commit 8bc7b2bf58c015c98c8abb93736ff7fe2211224f
Author: Félix MARQUET <fpmovie4@gmail.com>
Date:   Wed Dec 18 10:13:48 2024 +0100

    Initial commit

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..7224328
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,2 @@
+.idea
+.idea/
\ No newline at end of file
diff --git a/TD/.Rhistory b/TD/.Rhistory
new file mode 100644
index 0000000..115b06b
--- /dev/null
+++ b/TD/.Rhistory
@@ -0,0 +1,45 @@
+print("Hello World")
+x+2
+print(x+2)
+x+2
+(5^2+5)/3
+sum(log(32,2), 8^4, 4+5, 12/3)
+sum(50, 3, 5)
+log10(90+5*2)
+variable2
+variable2 + 2
+mean(variable2)
+variable2 <- c(12, 1, 15, 3, 20, 6, 11)
+variable2
+mean(variable2)
+variable2 + 2
+variable2 <- c(12, 1, 15, 3, 20, 6, 11)
+variable2
+mean(variable2)
+variable2 + 2
+x = c(1, 3, 5, 7, 9)
+y = c(2, 3, 5, 7, 11, 13)
+z = c(9, 3, 2, 5, 9, 2, 3, 9, 1)
+x + 2
+y * 3
+length(x)
+x + y
+sum(x > 5)
+sum(x[x > 5])
+sum(x > 5 | x < 3)
+y[3]
+y[-3]
+y[x]
+(y > 7)
+y[y > 7]
+sort(z)
+sort(z, dec = TRUE)
+rev(z)
+order(z)
+unique(z)
+duplicated(z)
+table(z)
+rep(z, 3)
+vector1 <- c(1, 2, 3)
+vector2 <- c(4, 5, 6)
+vector3 <- c(vector1[1:2], vector2, vector1[3:length(vector1)])
diff --git a/TD/.Rproj.user/F9ECB55E/pcs/files-pane.pper b/TD/.Rproj.user/F9ECB55E/pcs/files-pane.pper
new file mode 100644
index 0000000..7d5ef91
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/pcs/files-pane.pper
@@ -0,0 +1,9 @@
+{
+    "sortOrder": [
+        {
+            "columnIndex": 2,
+            "ascending": true
+        }
+    ],
+    "path": "C:/Users/BreizhHardware/Nextcloud/Programation/R/TD"
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/pcs/source-pane.pper b/TD/.Rproj.user/F9ECB55E/pcs/source-pane.pper
new file mode 100644
index 0000000..ddca97d
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/pcs/source-pane.pper
@@ -0,0 +1,3 @@
+{
+    "activeTab": 2
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/pcs/windowlayoutstate.pper b/TD/.Rproj.user/F9ECB55E/pcs/windowlayoutstate.pper
new file mode 100644
index 0000000..de81620
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/pcs/windowlayoutstate.pper
@@ -0,0 +1,14 @@
+{
+    "left": {
+        "splitterpos": 393,
+        "topwindowstate": "NORMAL",
+        "panelheight": 945,
+        "windowheight": 983
+    },
+    "right": {
+        "splitterpos": 589,
+        "topwindowstate": "NORMAL",
+        "panelheight": 945,
+        "windowheight": 983
+    }
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/pcs/workbench-pane.pper b/TD/.Rproj.user/F9ECB55E/pcs/workbench-pane.pper
new file mode 100644
index 0000000..75e70e9
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/pcs/workbench-pane.pper
@@ -0,0 +1,5 @@
+{
+    "TabSet1": 0,
+    "TabSet2": 0,
+    "TabZoom": {}
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/rmd-outputs b/TD/.Rproj.user/F9ECB55E/rmd-outputs
new file mode 100644
index 0000000..3f2ff2d
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/rmd-outputs
@@ -0,0 +1,5 @@
+
+
+
+
+
diff --git a/TD/.Rproj.user/F9ECB55E/saved_source_markers b/TD/.Rproj.user/F9ECB55E/saved_source_markers
