Combinations Of Coins - Medium
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Given a number of different denominations of coins (e.g., 1 cent, 5 cents, 10 cents, 25 cents), get all the possible ways to pay a target number of cents.
Arguments
- coins - an array of positive integers representing the different denominations of coins, there are no duplicate numbers and the numbers are sorted by descending order, eg. {25, 10, 5, 2, 1}
- target - a non-negative integer representing the target number of cents, eg. 99
Assumptions
- coins is not null and is not empty, all the numbers in coins are positive
- target >= 0
- You have infinite number of coins for each of the denominations, you can pick any number of the coins.
Return
- a list of ways of combinations of coins to sum up to be target.
- each way of combinations is represented by list of integer, the number at each index means the number of coins used for the denomination at corresponding index.
Examples
coins = {2, 1}, target = 4, the return should be
[
[0, 4], (4 cents can be conducted by 0 * 2 cents + 4 * 1 cents)
[1, 2], (4 cents can be conducted by 1 * 2 cents + 2 * 1 cents)
[2, 0] (4 cents can be conducted by 2 * 2 cents + 0 * 1 cents)
]
DFS
一共分 n = coins.length 层,每层的分叉数为 amountLeft / coins[i]
time: O(k ^ n), -- n = amount / min(element of coins), k - length of coins
space: O(k ^ n)
public class Solution { public List<List<Integer>> combinations(int target, int[] coins) { // Write your solution here List<List<Integer>> res = new ArrayList<>(); dfs(target, coins, 0, new ArrayList<>(), res); return res; } private void dfs(int targetLeft, int[] coins, int index, List<Integer> list, List<List<Integer>> res) { if(index == coins.length - 1) { if(targetLeft % coins[index] == 0) { list.add(targetLeft / coins[index]); res.add(new ArrayList<>(list)); list.remove(list.size() - 1); } return; } int max = targetLeft / coins[index]; for(int i = 0; i <= max; i++) { list.add(i); dfs(targetLeft - i * coins[index], coins, index + 1, list, res); list.remove(list.size() - 1); } } }
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