From 7900c3d3a70ae416205e1d72dc34b208ceb380eb Mon Sep 17 00:00:00 2001
From: Vasko Zdravevski <vaskoz@users.noreply.github.com>
Date: Mon, 30 Dec 2019 10:52:07 -0700
Subject: [PATCH 1/2] day 406 is exactly day 308

---
 day406/problem.go      | 62 ++++++++++++++++++++++++++++++++++++++++++
 day406/problem_test.go | 30 ++++++++++++++++++++
 2 files changed, 92 insertions(+)
 create mode 100644 day406/problem.go
 create mode 100644 day406/problem_test.go

diff --git a/day406/problem.go b/day406/problem.go
new file mode 100644
index 0000000..a872903
--- /dev/null
+++ b/day406/problem.go
@@ -0,0 +1,62 @@
+package day406
+
+// CountParensEqualTrue returns the number of possible
+// paren patterns that evaluate to True.
+// Runs in O(N^3) time and O(N^2) extra space.
+func CountParensEqualTrue(input []rune) int {
+	var sym, ops []rune
+
+	for i := range input {
+		if i%2 == 0 {
+			sym = append(sym, input[i])
+		} else {
+			ops = append(ops, input[i])
+		}
+	}
+
+	f := make([][]int, len(sym))
+	t := make([][]int, len(sym))
+
+	for i := range f {
+		f[i] = make([]int, len(sym))
+		t[i] = make([]int, len(sym))
+
+		if sym[i] == 'F' {
+			f[i][i] = 1
+		}
+
+		if sym[i] == 'T' {
+			t[i][i] = 1
+		}
+	}
+
+	for gap := 1; gap < len(sym); gap++ {
+		for i, j := 0, gap; j < len(sym); i, j = i+1, j+1 {
+			t[i][j] = 0
+			f[i][j] = 0
+
+			for g := 0; g < gap; g++ {
+				k := i + g
+				tik := t[i][k] + f[i][k]
+				tkj := t[k+1][j] + f[k+1][j]
+
+				if ops[k] == '&' {
+					t[i][j] += t[i][k] * t[k+1][j]
+					f[i][j] += tik*tkj - t[i][k]*t[k+1][j]
+				}
+
+				if ops[k] == '|' {
+					f[i][j] += f[i][k] * f[k+1][j]
+					t[i][j] += tik*tkj - f[i][k]*f[k+1][j]
+				}
+
+				if ops[k] == '^' {
+					t[i][j] += f[i][k]*t[k+1][j] + t[i][k]*f[k+1][j]
+					f[i][j] += t[i][k]*t[k+1][j] + f[i][k]*f[k+1][j]
+				}
+			}
+		}
+	}
+
+	return t[0][len(t[0])-1]
+}
diff --git a/day406/problem_test.go b/day406/problem_test.go
new file mode 100644
index 0000000..cb299c2
--- /dev/null
+++ b/day406/problem_test.go
@@ -0,0 +1,30 @@
+package day406
+
+import "testing"
+
+// nolint
+var testcases = []struct {
+	input    []rune
+	expected int
+}{
+	{[]rune{'F', '|', 'T', '&', 'T'}, 2},
+	{[]rune{'T', '|', 'T', '&', 'F', '^', 'T'}, 4},
+}
+
+func TestCountParensEqualTrue(t *testing.T) {
+	t.Parallel()
+
+	for _, tc := range testcases {
+		if result := CountParensEqualTrue(tc.input); result != tc.expected {
+			t.Errorf("Expected %v, got %v", tc.expected, result)
+		}
+	}
+}
+
+func BenchmarkCountParensEqualTrue(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		for _, tc := range testcases {
+			CountParensEqualTrue(tc.input)
+		}
+	}
+}

From 508bc5a9a10ecb48997a4452e917dacfc1e06709 Mon Sep 17 00:00:00 2001
From: Vasko Zdravevski <vaskoz@users.noreply.github.com>
Date: Mon, 30 Dec 2019 10:52:33 -0700
Subject: [PATCH 2/2] add day 406 to readme

---
 README.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/README.md b/README.md
index 9ba14eb..71bbb13 100644
--- a/README.md
+++ b/README.md
@@ -403,4 +403,5 @@ problems from
 * [Day 403](https://github.com/vaskoz/dailycodingproblem-go/issues/815)
 * [Day 404](https://github.com/vaskoz/dailycodingproblem-go/issues/817)
 * [Day 405](https://github.com/vaskoz/dailycodingproblem-go/issues/819)
+* [Day 406](https://github.com/vaskoz/dailycodingproblem-go/issues/821)