new file mode 100644
index 0000000..2b1bef1
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/saved_source_markers
@@ -0,0 +1 @@
+{"active_set":"","sets":[]}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/per/t/B62E70DA b/TD/.Rproj.user/F9ECB55E/sources/per/t/B62E70DA
new file mode 100644
index 0000000..eef4266
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/per/t/B62E70DA
@@ -0,0 +1,26 @@
+{
+    "id": "B62E70DA",
+    "path": "C:/Users/BreizhHardware/Nextcloud/Programation/R/TD/Exo3.R",
+    "project_path": "Exo3.R",
+    "type": "r_source",
+    "hash": "340809373",
+    "contents": "",
+    "dirty": false,
+    "created": 1733479137294.0,
+    "source_on_save": false,
+    "relative_order": 3,
+    "properties": {
+        "source_window_id": "",
+        "Source": "Source",
+        "cursorPosition": "0,0",
+        "scrollLine": "0"
+    },
+    "folds": "",
+    "lastKnownWriteTime": 1733479598,
+    "encoding": "UTF-8",
+    "collab_server": "",
+    "source_window": "",
+    "last_content_update": 1733479598,
+    "read_only": false,
+    "read_only_alternatives": []
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/per/t/B62E70DA-contents b/TD/.Rproj.user/F9ECB55E/sources/per/t/B62E70DA-contents
new file mode 100644
index 0000000..392f752
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/per/t/B62E70DA-contents
@@ -0,0 +1,14 @@
+# Crée des vecteurs
+# y0 constitué de la suite des entiers de 0 à 10 par pas de 2
+y0 <- seq(0, 10, by=2)
+# y1 constitué de tous les entiers pairs entre 1 et 18
+y1 <- seq(2, 18, by=2)
+# y2 constitué de 20 fois de suite la valeur 4
+y2 <- rep(4, 20)
+# y3 constitué de 20 nombres entre 0 et 10
+y3 <- runif(20, 0, 10)
+
+# Extraire de y3
+# le troisième élément
+y33 <- y3[2]
+# tous les éléments sauf le troisième
diff --git a/TD/.Rproj.user/F9ECB55E/sources/per/t/C229FEB4 b/TD/.Rproj.user/F9ECB55E/sources/per/t/C229FEB4
new file mode 100644
index 0000000..7ba97ca
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/per/t/C229FEB4
@@ -0,0 +1,26 @@
+{
+    "id": "C229FEB4",
+    "path": "C:/Users/BreizhHardware/Nextcloud/Programation/R/TD/Exo2.R",
+    "project_path": "Exo2.R",
+    "type": "r_source",
+    "hash": "3327678100",
+    "contents": "",
+    "dirty": false,
+    "created": 1733478990873.0,
+    "source_on_save": false,
+    "relative_order": 2,
+    "properties": {
+        "source_window_id": "",
+        "Source": "Source",
+        "cursorPosition": "3,63",
+        "scrollLine": "0"
+    },
+    "folds": "",
+    "lastKnownWriteTime": 1733479100,
+    "encoding": "UTF-8",
+    "collab_server": "",
+    "source_window": "",
+    "last_content_update": 1733479100521,
+    "read_only": false,
+    "read_only_alternatives": []
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/per/t/C229FEB4-contents b/TD/.Rproj.user/F9ECB55E/sources/per/t/C229FEB4-contents
new file mode 100644
index 0000000..494704d
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/per/t/C229FEB4-contents
@@ -0,0 +1,4 @@
+vector1 <- c(1, 2, 3)
+vector2 <- c(4, 5, 6)
+
+vector3 <- c(vector1[1:2], vector2, vector1[3:length(vector1)])
