From 954db83ffb00b9e5a91738474f0b2532003d8183 Mon Sep 17 00:00:00 2001
From: Konstantinos Fezos <161313113+feezz8@users.noreply.github.com>
Date: Wed, 19 Feb 2025 13:57:12 +0200
Subject: [PATCH 1/9] Linemarket dana implementation

    This is an implemenation of my solution for the first exercise in
    the first coding exercises set for the Algorithms course during the
    2024-2025 winter Semester @ ECE/NTUA. The full description of the
    problem can be found in the web page of the course in Helios.
---
 dana/programs/linemarket.dana   | 125 ++++++++++++++++++++++++++++++++
 dana/programs/linemarket.input  |  11 +++
 dana/programs/linemarket.output |   5 ++
 3 files changed, 141 insertions(+)
 create mode 100644 dana/programs/linemarket.dana
 create mode 100644 dana/programs/linemarket.input
 create mode 100644 dana/programs/linemarket.output

diff --git a/dana/programs/linemarket.dana b/dana/programs/linemarket.dana
new file mode 100644
index 0000000..cd78324
--- /dev/null
+++ b/dana/programs/linemarket.dana
@@ -0,0 +1,125 @@
+(*
+    This is an implemenation of my solution for the first exercise in
+    the first coding exercises set for the Algorithms course during the
+    2024-2025 winter Semester @ ECE/NTUA. The full description of the 
+    problem can be found in the web page of the course in Helios.
+
+*)
+
+def main    
+    def bsort: n as int, x as int[]
+        def swap: x y as ref int
+            var t is int
+            t := x
+            x := y
+            y := t
+        
+        var changed is byte
+        var i is int
+        
+        loop:
+            changed := false
+            i := 0
+            loop:
+                if i < n-1:
+                    if x[i] > x[i+1]:
+                        swap x[i], x[i+1]
+                        changed := true
+                    i := i + 1
+                else: break
+            if not changed: break
+        
+    def possible_store is byte: arr as int[], mid spaces stores as int:
+        var last_position placed_stores i is int
+        last_position := -1000000000
+        placed_stores := 0
+        i := 0
+        loop:
+            if i >= (spaces/2): break
+            else:
+                var j is int
+                j := 2*i
+                var position is int
+                if (last_position + mid) > arr[j]: position := last_position + mid
+                else: position := arr[j]
+                loop:
+                    if position > arr[j + 1]: break
+                    else:
+                        placed_stores := placed_stores + 1
+                        last_position := position
+                        position := position + mid
+                        if placed_stores >= stores: return true
+            i := i + 1
+        return false
+
+    def largest_minimum_distance is int: arr as int[], spaces stores as int:
+        bsort(arr, spaces)
+        var result left right is int
+        result := 0
+        left := 0
+        right := arr[spaces - 1] - arr[0]
+        
+        #Simple Binary Search for finding the sweet spot
+        loop:
+            if left > right: break
+            else:
+                var distance is int
+                distance := (left + right) / 2
+                if possible_store(arr, distance, spaces, stores):
+                    result := distance
+                    left := distance + 1
+                else:
+                    right = distance + 1
+        return result
+
+    var stores size s f N tail is int
+    tail := 0
+    stores := readInteger()
+    N := readInteger()
+
+    var MAX_SIZE MAX_PLACES is int
+    
+    MAX_STORES := 1000000 #Change accordingly for larger sizes
+    MAX_PLACES := 100000  #Change accordingly for larger sizes
+
+    (*
+        The program handles out of bound inputs by 
+        asking the user again for a correct one.
+        Maybe the two "if" statements can be combined into one.
+    *)
+
+    if stores > MAX_STORES or stores < 1:
+        writeString "Wrong starting input, let's try again!"
+        stores := readInteger()
+
+    if N > MAX_PLACES or N < 1:
+        writeString "Wrong starting input, let's try again!"
+        N := readInteger()
+
+    var arr is int[2*N]
+
+    var i is int
+    i := 0
+
+    loop:
+        if i >= N: break
+        else:
+            s := readInteger()  #We assume correct values for the limits of the spaces
+            f := readInteger()
+
+            arr[i*2] := s
+            arr[i*2 + 1] := f
+            tail := tail + 2
+            i := i + 1
+    
+    writeInteger: largest_minimum_distance(arr, tail, stores)
+    writeString: "\n"
+
+        
+    
+
+ 
+
+
+
+                    
\ No newline at end of file
diff --git a/dana/programs/linemarket.input b/dana/programs/linemarket.input
new file mode 100644
index 0000000..f077daa
--- /dev/null
+++ b/dana/programs/linemarket.input
@@ -0,0 +1,11 @@
+#Input 1
+5 3
+5 9
+0 3
+12 12
+
+#Input 2
+6 3
+10 12
+0 4
+5 8
\ No newline at end of file
diff --git a/dana/programs/linemarket.output b/dana/programs/linemarket.output
new file mode 100644
index 0000000..4f4f467
--- /dev/null
+++ b/dana/programs/linemarket.output
@@ -0,0 +1,5 @@
+#Output 1
+3
+
+#Output 2
+2
\ No newline at end of file

