Sum to 100: Difference between revisions
→{{header|Mathematica}}
Line 3,919:
3456786 = - 1 - 2 + 3456789
</pre>
=={{header|Lua}}==
{{trans|C}}
<lang lua>local expressionsLength = 0
function compareExpressionBySum(a, b)
return a.sum - b.sum
end
local countSumsLength = 0
function compareCountSumsByCount(a, b)
return a.counts - b.counts
end
function evaluate(code)
local value = 0
local number = 0
local power = 1
for k=9,1,-1 do
number = power*k + number
local mod = code % 3
if mod == 0 then
-- ADD
value = value + number
number = 0
power = 1
elseif mod == 1 then
-- SUB
value = value - number
number = 0
power = 1
elseif mod == 2 then
-- JOIN
power = 10 * power
else
print("This should not happen.")
end
code = math.floor(code / 3)
end
return value
end
function printCode(code)
local a = 19683
local b = 6561
local s = ""
for k=1,9 do
local temp = math.floor((code % a) / b)
if temp == 0 then
-- ADD
if k>1 then
s = s .. '+'
end
elseif temp == 1 then
-- SUB
s = s .. '-'
end
a = b
b = math.floor(b/3)
s = s .. tostring(k)
end
print("\t"..evaluate(code).." = "..s)
end
-- Main
local nexpr = 13122
print("Show all solutions that sum to 100")
for i=0,nexpr-1 do
if evaluate(i) == 100 then
printCode(i)
end
end
print()
print("Show the sum that has the maximum number of solutions")
local nbest = -1
for i=0,nexpr-1 do
local test = evaluate(i)
if test>0 then
local ntest = 0
for j=0,nexpr-1 do
if evaluate(j) == test then
ntest = ntest + 1
end
if ntest > nbest then
best = test
nbest = ntest
end
end
end
end
print(best.." has "..nbest.." solutions\n")
print("Show the lowest positive number that can't be expressed")
local code = -1
for i=0,123456789 do
for j=0,nexpr-1 do
if evaluate(j) == i then
code = j
break
end
end
if evaluate(code) ~= i then
code = i
break
end
end
print(code.."\n")
print("Show the ten highest numbers that can be expressed")
local limit = 123456789 + 1
for i=1,10 do
local best=0
for j=0,nexpr-1 do
local test = evaluate(j)
if (test<limit) and (test>best) then
best = test
end
end
for j=0,nexpr-1 do
if evaluate(j) == best then
printCode(j)
end
end
limit = best
end</lang>
{{out}}
<pre>Show all solutions that sum to 100
100 = 1+2+3-4+5+6+78+9
100 = 1+2+34-5+67-8+9
100 = 1+23-4+5+6+78-9
100 = 1+23-4+56+7+8+9
100 = 12+3+4+5-6-7+89
100 = 12+3-4+5+67+8+9
100 = 12-3-4+5-6+7+89
100 = 123+4-5+67-89
100 = 123+45-67+8-9
100 = 123-4-5-6-7+8-9
100 = 123-45-67+89
100 = -1+2-3+4+5+6+78+9
Show the sum that has the maximum number of solutions
9 has 46 solutions
Show the lowest positive number that can't be expressed
211
Show the ten highest numbers that can be expressed
123456789 = 123456789
23456790 = 1+23456789
23456788 = -1+23456789
12345687 = 12345678+9
12345669 = 12345678-9
3456801 = 12+3456789
3456792 = 1+2+3456789
3456790 = -1+2+3456789
3456788 = 1-2+3456789
3456786 = -1-2+3456789</pre>
=={{header|Mathematica}}==
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