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/per/t/DA0B538E b/TD/.Rproj.user/F9ECB55E/sources/per/t/DA0B538E
new file mode 100644
index 0000000..16dc965
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/per/t/DA0B538E
@@ -0,0 +1,26 @@
+{
+    "id": "DA0B538E",
+    "path": "C:/Users/BreizhHardware/Nextcloud/Programation/R/TD/Exo1.R",
+    "project_path": "Exo1.R",
+    "type": "r_source",
+    "hash": "1460566234",
+    "contents": "",
+    "dirty": false,
+    "created": 1733478588935.0,
+    "source_on_save": false,
+    "relative_order": 1,
+    "properties": {
+        "source_window_id": "",
+        "Source": "Source",
+        "cursorPosition": "19,8",
+        "scrollLine": "0"
+    },
+    "folds": "",
+    "lastKnownWriteTime": 1733478955,
+    "encoding": "UTF-8",
+    "collab_server": "",
+    "source_window": "",
+    "last_content_update": 1733478955036,
+    "read_only": false,
+    "read_only_alternatives": []
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/per/t/DA0B538E-contents b/TD/.Rproj.user/F9ECB55E/sources/per/t/DA0B538E-contents
new file mode 100644
index 0000000..4495958
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/per/t/DA0B538E-contents
@@ -0,0 +1,24 @@
+x = c(1, 3, 5, 7, 9)
+y = c(2, 3, 5, 7, 11, 13)
+z = c(9, 3, 2, 5, 9, 2, 3, 9, 1)
+
+x + 2
+y * 3
+length(x)
+x + y
+sum(x > 5)
+sum(x[x > 5])
+sum(x > 5 | x < 3)
+y[3]
+y[-3]
+y[x]
+(y > 7)
+y[y > 7]
+sort(z)
+sort(z, dec = TRUE)
+rev(z)
+order(z)
+unique(z)
+duplicated(z)
+table(z)
+rep(z, 3)
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/prop/1489AED4 b/TD/.Rproj.user/F9ECB55E/sources/prop/1489AED4
new file mode 100644
index 0000000..421141e
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/prop/1489AED4
@@ -0,0 +1,6 @@
+{
+    "source_window_id": "",
+    "Source": "Source",
+    "cursorPosition": "0,0",
+    "scrollLine": "0"
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/prop/57E49702 b/TD/.Rproj.user/F9ECB55E/sources/prop/57E49702
new file mode 100644
index 0000000..d136f0a
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/prop/57E49702
@@ -0,0 +1,6 @@
+{
+    "source_window_id": "",
+    "Source": "Source",
+    "cursorPosition": "3,63",
+    "scrollLine": "0"
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/prop/74FBB217 b/TD/.Rproj.user/F9ECB55E/sources/prop/74FBB217
new file mode 100644
index 0000000..895734f
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/prop/74FBB217
@@ -0,0 +1,6 @@
+{
+    "source_window_id": "",
+    "Source": "Source",
+    "cursorPosition": "19,8",
+    "scrollLine": "0"
+}
\ No newline at end of file
diff --git a/TD/.Rproj.user/F9ECB55E/sources/prop/INDEX b/TD/.Rproj.user/F9ECB55E/sources/prop/INDEX
new file mode 100644
index 0000000..0603ee1
--- /dev/null
+++ b/TD/.Rproj.user/F9ECB55E/sources/prop/INDEX
@@ -0,0 +1,3 @@
+C%3A%2FUsers%2FBreizhHardware%2FNextcloud%2FProgramation%2FR%2FTD%2FExo1.R="74FBB217"
+C%3A%2FUsers%2FBreizhHardware%2FNextcloud%2FProgramation%2FR%2FTD%2FExo2.R="57E49702"
+C%3A%2FUsers%2FBreizhHardware%2FNextcloud%2FProgramation%2FR%2FTD%2FExo3.R="1489AED4"
