Data commit

Task/Fraction-reduction/Lua/fraction-reduction.lua

@@ -0,0 +1,103 @@
+function indexOf(haystack, needle)
+    for idx,straw in pairs(haystack) do
+        if straw == needle then
+            return idx
+        end
+    end
+
+    return -1
+end
+
+function getDigits(n, le, digits)
+    while n > 0 do
+        local r = n % 10
+        if r == 0 or indexOf(digits, r) > 0 then
+            return false
+        end
+        le = le - 1
+        digits[le + 1] = r
+        n = math.floor(n / 10)
+    end
+    return true
+end
+
+function removeDigit(digits, le, idx)
+    local pows = { 1, 10, 100, 1000, 10000 }
+
+    local sum = 0
+    local pow = pows[le - 2 + 1]
+    for i = 1, le do
+        if i ~= idx then
+            sum = sum + digits[i] * pow
+            pow = math.floor(pow / 10)
+        end
+    end
+    return sum
+end
+
+function main()
+    local lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} }
+    local count = { 0, 0, 0, 0, 0 }
+    local omitted = {
+        { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
+        { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
+        { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
+        { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
+        { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
+    }
+
+    for i,_ in pairs(lims) do
+        local nDigits = {}
+        local dDigits = {}
+        for j = 1, i + 2 - 1 do
+            nDigits[j] = -1
+            dDigits[j] = -1
+        end
+
+        for n = lims[i][1], lims[i][2] do
+            for j,_ in pairs(nDigits) do
+                nDigits[j] = 0
+            end
+            local nOk = getDigits(n, i + 2 - 1, nDigits)
+            if nOk then
+                for d = n + 1, lims[i][2] + 1 do
+                    for j,_ in pairs(dDigits) do
+                        dDigits[j] = 0
+                    end
+                    local dOk = getDigits(d, i + 2 - 1, dDigits)
+                    if dOk then
+                        for nix,_ in pairs(nDigits) do
+                            local digit = nDigits[nix]
+                            local dix = indexOf(dDigits, digit)
+                            if dix >= 0 then
+                                local rn = removeDigit(nDigits, i + 2 - 1, nix)
+                                local rd = removeDigit(dDigits, i + 2 - 1, dix)
+                                if (n / d) == (rn / rd) then
+                                    count[i] = count[i] + 1
+                                    omitted[i][digit + 1] = omitted[i][digit + 1] + 1
+                                    if count[i] <= 12 then
+                                        print(string.format("%d/%d = %d/%d by omitting %d's", n, d, rn, rd, digit))
+                                    end
+                                end
+                            end
+                        end
+                    end
+                end
+            end
+        end
+
+        print()
+    end
+
+    for i = 2, 5 do
+        print("There are "..count[i - 2 + 1].." "..i.."-digit fractions of which:")
+        for j = 1, 9 do
+            if omitted[i - 2 + 1][j + 1] > 0 then
+                print(string.format("%6d have %d's omitted", omitted[i - 2 + 1][j + 1], j))
+            end
+        end
+        print()
+    end
+end
+
+main()