From 998db5259fb828e2d1de8579bf8cf60805d9ed39 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Thu, 1 Feb 2018 14:50:58 -0200
Subject: [PATCH] Add ternary_search
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
graph/bfs.cpp | 1 +
graph/dfs.cpp | 1 +
graph/dijkstra.cpp | 1 +
paradigm/ternary_search.cpp | 35 +++++++++++++++++++++++++++++++++++
structure/bit.cpp | 2 +-
structure/bit2d.cpp | 2 +-
structure/bitmask.cpp | 1 +
structure/segment_tree.cpp | 7 ++++---
8 files changed, 45 insertions(+), 5 deletions(-)
create mode 100644 paradigm/ternary_search.cpp
diff --git a/graph/bfs.cpp b/graph/bfs.cpp
index 6730824..5a7179a 100644
--- a/graph/bfs.cpp
+++ b/graph/bfs.cpp
@@ -1,5 +1,6 @@
/**
* Breadth First Search - BFS
+ *
* Complexity (Time): O(|V| + |E|)
* Complexity (Space): O(|V| + |E|)
*/
diff --git a/graph/dfs.cpp b/graph/dfs.cpp
index e01c0ca..8748a19 100644
--- a/graph/dfs.cpp
+++ b/graph/dfs.cpp
@@ -1,5 +1,6 @@
/**
* Depth First Search - DFS
+ *
* Complexity (Time): O(|V| + |E|)
* Complexity (Space): O(|V| + |E|)
*/
diff --git a/graph/dijkstra.cpp b/graph/dijkstra.cpp
index a0c8b1b..86a350c 100644
--- a/graph/dijkstra.cpp
+++ b/graph/dijkstra.cpp
@@ -1,5 +1,6 @@
/**
* Dijkstra
+ *
* Complexity (Time): O(|E| + |V| log |V|)
* Complexity (Space): O(|E| + |V|)
*/
diff --git a/paradigm/ternary_search.cpp b/paradigm/ternary_search.cpp
new file mode 100644
index 0000000..55ee026
--- /dev/null
+++ b/paradigm/ternary_search.cpp
@@ -0,0 +1,35 @@
+/**
+ * Ternary Search
+ *
+ * Complexity (Time): O(log n)
+ * Complexity (Space): O(1)
+ */
+
+#define EPS 1e-6
+
+// Unimodal function
+double f(double x) {
+ return x * x;
+}
+
+// Execute ternary search to find maximum or minimum between l and r
+double ternary_search(double l, double r) {
+ double rt, lt;
+
+ for (int i = 0; i < 500; ++i) {
+ if (fabs(r - l) < EPS)
+ return (l + r) / 2.0;
+
+ lt = l + (r - l) / 3.0;
+ rt = r - (r - l) / 3.0;
+
+ // < | minimum of f
+ // > | maximum of f
+ if (f(lt) < f(rt))
+ l = lt;
+ else
+ r = rt;
+ }
+
+ return (l + r) / 2.0;
+}
diff --git a/structure/bit.cpp b/structure/bit.cpp
index 73165d3..b7cbe39 100644
--- a/structure/bit.cpp
+++ b/structure/bit.cpp
@@ -1,9 +1,9 @@
/**
* Binary Indexed Tree - BIT
+ *
* Complexity (Time):
* Update -> O(log n)
* Query -> O(log n)
- *
* Complexity (Space): O(n)
*/
diff --git a/structure/bit2d.cpp b/structure/bit2d.cpp
index 917cd97..43aa801 100644
--- a/structure/bit2d.cpp
+++ b/structure/bit2d.cpp
@@ -1,9 +1,9 @@
/**
* Binary Indexed Tree 2D - BIT2D
+ *
* Complexity (Time):
* Update -> O(log^2 n)
* Query -> O(log^2 n)
- *
* Complexity (Space): O(n^2)
*/
diff --git a/structure/bitmask.cpp b/structure/bitmask.cpp
index f6c8e2c..65b05fd 100644
--- a/structure/bitmask.cpp
+++ b/structure/bitmask.cpp
@@ -1,5 +1,6 @@
/**
* Bitmask
+ *
* Complexity (Time): O(1)
* Complexity (Space): O(1)
*/
diff --git a/structure/segment_tree.cpp b/structure/segment_tree.cpp
index a78608d..e825ed9 100644
--- a/structure/segment_tree.cpp
+++ b/structure/segment_tree.cpp
@@ -1,9 +1,10 @@
/**
* Segment Tree
+ *
* Complexity (Time):
- * Build -> O(n log n)
- * Update -> O(log n)
- * Query -> O(log n)
+ * Build -> O(n log n)
+ * Update -> O(log n)
+ * Query -> O(log n)
* Complexity (Space): O(n)
*/
--
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