diff --git a/TD/.Rproj.user/shared/notebooks/patch-chunk-names b/TD/.Rproj.user/shared/notebooks/patch-chunk-names
new file mode 100644
index 0000000..e69de29
diff --git a/TD/Exo1.R b/TD/Exo1.R
new file mode 100644
index 0000000..4495958
--- /dev/null
+++ b/TD/Exo1.R
@@ -0,0 +1,24 @@
+x = c(1, 3, 5, 7, 9)
+y = c(2, 3, 5, 7, 11, 13)
+z = c(9, 3, 2, 5, 9, 2, 3, 9, 1)
+
+x + 2
+y * 3
+length(x)
+x + y
+sum(x > 5)
+sum(x[x > 5])
+sum(x > 5 | x < 3)
+y[3]
+y[-3]
+y[x]
+(y > 7)
+y[y > 7]
+sort(z)
+sort(z, dec = TRUE)
+rev(z)
+order(z)
+unique(z)
+duplicated(z)
+table(z)
+rep(z, 3)
\ No newline at end of file
diff --git a/TD/Exo2.R b/TD/Exo2.R
new file mode 100644
index 0000000..494704d
--- /dev/null
+++ b/TD/Exo2.R
@@ -0,0 +1,4 @@
+vector1 <- c(1, 2, 3)
+vector2 <- c(4, 5, 6)
+
+vector3 <- c(vector1[1:2], vector2, vector1[3:length(vector1)])
\ No newline at end of file
diff --git a/TD/Exo3.R b/TD/Exo3.R
new file mode 100644
index 0000000..533e249
--- /dev/null
+++ b/TD/Exo3.R
@@ -0,0 +1,39 @@
+# Crée des vecteurs
+# y0 constitué de la suite des entiers de 0 à 10 par pas de 2
+y0 <- seq(0, 10, by=2)
+# y1 constitué de tous les entiers pairs entre 1 et 18
+y1 <- seq(2, 18, by=2)
+# y2 constitué de 20 fois de suite la valeur 4
+y2 <- rep(4, 20)
+# y3 constitué de 20 nombres entre 0 et 10
+y3 <- runif(20, 0, 10)
+
+# Extraire de y3
+# le troisième élément
+y33 <- y3[3]
+# tous les éléments sauf le troisième
+y34 <- y3[-3]
+
+# Comparer les commandes suivantes
+matrix(y3, nrow = 2)
+matrix(y3, byrow = TRUE)
+
+# Construire une matrice A comportant quatre lignes et trois colonnes remplies par lignes
+# successives avec les éléments du vecteur 1:12
+A <- matrix(1:12, nrow = 4, byrow = TRUE)
+
+# Construire une matrice B comportant quatre lignes et trois colonnes remplies par
+# colonnes successives avec les éléments du vecteur 1:12
+B <- matrix(1:12, nrow = 4, byrow = FALSE)
+
+# Extraire l’élément situé en deuxième ligne et troisième colonne de A
+A[2, 3]
+
+# Extraire la première colonne de A, puis la deuxième ligne de A.
+A[, 1]
+A[2, ]
+
+# Construire une matrice C constituée des lignes 1 et 4 de A.
+C <- A[c(1, 4), ]
+print(A)
+print(C)
\ No newline at end of file
diff --git a/TD/Exo4.R b/TD/Exo4.R
new file mode 100644
index 0000000..2df4ce3
--- /dev/null
+++ b/TD/Exo4.R
@@ -0,0 +1,3 @@
+# Construire une matrice comportant 9 lignes et 9 colonnes avec des 0 sur la diagonale et des 1
+# partout ailleurs (on pourra utiliser la commande diag)
+D <- matrix(1, nrow = 9, ncol = 9)
\ No newline at end of file
diff --git a/TD/Exo5.R b/TD/Exo5.R
new file mode 100644
index 0000000..afaabc5
--- /dev/null
+++ b/TD/Exo5.R
@@ -0,0 +1,23 @@
+# Créer un vecteur x = (x1, . . . , x11) contenant les réels compris entre 0 et 1 par pas de 0.1
+x <- seq(0, 1, by=0.1)
+
+# Afficher la longueur de x
+print(length(x))
+
+# En utilisant les opérations vectorielles, créer un vecteur y = 4x(1 − x)
+y <- 4*x*(1-x)
+
+# Tracer la courbe rejoignant les points (x1, y1), . . . , (x11, y11) avec la commande plot
+plot(x, y)
+
+# Calculer le maximum des y1, . . . , y11
+print(max(y))
+
+# En quel point le maximum est-il atteint ?