From af8cf609c901a9a9f56653117bb083f7a954c39d Mon Sep 17 00:00:00 2001
From: Kostis Sagonas <kostis@cs.ntua.gr>
Date: Wed, 19 Feb 2025 23:03:03 +0100
Subject: [PATCH 2/9] Fix spellcheck error & cleanup

---
 dana/programs/linemarket.dana | 12 +-----------
 1 file changed, 1 insertion(+), 11 deletions(-)

diff --git a/dana/programs/linemarket.dana b/dana/programs/linemarket.dana
index cd78324..c876b4b 100644
--- a/dana/programs/linemarket.dana
+++ b/dana/programs/linemarket.dana
@@ -1,9 +1,8 @@
 (*
-    This is an implemenation of my solution for the first exercise in
+    This is an implementation of my solution for the first exercise in
     the first coding exercises set for the Algorithms course during the
     2024-2025 winter Semester @ ECE/NTUA. The full description of the 
     problem can be found in the web page of the course in Helios.
-
 *)
 
 def main    
@@ -114,12 +113,3 @@ def main
     
     writeInteger: largest_minimum_distance(arr, tail, stores)
     writeString: "\n"
-
-        
-    
-
- 
-
-
-
-                    
\ No newline at end of file

From de38fd3937c621715347a16cc967904b449749a1 Mon Sep 17 00:00:00 2001
From: Konstantinos Fezos <161313113+feezz8@users.noreply.github.com>
Date: Wed, 26 Feb 2025 13:23:13 +0200
Subject: [PATCH 3/9] Update linemarket.dana

Added problem description as a comment
---
 dana/programs/linemarket.dana | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/dana/programs/linemarket.dana b/dana/programs/linemarket.dana
index c876b4b..55ab4a0 100644
--- a/dana/programs/linemarket.dana
+++ b/dana/programs/linemarket.dana
@@ -3,6 +3,27 @@
     the first coding exercises set for the Algorithms course during the
     2024-2025 winter Semester @ ECE/NTUA. The full description of the 
     problem can be found in the web page of the course in Helios.
+
+    Our goal is to place N stores in M non-overlapping integer intervals[s_i, x_i]. 
+    A store can be placed in any integer number that belongs to an interval. We want our 
+    program to calculate the smallest possible distance between two consecutive stores such as 
+    that distance is maximized.
+    
+    Input: The program reads from the standard input two positive integers, N amount of stores and M amount of spaces(intervals) to place them. 
+           After that for the next M lines it reads from the standard input two non-negative integers defining the begining and the end of each space(interval).
+           We assume the spaces are given in a random order and their total length is not shorter than N.
+
+    Output: Our program prints in the standard output a positive integer, 
+            the minimum required distance between two consecutive stores in a 
+            placement of all stores such as that minimum distance is maximized.
+
+    Example Input:  6 3
+                    10 12
+                    0 4
+                    5 8
+
+    Example Output: 2
+    
 *)
 
 def main    

From 03867f553aa6baf998f605c2cce1c212aa8ad3ef Mon Sep 17 00:00:00 2001
From: Konstantinos Fezos <161313113+feezz8@users.noreply.github.com>
Date: Wed, 26 Feb 2025 13:26:38 +0200
Subject: [PATCH 4/9] Update linemarket.dana

fixed typo in problem desc
---
 dana/programs/linemarket.dana | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/dana/programs/linemarket.dana b/dana/programs/linemarket.dana
index 55ab4a0..15a2586 100644
--- a/dana/programs/linemarket.dana
+++ b/dana/programs/linemarket.dana
@@ -10,7 +10,7 @@
     that distance is maximized.
     
     Input: The program reads from the standard input two positive integers, N amount of stores and M amount of spaces(intervals) to place them. 
-           After that for the next M lines it reads from the standard input two non-negative integers defining the begining and the end of each space(interval).
+           After that for the next M lines it reads from the standard input two non-negative integers defining the beginning and the end of each space(interval).
            We assume the spaces are given in a random order and their total length is not shorter than N.
 
