Add Josephus Problem in Tcl (#5063)

Author: pascalecu

archive/t/tcl/josephus-problem.tcl

@@ -0,0 +1,40 @@
+proc usage {} {
+    puts stderr {Usage: please input the total number of people and number of people to skip.}
+    exit 1
+}
+
+proc parseInt {s} {
+    set s [string trim $s]
+    if {[string is integer -strict $s]} { return $s }
+    usage
+}
+
+proc josephus {total skip} {
+    if {$skip < 1 || $total < 1} { usage }
+
+    # If skip = 1, survivor is the last person
+    if {$skip == 1} { return $total }
+
+    # Optimized case for skip = 2
+    if {$skip == 2} {
+        set power 1
+        while {($power << 1) <= $total} {
+            set power [expr {$power << 1}]
+        }
+        return [expr {2 * ($total - $power) + 1}]
+    }
+
+    set result 0
+    for {set i 2} {$i <= $total} {incr i} {
+        set result [expr {($result + $skip) % $i}]
+    }
+
+    return [expr {$result + 1}]
+}
+
+if {$argc != 2} { usage }
+
+set total [parseInt [lindex $argv 0]]
+set skip  [parseInt [lindex $argv 1]]
+
+puts [josephus $total $skip]