LeetCode-in-All

494. Target Sum

Medium

You are given an integer array nums and an integer target.

You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.

• For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression "+2-1".

Return the number of different expressions that you can build, which evaluates to target.

Example 1:

Input: nums = [1,1,1,1,1], target = 3

Output: 5

Explanation: There are 5 ways to assign symbols to make the sum of nums be target 3.

-1 + 1 + 1 + 1 + 1 = 3

+1 - 1 + 1 + 1 + 1 = 3

+1 + 1 - 1 + 1 + 1 = 3

+1 + 1 + 1 - 1 + 1 = 3

+1 + 1 + 1 + 1 - 1 = 3

Example 2:

Input: nums = [1], target = 1

Output: 1

Constraints:

• 1 <= nums.length <= 20
• 0 <= nums[i] <= 1000
• 0 <= sum(nums[i]) <= 1000
• -1000 <= target <= 1000

Solution

-spec find_target_sum_ways(Nums :: [integer()], Target :: integer()) -> integer().
find_target_sum_ways(Nums, Target) ->
    TotalSum = lists:sum(Nums),
    Sum = TotalSum - Target,
    case Sum < 0 orelse Sum rem 2 =:= 1 of
        true -> 0;
        false -> solve(Nums, Sum div 2)
    end.

-spec solve(Nums :: [integer()], Target :: integer()) -> integer().
solve([First|_] = Nums, Target) ->
    Prev = lists:duplicate(Target + 1, 0),
    InitPrev = case First of
        0 -> lists:sublist([2|lists:duplicate(Target, 0)], Target + 1);
        _ when First =< Target -> 
            lists:sublist([1] ++ lists:duplicate(First - 1, 0) ++ [1] ++ 
                         lists:duplicate(Target - First, 0), Target + 1);
        _ -> [1|lists:duplicate(Target, 0)]
    end,
    process_nums(tl(Nums), Target, InitPrev).

process_nums([], _Target, Prev) ->
    lists:last(Prev);
process_nums([Num|Rest], Target, Prev) ->
    Curr = lists:foldl(fun(J, Acc) ->
        Taken = case J >= Num of
            true -> lists:nth(J - Num + 1, Prev);
            false -> 0
        end,
        NonTaken = lists:nth(J + 1, Prev),
        Acc ++ [Taken + NonTaken]
    end, [], lists:seq(0, Target)),
    process_nums(Rest, Target, Curr).

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