+print(x[which.max(y)])
+
+# Tracer la courbe de la fonction f (x) = 4x2(1 − x), x
+# ∈ [−2, 1], en rouge
+x <- seq(-2, 1, by=0.1)
+y <- 4*x^2*(1-x)
+plot(x, y, col="red")
\ No newline at end of file
diff --git a/TD/Exo6.R b/TD/Exo6.R
new file mode 100644
index 0000000..e734fa3
--- /dev/null
+++ b/TD/Exo6.R
@@ -0,0 +1,20 @@
+# Utiliser R pour donner les valeurs numériques attendues :
+# Combien y-a-t-il de carrés (4 cartes de même valeur) dans un jeu de 32 cartes ?
+nb_carres <- 8
+nb_carres
+
+# Combien d’anagrammes peut-on faire avec le mot "dinosaure" ?
+anagrammes <- factorial(9) / factorial(2)
+anagrammes
+
+# Combien de chances a-t-on de gagner le super jackpot à l’euromillion ? (donc d’avoir 5
+# bons numéros parmi 49, et 2 bons numéros étoilés parmi 10)
+chances <- choose(49, 5) * choose(10, 2)
+chances
+
+# Chaque pièce d’un nouveau jeu de domino est de la forme : a b avec (a, b) ∈ {0, . . . , 9}2
+# en sachant qu’un domino reste le même si on le tourne à 180 degrés (par exemple, 8 = 8
+# est un, et un seul domino). Déterminer le nombre de pièces différentes que contient un
+# jeu complet de dominos
+nb_dominos <- choose(10, 2) + 10
+nb_dominos
\ No newline at end of file
diff --git a/TD/Rplots.pdf b/TD/Rplots.pdf
new file mode 100644
index 0000000..e91b9a1
Binary files /dev/null and b/TD/Rplots.pdf differ
diff --git a/TD/TD.Rproj b/TD/TD.Rproj
new file mode 100644
index 0000000..8e3c2eb
--- /dev/null
+++ b/TD/TD.Rproj
@@ -0,0 +1,13 @@
+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX
diff --git a/TD1/Exercice39.R b/TD1/Exercice39.R
new file mode 100644
index 0000000..d301fa0
--- /dev/null
+++ b/TD1/Exercice39.R
@@ -0,0 +1,17 @@
+# Question a
+# Ici on cherche P(X <= 30) via une loi binomial avec 70 et 0.4
+sum(dbinom(x=0:30,size=70,prob=0.4))
+
+# Question b
+# Ici on cherche P(X) >= 0.9 via la même loi binomial qu'avant
+i <- 0
+j <- 30
+while (i < 0.9) {
+  i <- sum(dbinom(x=0:j, size=70, prob=0.4))
+  j <- j + 1
+}
+print(i)
+print(j - 1)
+
+# Bonus
+print(dbinom(x=0:70, size=70, prob=0.4))
diff --git a/TD1/Exercice51.R b/TD1/Exercice51.R
new file mode 100644
index 0000000..32ef563
--- /dev/null
+++ b/TD1/Exercice51.R
@@ -0,0 +1,16 @@
+# Dans une station-service, la demande hebdomadaire en essence, en milliers de litres, est
+# une variable aléatoire X de densité f (x) = c(1 − x)^4 1[0,1].
+# a) Déterminer c
+f <- function(x) {(1-x)^4}
+result <- integrate(f, lower = 0, upper = 1)
+# Je détermine C car intérale de c*f(x) = 1
+c <- 1 / result$value
+print(c)
+# b) La station est réapprovisionnée chaque lundi à 20h. Quelle doit être la capacité du réservoir
+# d’essence pour que la probabilité d’épuiser ce réservoir soit inférieure à 10^−5 ?
