LeetCode-in-All

322. Coin Change

Medium

You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.

Return the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.

You may assume that you have an infinite number of each kind of coin.

Example 1:

Input: coins = [1,2,5], amount = 11

Output: 3

Explanation: 11 = 5 + 5 + 1

Example 2:

Input: coins = [2], amount = 3

Output: -1

Example 3:

Input: coins = [1], amount = 0

Output: 0

Constraints:

• 1 <= coins.length <= 12
• 1 <= coins[i] <= 231 - 1
• 0 <= amount <= 104

Solution

-spec coin_change(Coins :: [integer()], Amount :: integer()) -> integer().
coin_change(Coins, Amount) ->
    % Sort coins in ascending order
    SortedCoins = lists:sort(Coins),
    
    % Initialize DP map with base case
    InitDP = #{0 => 0},
    
    % Build DP table for amounts from 1 to target
    case Amount of
        0 -> 0;
        _ ->
            FinalDP = build_dp_table(SortedCoins, lists:seq(1, Amount), InitDP),
            % Get result or return -1 if not possible
            maps:get(Amount, FinalDP, -1)
    end.

% Build DP table for all amounts
-spec build_dp_table([integer()], [integer()], map()) -> map().
build_dp_table(_Coins, [], DP) -> DP;
build_dp_table(Coins, [Amount|Rest], DP) ->
    NewDP = process_coins_for_amount(Coins, Amount, DP),
    build_dp_table(Coins, Rest, NewDP).

% Process all coins for current amount
-spec process_coins_for_amount([integer()], integer(), map()) -> map().
process_coins_for_amount([], _Amount, DP) -> DP;
process_coins_for_amount([Coin|Rest], Amount, DP) ->
    case Coin > Amount of
        true ->
            % Stop if coin is larger than current amount
            DP;
        false ->
            % Try using current coin
            case maps:get(Amount - Coin, DP, undefined) of
                undefined ->
                    % Can't use this coin, try next
                    process_coins_for_amount(Rest, Amount, DP);
                PrevCount ->
                    % Can use this coin, update minimum coins needed
                    NewCount = PrevCount + 1,
                    NewDP = maps:update_with(Amount, 
                                           fun(OldVal) -> min(OldVal, NewCount) end,
                                           NewCount, 
                                           DP),
                    process_coins_for_amount(Rest, Amount, NewDP)
            end
    end.

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