Leetcode: Split Array With Same Average

Split Array With Same Average

Similar Problems:

In a given integer array A, we must move every element of A to either list B or list C. (B and C initially start empty.)

Return true if and only if after such a move, it is possible that the average value of B is equal to the average value of C, and B and C are both non-empty.

Example :
Output: true
Explanation: We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have the average of 4.5.


  • The length of A will be in the range [1, 30].
  • A[i] will be in the range of [0, 10000].Given an integer array of size n, find all elements that appear more than n/3 times. The algorithm should run in linear time and in O(1) space.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

// Blog link: https://code.dennyzhang.com/split-array-with-same-average
// Basic Ideas: BFS pruning
// Observation:
//  avg(A) == avg(B) == avg(C)
//  We only need to check combination which has no more than len(A)/2 items.
//          Apparently max(len(B), len(C)) <= len(A)/2 
//  Avoid duplicated caculation by using a hashmap
//  If we sort A, once avg(B) >= avg(A), we can't add any more item which is bigger than avg(A)
// Complexity:
import "sort"
type Entity struct {
  count, sum int

func splitArraySameAverage(A []int) bool {
    if len(A)<=1 { return false }

    sum_a := 0
    for _, v:= range A { sum_a+=v }
    visited := map[Entity]bool{}

    // count, sum
    queue := [][]int{}
    for _, v:= range A {
        // add current item to queue
        if v*len(A) == sum_a { return true }
        entity := Entity{1, v}
        if visited[entity] == false {
            queue = append(queue, []int{1, v})
            visited[entity] = true
        // whether add current item to existings items in the queue
        list := [][]int{}
        for _, item:= range queue {
            // whether to explore
            if item[0]*2<len(A) {
                v1, v2:= (item[1]+v)*len(A), (item[0]+1)*sum_a
                if v1==v2{
                    return true
                } else {
                    if v1<v2 {
                        entity = Entity{item[0]+1, item[1]+v}
                        if visited[entity] == false {
                            list = append(list, []int{item[0]+1, item[1]+v})
                            visited[entity] = true
        // update queue
        for _, v:= range list { queue = append(queue, v) }
    return false

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