+F <- function(x) {
+  integrate(function(t) c * (1 - t)^4, lower = 0, upper = x)$value
+}
+cible <- 1 - 10^(-5)
+capacite <- uniroot(function(x) F(x) - cible, lower = 0, upper = 1)$root
+print(capacite * 1000)
diff --git a/TD1/Exo1.R b/TD1/Exo1.R
new file mode 100644
index 0000000..8f851d3
--- /dev/null
+++ b/TD1/Exo1.R
@@ -0,0 +1,17 @@
+# Une course oppose 20 concurrents, dont Émile
+# a) Combien y-a-t-il de podiums possibles ?
+podiums_total <- factorial(20) / factorial(20 - 3)
+podiums_total
+
+# b) Combien y-a-t-il de podiums possibles où Émile est premier ?
+emile_premier <- 1 * (factorial(19) / factorial(17))
+emile_premier
+
+# c) Combien y-a-t-il de podiums possibles dont Émile fait partie ?
+emile_podium <- 3 * (factorial(19) / factorial(17))
+emile_podium
+
+# d) On souhaite récompenser les 3 premiers en leur offrant un prix identique à chacun. Combien
+# y-a-t-il de distributions de récompenses possibles ?
+distributions <- choose(20, 3)
+distributions
\ No newline at end of file
diff --git a/TD1/advent_of_code_06_12_2024.R b/TD1/advent_of_code_06_12_2024.R
new file mode 100644
index 0000000..9266927
--- /dev/null
+++ b/TD1/advent_of_code_06_12_2024.R
@@ -0,0 +1,75 @@
+simulate_guard <- function(input) {
+  # Transform the input into a matrix
+  rows <- unlist(strsplit(input, "\n"))
+  grid <- do.call(rbind, lapply(rows, function(row) unlist(strsplit(row, NULL))))
+
+  # Find the starting position and initial direction
+  start_pos <- which(grid %in% c("^", ">", "v", "<"), arr.ind = TRUE)
+  if (length(start_pos) == 0) {
+    stop("No starting position found in the input grid.")
+  }
+  if (is.vector(start_pos)) {
+    start_pos <- matrix(start_pos, nrow = 1)
+  }
+  directions <- list("^" = c(-1, 0), ">" = c(0, 1), "v" = c(1, 0), "<" = c(0, -1))
+  turns <- c("^" = ">", ">" = "v", "v" = "<", "<" = "^")
+
+  direction <- grid[start_pos[1, 1], start_pos[1, 2]]
+  visited <- list()  # List of visited positions
+
+  # Initialize the position
+  x <- start_pos[1, 1]
+  print(x)
+  y <- start_pos[1, 2]
+
+  # Function to check the bounds of the grid
+  in_bounds <- function(x, y, grid) {
+    x > 0 && x <= nrow(grid) && y > 0 && y <= ncol(grid)
+  }
+
+  # Mark the initial position as visited
+  visited[[paste(x, y, sep = ",")]] <- TRUE
+
+  # Simulate the movement
+  repeat {
+    # Calculate the next position in the current direction
+    dx <- directions[[direction]][1]
+    dy <- directions[[direction]][2]
+    nx <- x + dx
+    ny <- y + dy
+
+    # If out of bounds or obstacle ahead, turn right
+    if (!in_bounds(nx, ny, grid) || grid[nx, ny] == "#") {
+      direction <- turns[direction]
+    } else {
+      # Move forward
+      x <- nx
+      y <- ny
+
+      # Mark the new position as visited
+      visited[[paste(x, y, sep = ",")]] <- TRUE
+
+      # If out of bounds, stop the simulation
+      if (!in_bounds(x, y, grid)) break
+    }
+  }
+
+  # Return the number of distinct positions visited
+  length(visited)
+}
+
+# Input as a single string (provided)
+input <- "....#.....
+.........#
+..........
+..#.......
+.......#..
+..........
+.#..^.....
+........#.
+#.........
+......#..."
+
+# Call the function
+distinct_positions <- simulate_guard(input)
+cat("Distinct positions visited:", distinct_positions, "\n")
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