377. Combination Sum IV
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package LeetCode_377 /** * 377. Combination Sum IV * https://leetcode.com/problems/combination-sum-iv/description/ * * Given an integer array with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target. Example: nums = [1, 2, 3] target = 4 The possible combination ways are: (1, 1, 1, 1) (1, 1, 2) (1, 2, 1) (1, 3) (2, 1, 1) (2, 2) (3, 1) Note that different sequences are counted as different combinations. Therefore the output is 7. Follow up: What if negative numbers are allowed in the given array? How does it change the problem? What limitation we need to add to the question to allow negative numbers? * */ class Solution { private var result = 0 private var array: Array<Int>? = null fun combinationSum4(nums: IntArray, target: Int): Int { //1. recursion //help(nums, target) //2. recursion + memorization /*array = Array(target + 1, { -1 }) array?.set(0, 1) return help2(nums, target)*/ //3. dp return dp(nums, target) } /* * method 1: recursion * Time complexity: O(2^target), Space complexity: O(1); * TLE, 11/17 test cases passed * */ private fun help(nums: IntArray, target: Int) { if (target == 0) { result += 1 } if (target < 0) { return } for (num in nums) { help(nums, target - num) } } /* * method 2: recursion + memorization * Time complexity: O(sum({target/num_i})), Space complexity: O(target) * */ private fun help2(nums: IntArray, target: Int): Int { if (target < 0) { return 0 } if (array!![target] != -1) { return array!![target] } var res = 0 for (num in nums) { res += help2(nums, target - num) } array!![target] = res return res } /* * method 3:dp * Time complexity: O(target * n), Space complexity: O(target) * */ private fun dp(nums: IntArray, target: Int): Int { //dp[i] represent number of combinations sum up to i val dp = Array(target + 1, { 0 }) dp[0] = 1//there are is 1 combination sum up to 0 for (i in 1..target) { for (num in nums) { if (i - num >= 0) { dp[i] += dp[i - num] } } } return dp[target] } }
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