From 397678de06d3a36e5a7d03d3c54ca4cdef94a720 Mon Sep 17 00:00:00 2001
From: Lorenzo Tinfena <lorenzo.tinfena.personal@gmail.com>
Date: Wed, 27 Mar 2024 14:19:55 +0100
Subject: [PATCH] .

---
 math/combinatorics/permutation.go             | 11 +++++
 .../combinatorics/robinsonschenstedmapping.go | 49 +++++++++++++++++++
 .../robinsonschenstedmapping_test.go          | 18 +++++++
 3 files changed, 78 insertions(+)
 create mode 100644 math/combinatorics/permutation.go
 create mode 100644 math/combinatorics/robinsonschenstedmapping.go
 create mode 100644 math/combinatorics/robinsonschenstedmapping_test.go

diff --git a/math/combinatorics/permutation.go b/math/combinatorics/permutation.go
new file mode 100644
index 0000000..22e22b2
--- /dev/null
+++ b/math/combinatorics/permutation.go
@@ -0,0 +1,11 @@
+package combinatorics
+
+import "github.com/lorenzotinfena/goji/utils/constraints"
+
+func InversePermutation[T constraints.Integer](permutation []T) []T {
+	inverse := make([]T, len(permutation))
+	for i := 0; i < len(permutation); i++ {
+		inverse[permutation[i]-1] = T(i + 1)
+	}
+	return inverse
+}
diff --git a/math/combinatorics/robinsonschenstedmapping.go b/math/combinatorics/robinsonschenstedmapping.go
new file mode 100644
index 0000000..8345296
--- /dev/null
+++ b/math/combinatorics/robinsonschenstedmapping.go
@@ -0,0 +1,49 @@
+package combinatorics
+
+import (
+	"github.com/lorenzotinfena/goji/sort"
+	"github.com/lorenzotinfena/goji/utils"
+)
+
+// Using code from: codeforces.com/blog/entry/98167
+func RobinsonSchenstedMapping(permutation []int) (p, q [][]int) {
+	sqrt := 1
+	for sqrt*sqrt < len(permutation) {
+		sqrt++
+	}
+	partialRobinsonSchenstedMapping := func(permutation []int) (p [][]int) {
+		youngTableaux := [][]int{}
+		for i := 0; i < len(permutation); i++ {
+			element := permutation[i]
+			for j := 0; j < sqrt; j++ {
+				if len(youngTableaux) == j {
+					youngTableaux = append(youngTableaux, []int{})
+				}
+				ind := sort.UpperBound(youngTableaux[j], element, utils.Prioritize[int]())
+				if ind == len(youngTableaux[j]) {
+					youngTableaux[j] = append(youngTableaux[j], element)
+					break
+				}
+				element, youngTableaux[j][ind] = youngTableaux[j][ind], element
+			}
+		}
+		return youngTableaux
+	}
+
+	p = partialRobinsonSchenstedMapping(permutation)
+	q = partialRobinsonSchenstedMapping(InversePermutation(permutation))
+	for i, j := 0, len(permutation)-1; i < j; i, j = i+1, j-1 {
+		permutation[i], permutation[j] = permutation[j], permutation[i]
+	}
+	pt := partialRobinsonSchenstedMapping(permutation)
+	qt := partialRobinsonSchenstedMapping(InversePermutation(permutation))
+	for i := len(p); i < len(pt[0]); i++ {
+		p = append(p, []int{})
+		q = append(q, []int{})
+		for j := 0; j < len(pt) && i < len(pt[j]); j++ {
+			p[i] = append(p[i], pt[j][i])
+			q[i] = append(q[i], qt[j][i])
+		}
+	}
+	return
+}
diff --git a/math/combinatorics/robinsonschenstedmapping_test.go b/math/combinatorics/robinsonschenstedmapping_test.go
new file mode 100644
index 0000000..7c6a50c
--- /dev/null
+++ b/math/combinatorics/robinsonschenstedmapping_test.go
@@ -0,0 +1,18 @@
+package combinatorics_test
+
+import (
+	"testing"
+
+	"github.com/lorenzotinfena/goji/math/combinatorics"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestRobinsonSchenstedMapping(t *testing.T) {
+	p, q := combinatorics.RobinsonSchenstedMapping([]int{3, 2, 5, 4, 6, 1})
+	assert.Equal(t, p, [][]int{{1, 4, 6}, {2, 5}, {3}})
+	assert.Equal(t, q, [][]int{{1, 3, 5}, {2, 4}, {6}})
+
+	p, q = combinatorics.RobinsonSchenstedMapping([]int{3, 2, 1})
+	assert.Equal(t, p, [][]int{{1}, {2}, {3}})
+	assert.Equal(t, q, [][]int{{1}, {2}, {3}})
+}