     Output: Our program prints in the standard output a positive integer, 

From 60db36ecd9b6675824e75caae10fbef38d8a20eb Mon Sep 17 00:00:00 2001
From: Konstantinos Fezos <161313113+feezz8@users.noreply.github.com>
Date: Wed, 26 Feb 2025 13:33:39 +0200
Subject: [PATCH 5/9] Update and rename linemarket.output to linemarket.result

---
 dana/programs/linemarket.output | 5 -----
 dana/programs/linemarket.result | 2 ++
 2 files changed, 2 insertions(+), 5 deletions(-)
 delete mode 100644 dana/programs/linemarket.output
 create mode 100644 dana/programs/linemarket.result

diff --git a/dana/programs/linemarket.output b/dana/programs/linemarket.output
deleted file mode 100644
index 4f4f467..0000000
--- a/dana/programs/linemarket.output
+++ /dev/null
@@ -1,5 +0,0 @@
-#Output 1
-3
-
-#Output 2
-2
\ No newline at end of file
diff --git a/dana/programs/linemarket.result b/dana/programs/linemarket.result
new file mode 100644
index 0000000..8148ef7
--- /dev/null
+++ b/dana/programs/linemarket.result
@@ -0,0 +1,2 @@
+3
+

From c19bf88972f6fad1d2fe7ab469beb896579dafb1 Mon Sep 17 00:00:00 2001
From: Konstantinos Fezos <161313113+feezz8@users.noreply.github.com>
Date: Wed, 26 Feb 2025 13:34:03 +0200
Subject: [PATCH 6/9] Update linemarket.input

---
 dana/programs/linemarket.input | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/dana/programs/linemarket.input b/dana/programs/linemarket.input
index f077daa..642ab94 100644
--- a/dana/programs/linemarket.input
+++ b/dana/programs/linemarket.input
@@ -1,11 +1,5 @@
-#Input 1
 5 3
 5 9
 0 3
 12 12
 
-#Input 2
-6 3
-10 12
-0 4
-5 8
\ No newline at end of file

From e8ee4058d8b8168086d0510b23057e2ceeae8f24 Mon Sep 17 00:00:00 2001
From: Konstantinos Fezos <161313113+feezz8@users.noreply.github.com>
Date: Wed, 26 Feb 2025 13:35:28 +0200
Subject: [PATCH 7/9] Update linemarket.result

---
 dana/programs/linemarket.result | 1 -
 1 file changed, 1 deletion(-)

diff --git a/dana/programs/linemarket.result b/dana/programs/linemarket.result
index 8148ef7..00750ed 100644
--- a/dana/programs/linemarket.result
+++ b/dana/programs/linemarket.result
@@ -1,2 +1 @@
 3
-

From 3d8ab8cf36264d820f98b9f86c176403c22313d9 Mon Sep 17 00:00:00 2001
From: Konstantinos Fezos <161313113+feezz8@users.noreply.github.com>
Date: Wed, 26 Feb 2025 13:35:35 +0200
Subject: [PATCH 8/9] Update linemarket.input

---
 dana/programs/linemarket.input | 1 -
 1 file changed, 1 deletion(-)

diff --git a/dana/programs/linemarket.input b/dana/programs/linemarket.input
index 642ab94..d866ca8 100644
--- a/dana/programs/linemarket.input
+++ b/dana/programs/linemarket.input
@@ -2,4 +2,3 @@
 5 9
 0 3
 12 12
-

From 4dd621b15159f26ee46a44e1a68e70ef22833da0 Mon Sep 17 00:00:00 2001
From: Kostis Sagonas <kostis@cs.ntua.gr>
Date: Wed, 26 Feb 2025 12:35:45 +0100
Subject: [PATCH 9/9] Cosmetic change

---
 dana/programs/linemarket.dana | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/dana/programs/linemarket.dana b/dana/programs/linemarket.dana
index 15a2586..b659880 100644
--- a/dana/programs/linemarket.dana
+++ b/dana/programs/linemarket.dana
@@ -5,9 +5,9 @@
     problem can be found in the web page of the course in Helios.
 
     Our goal is to place N stores in M non-overlapping integer intervals[s_i, x_i]. 
-    A store can be placed in any integer number that belongs to an interval. We want our 
-    program to calculate the smallest possible distance between two consecutive stores such as 
-    that distance is maximized.
+    A store can be placed in any integer number that belongs to an interval.
+    We want our program to calculate the smallest possible distance between
+    two consecutive stores such as that distance is maximized.
     
     Input: The program reads from the standard input two positive integers, N amount of stores and M amount of spaces(intervals) to place them. 
            After that for the next M lines it reads from the standard input two non-negative integers defining the beginning and the end of each space(interval).