Merge pull request #7852 from Firedrake/rogerbw-challenge-211

RogerBW solutions for challenge no. 211

2 files changed, 124 insertions, 0 deletions

diff --git a/challenge-211/roger-bell-west/lua/ch-1.lua b/challenge-211/roger-bell-west/lua/ch-1.lua
new file mode 100755
index 0000000000..50dfb58b1c
--- /dev/null
+++ b/challenge-211/roger-bell-west/lua/ch-1.lua
@@ -0,0 +1,46 @@
+#! /usr/bin/lua
+
+function toeplitzmatrix(a)
+   local ym = #a - 1
+   local xm = #(a[1]) - 1
+   local toeplitz = true
+   for xb = (1 - xm), (ym - 1) do
+      local init = true
+      local tv = 0
+      for xi = xb, xb + xm do
+         if xi >= 0 and xi <= xm then
+            local x = xi + 1
+            local yi = xi - xb
+            if yi >= 0 and yi <= ym then
+               local y = yi + 1
+               if init then
+                  init = false
+                  tv = a[y][x]
+               elseif a[y][x] ~= tv then
+                  toeplitz = false
+                  break
+               end
+            end
+         end
+      end
+      if not toeplitz then
+         break
+      end
+   end
+   return toeplitz
+end
+
+if toeplitzmatrix({{4, 3, 2, 1}, {5, 4, 3, 2}, {6, 5, 4, 3}}) then
+  io.write("Pass")
+else
+  io.write("FAIL")
+end
+io.write(" ")
+
+if not toeplitzmatrix({{1, 2, 3}, {3, 2, 1}}) then
+  io.write("Pass")
+else
+  io.write("FAIL")
+end
+print("")
+
diff --git a/challenge-211/roger-bell-west/lua/ch-2.lua b/challenge-211/roger-bell-west/lua/ch-2.lua
new file mode 100755
index 0000000000..c524e76c6d
--- /dev/null
+++ b/challenge-211/roger-bell-west/lua/ch-2.lua
@@ -0,0 +1,78 @@
+#! /usr/bin/lua
+
+function combinations(arr, k)
+   local c = {}
+   for i = 1, k do
+      table.insert(c, i)
+   end
+   table.insert(c, #arr + 1)
+   table.insert(c, 0)
+   local out = {}
+   while true do
+      local inner = {}
+      for i = k, 1, -1 do
+         table.insert(inner, arr[c[i]])
+      end
+      table.insert(out, inner)
+      local j = 1
+      while c[j] + 1 == c[j + 1] do
+         c[j] = j
+         j = j + 1
+      end
+      if j > k then
+         break
+      end
+      c[j] = c[j] + 1
+   end
+   return ipairs(out)
+end
+
+function sum(t)
+   local ss = 0
+   for i, k in ipairs(t) do
+      ss = ss + k
+   end
+   return ss
+end
+
+function splitsameaverage(a)
+   local ss = sum(a)
+   local ml = #a
+   local mx = ml // 2
+   local ssa = false
+   for n = 1, mx do
+      for i, c in combinations(a, n) do
+         local ca = sum(c)
+         if (ca / n) == (ss - ca) / (ml - n) then
+            ssa = true
+            break
+         end
+      end
+      if ssa then
+         break
+      end
+   end
+   return ssa
+end
+
+if splitsameaverage({1, 2, 3, 4, 5, 6, 7, 8}) then
+  io.write("Pass")
+else
+  io.write("FAIL")
+end
+io.write(" ")
+
+if not splitsameaverage({1, 3}) then
+  io.write("Pass")
+else
+  io.write("FAIL")
+end
+io.write(" ")
+
+if splitsameaverage({1, 2, 3}) then
+  io.write("Pass")
+else
+  io.write("FAIL")
+end
+print("")
+