decomposition.cpp
@@ -0,0 +1,62 @@
+/**
+ * Sqrt Decomposition
+ *
+ * Complexity (time):
+ * Preprocess -> O(n)
+ * Query -> O(sqrt(n))
+ * Update -> O(1)
+ * Complexity (space): O(n)
+ */
+
+int v[MAX];
+int block[MAX];
+int block_size;
+
+/**
+ * Update v[idx] with val.
+ * @param idx index of v
+ * @param val new value of v[idx]
+ */
+void update(int idx, int val) {
+ block[idx / block_size] += val - v[idx];
+ v[idx] = val;
+}
+
+/**
+ * Range sum query of v[l..r].
+ * @param l,r range
+ */
+int query(int l, int r) {
+ int ans = 0;
+
+ // Query sum of elements in case l is inside a block
+ for (; l < r && ((l % block_size) != 0); ++l)
+ ans += v[l];
+
+ // Query sum of each block between l and r
+ for (; l + block_size <= r; l += block_size)
+ ans += block[l / block_size];
+
+ // Query sum of remaining blocks (e.g. r is inside a block)
+ for (; l <= r; ++l)
+ ans += v[l];
+
+ return ans;
+}
+
+/**
+ * Fills block array with necessary data to perform update and query in
+ * less than linear time.
+ * @param n number of elements of v
+ */
+void preprocess(int n) {
+ block_size = sqrt(n);
+
+ int idx = -1;
+ for (int i = 0; i < n; ++i) {
+ if (i % block_size == 0)
+ block[++idx] = 0;
+
+ block[idx] += v[i];
+ }
+}
--
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