Given an array of integers nums and a positive integer k, find whether it‘s possible to divide this array into k non-empty subsets whose sums are all equal.
Example 1:
Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4 Output: True Explanation: It‘s possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.
Note:
1 <= k <= len(nums) <= 16.0 < nums[i] < 10000.
给定一个整数数组
nums 和一个正整数 k，找出是否有可能把这个数组分成 k 个非空子集，其总和都相等。
示例 1：
输入： nums = [4, 3, 2, 3, 5, 2, 1], k = 4 输出： True 说明： 有可能将其分成 4 个子集（5），（1,4），（2,3），（2,3）等于总和。
注意:
1 <= k <= len(nums) <= 160 < nums[i] < 10000
16ms
1 class Solution {
2 func canPartitionKSubsets(_ nums: [Int], _ k: Int) -> Bool {
3
4 // do a quick check to make sure its even possible
5 let sum = nums.reduce(0, +)
6 guard sum % k == 0 else {
7 return false
8 }
9
10 // sum we want to achieve for each partition
11 let partitionSum = sum / k
12
13 var isVisited = [Bool](repeating: false, count: nums.count)
14
15 return canPartitionKSubsets(
16 nums: nums,
17 numsIndex: 0,
18 k: k,
19 currentSum: 0,
20 expectedSum: partitionSum,
21 isVisited: &isVisited)
22 }
23
24 func canPartitionKSubsets(
25 nums: [Int],
26 numsIndex: Int,
27 k: Int,
28 currentSum: Int,
29 expectedSum: Int,
30 isVisited: inout [Bool]
31 ) -> Bool {
32 guard currentSum <= expectedSum else {
33 // exceed the expected sum so we can‘t form a partition
34 return false
35 }
36
37 if k == 0 {
38 return true
39 }
40
41 if currentSum == expectedSum {
42 return canPartitionKSubsets(
43 nums: nums,
44 numsIndex: 0, // start a brand new search from 0
45 k: k-1, // we found a partition!
46 currentSum: 0, // reset sum
47 expectedSum: expectedSum,
48 isVisited: &isVisited)
49 } else {
50
51 for i in numsIndex..<nums.count {
52 guard !isVisited[i] else {
53 // already used this number for a partition
54 continue
55 }
56
57 isVisited[i] = true // we will take this number for the partition
58 let canPartition = canPartitionKSubsets(
59 nums: nums,
60 numsIndex: i+1,
61 k: k,
62 currentSum: currentSum + nums[i],
63 expectedSum: expectedSum,
64 isVisited: &isVisited)
65
66 if canPartition {
67 return true
68 }
69
70 isVisited[i] = false
71 }
72 }
73
74 return false
75 }
76 }
32ms
1 class Solution {
2 func canPartitionKSubsets(_ nums: [Int], _ k: Int) -> Bool {
3 guard !nums.isEmpty else {
4 return false
5 }
6
7 let totalSum = nums.reduce(0, +)
8
9 guard totalSum % k == 0 else {
10 return false
11 }
12
13 let sum = totalSum / k
14
15 var visited = [Bool](repeating: false, count: nums.count)
16
17 return canPartitionKSubsets(numbers: nums, k: k, startIndex:0, currentSum: 0, sum: sum, visited: &visited)
18 }
19
20 func canPartitionKSubsets(numbers: [Int], k: Int, startIndex: Int, currentSum: Int, sum: Int, visited: inout [Bool]) -> Bool {
21 guard currentSum <= sum else {
22 return false
23 }
24
25 if currentSum == sum {
26
27 if k == 1 {
28 return true
29 } else {
30 // we formed a partition, go try to form another one
31 return canPartitionKSubsets(numbers: numbers, k: k-1, startIndex: 0, currentSum: 0, sum: sum, visited: &visited)
32 }
33 }
34 // currentSum < sum
35 else {
36
37 for i in startIndex..<numbers.count {
38 let number = numbers[i]
39
40 if visited[i] {
41 continue
42 }
43
44 visited[i] = true
45
46 if canPartitionKSubsets(numbers: numbers, k: k, startIndex: i+1, currentSum: currentSum + number, sum: sum, visited: &visited) {
47 return true
48 }
49
50 visited[i] = false
51 }
52 }
53
54 return false
55 }
56 }
60ms
1 class Solution {
2 func canPartitionKSubsets(_ nums: [Int], _ k: Int) -> Bool {
3 let sum = nums.reduce(0, +)
4 guard sum % k == 0 else { return false }
5 let bucketTarget = sum / k
6 let maxSubsets = (1<<nums.count)
7 var cache = [Bool?](repeating: nil, count: maxSubsets)
8 return canPartitionSubsets(nums, 0, bucketTarget, bucketTarget, &cache)
9 }
10
11 private func canPartitionSubsets(
12 _ nums: [Int],
13 _ bitset: Int,
14 _ remainingInBucket: Int,
15 _ bucketTarget: Int,
16 _ cache: inout [Bool?]) -> Bool {
17 if let cached = cache[bitset] {
18 return cached
19 }
20 let allElementBitSet = (1<<nums.count) - 1
21 if bitset == allElementBitSet && remainingInBucket == bucketTarget {
22 // All elements are set and all buckets are filled.
23 return true
24 }
25 for i in 0..<nums.count {
26 guard bitset & (1<<i) == 0 else { continue }
27 guard nums[i] <= remainingInBucket else { continue }
28 var updatedRemainingInBucket = remainingInBucket - nums[i]
29 if updatedRemainingInBucket == 0 {
30 updatedRemainingInBucket = bucketTarget // Create a new bucket
31 }
32 if canPartitionSubsets(
33 nums,
34 bitset | (1<<i),
35 updatedRemainingInBucket,
36 bucketTarget,
37 &cache) {
38 cache[bitset] = true
39 return true
40 }
41 }
42 cache[bitset] = false
43 return false
44 }
45 }
88ms
1 class Solution {
2 func canPartitionKSubsets(_ nums: [Int], _ k: Int) -> Bool {
3 if nums.count == 0 && k == 0 {
4 return true
5 }
6 guard nums.count > 0, k > 0 else {
7 return false
8 }
9 var target = nums.reduce(0, +)
10 if target % k != 0 {
11 return false
12 }
13 target = target/k
14
15
16 func canPart(index:Int, remain:Int, curSum: Int, visited:[Int: Bool]) -> Bool {
17 if remain == 0 {
18 return true
19 }
20
21 if index == nums.count {
22 return false
23 }
24
25 if curSum == target {
26 return canPart(index:0, remain:remain - 1, curSum:0, visited:visited)
27 } else if curSum > target {
28 return false
29 }
30
31 for i in index..<nums.count {
32 var visited = visited
33 if visited[i] == true {
34 continue
35 } else {
36 visited[i] = true
37 if canPart(index:i, remain:remain, curSum: curSum + nums[i], visited: visited) {
38 return true
39 }
40 visited[i] = false
41 }
42 }
43
44 return false
45 }
46
47 return canPart(index:0, remain:k, curSum: 0, visited:[Int: Bool]())
48 }
49 }
92ms
1 class Solution {
2 //We could use dfs. start from the first index, find the combination where num1 + num2 .. + num3 == target. Then start from index 0 with memory of which numbers has been used.
3 func canPartitionKSubsets(_ nums: [Int], _ k: Int) -> Bool {
4 if nums.count == 0 && k == 0 {
5 return true
6 }
7 guard nums.count > 0, k > 0 else {
8 return false
9 }
10 var target = nums.reduce(0, +)
11 //Remember to check if the target can be fully divided by k
12 if target % k != 0 {
13 return false
14 }
15 target = target/k
16
17 func canPart(index:Int, remain:Int, curSum: Int, visited:[Int: Bool]) -> Bool {
18 if remain == 0 {
19 return true
20 }
21
22 if index == nums.count {
23 return false
24 }
25
26 if curSum == target {
27 return canPart(index: 0, remain: remain - 1, curSum: 0, visited: visited)
28 } else if curSum > target {
29 return false
30 }
31
32 for i in index..<nums.count {
33 var visited = visited
34 if visited[i] == true {
35 continue
36 }
37 visited[i] = true
38 if canPart(index: i, remain: remain, curSum: curSum + nums[i], visited: visited) {
39 return true
40 }
41 }
42 return false
43 }
44 return canPart(index:0, remain:k, curSum: 0, visited:[Int: Bool]())
45 }
46 }
96ms
1 class Solution {
2 func canPartitionKSubsets(_ nums: [Int], _ k: Int) -> Bool {
3 var sum = 0
4 for num in nums {
5 sum += num
6 }
7 if k <= 0 || sum % k != 0 {
8 return false
9 }
10 var visited = Array(repeating: false, count: nums.count)
11 return canPartition(nums, &visited, 0, k, 0, 0, sum / k)
12 }
13
14 private func canPartition(_ nums: [Int], _ visited: inout [Bool], _ start_index: Int, _ k: Int, _ cur_sum: Int, _ cur_num: Int, _ target: Int) -> Bool {
15 if k == 1 {
16 return true
17 }
18 if cur_sum == target && cur_num > 0 {
19 return canPartition(nums, &visited, 0, k - 1, 0, 0, target)
20 }
21 for i in start_index..<nums.count {
22 if !visited[i] {
23 visited[i] = true
24 let match = canPartition(nums, &visited, i + 1, k, cur_sum + nums[i], cur_num + 1, target)
25 if match {
26 return true
27 }
28 visited[i] = false
29 }
30 }
31 return false
32 }
33 }
Runtime: 244 ms
Memory Usage: 19.1 MB
1 class Solution {
2 func canPartitionKSubsets(_ nums: [Int], _ k: Int) -> Bool {
3 var nums = nums
4 nums.sort()
5 var sum:Int = nums.reduce(0,+)
6 if sum % k != 0 {return false}
7 var v:[Int] = [Int](repeating:0,count:k)
8 return helper(&nums, sum / k, &v, nums.count - 1)
9 }
10
11 func helper(_ nums:inout [Int],_ target:Int,_ v:inout [Int],_ idx:Int) -> Bool
12 {
13 if idx == -1
14 {
15 for t in v
16 {
17 if t != target {return false}
18 }
19 return true
20 }
21 var num:Int = nums[idx]
22 for i in 0..<v.count
23 {
24 if v[i] + num > target {continue}
25 v[i] += num
26 if helper(&nums, target, &v, idx - 1)
27 {
28 return true
29 }
30 v[i] -= num
31 }
32 return false
33 }
34 }
原文地址：https://www.cnblogs.com/strengthen/p/10502747.html
时间： 2024-07-30 16:42:18