Question

1982. Find Array Given Subset Sums

中文文档

Description

You are given an integer n representing the length of an unknown array that you are trying to recover. You are also given an array sums containing the values of all 2n subset sums of the unknown array (in no particular order).

Return _the array _ans_ of length _n_ representing the unknown array. If multiple answers exist, return any of them_.

An array sub is a subset of an array arr if sub can be obtained from arr by deleting some (possibly zero or all) elements of arr. The sum of the elements in sub is one possible subset sum of arr. The sum of an empty array is considered to be 0.

Note: Test cases are generated such that there will always be at least one correct answer.

 

Example 1:

Input: n = 3, sums = [-3,-2,-1,0,0,1,2,3]
Output: [1,2,-3]
Explanation: [1,2,-3] is able to achieve the given subset sums:
- []: sum is 0
- [1]: sum is 1
- [2]: sum is 2
- [1,2]: sum is 3
- [-3]: sum is -3
- [1,-3]: sum is -2
- [2,-3]: sum is -1
- [1,2,-3]: sum is 0
Note that any permutation of [1,2,-3] and also any permutation of [-1,-2,3] will also be accepted.

Example 2:

Input: n = 2, sums = [0,0,0,0]
Output: [0,0]
Explanation: The only correct answer is [0,0].

Example 3:

Input: n = 4, sums = [0,0,5,5,4,-1,4,9,9,-1,4,3,4,8,3,8]
Output: [0,-1,4,5]
Explanation: [0,-1,4,5] is able to achieve the given subset sums.

 

Constraints:

• 1 <= n <= 15
• sums.length == 2n
• -104 <= sums[i] <= 104

Solutions

Solution 1

from sortedcontainers import SortedList


class Solution:
  def recoverArray(self, n: int, sums: List[int]) -> List[int]:
    m = -min(sums)
    sl = SortedList(x + m for x in sums)
    sl.remove(0)
    ans = [sl[0]]
    for i in range(1, n):
      for j in range(1 << i):
        if j >> (i - 1) & 1:
          s = sum(ans[k] for k in range(i) if j >> k & 1)
          sl.remove(s)
      ans.append(sl[0])
    for i in range(1 << n):
      s = sum(ans[j] for j in range(n) if i >> j & 1)
      if s == m:
        for j in range(n):
          if i >> j & 1:
            ans[j] *= -1
        break
    return ans

class Solution {
  public int[] recoverArray(int n, int[] sums) {
    int m = 1 << 30;
    for (int x : sums) {
      m = Math.min(m, x);
    }
    m = -m;
    TreeMap<Integer, Integer> tm = new TreeMap<>();
    for (int x : sums) {
      tm.merge(x + m, 1, Integer::sum);
    }
    int[] ans = new int[n];
    if (tm.merge(0, -1, Integer::sum) == 0) {
      tm.remove(0);
    }
    ans[0] = tm.firstKey();
    for (int i = 1; i < n; ++i) {
      for (int j = 0; j < 1 << i; ++j) {
        if ((j >> (i - 1) & 1) == 1) {
          int s = 0;
          for (int k = 0; k < i; ++k) {
            if (((j >> k) & 1) == 1) {
              s += ans[k];
            }
          }
          if (tm.merge(s, -1, Integer::sum) == 0) {
            tm.remove(s);
          }
        }
      }
      ans[i] = tm.firstKey();
    }
    for (int i = 0; i < 1 << n; ++i) {
      int s = 0;
      for (int j = 0; j < n; ++j) {
        if (((i >> j) & 1) == 1) {
          s += ans[j];
        }
      }
      if (s == m) {
        for (int j = 0; j < n; ++j) {
          if (((i >> j) & 1) == 1) {
            ans[j] *= -1;
          }
        }
        break;
      }
    }
    return ans;
  }
}

class Solution {
public:
  vector<int> recoverArray(int n, vector<int>& sums) {
    int m = *min_element(sums.begin(), sums.end());
    m = -m;
    multiset<int> st;
    for (int x : sums) {
      st.insert(x + m);
    }
    st.erase(st.begin());
    vector<int> ans;
    ans.push_back(*st.begin());
    for (int i = 1; i < n; ++i) {
      for (int j = 0; j < 1 << i; ++j) {
        if (j >> (i - 1) & 1) {
          int s = 0;
          for (int k = 0; k < i; ++k) {
            if (j >> k & 1) {
              s += ans[k];
            }
          }
          st.erase(st.find(s));
        }
      }
      ans.push_back(*st.begin());
    }
    for (int i = 0; i < 1 << n; ++i) {
      int s = 0;
      for (int j = 0; j < n; ++j) {
        if (i >> j & 1) {
          s += ans[j];
        }
      }
      if (s == m) {
        for (int j = 0; j < n; ++j) {
          if (i >> j & 1) {
            ans[j] = -ans[j];
          }
        }
        break;
      }
    }
    return ans;
  }
};

func recoverArray(n int, sums []int) []int {
  m := -slices.Min(sums)
  rbt := redblacktree.NewWithIntComparator()
  merge := func(key int, value int) {
    if v, ok := rbt.Get(key); ok {
      nxt := v.(int) + value
      if nxt == 0 {
        rbt.Remove(key)
      } else {
        rbt.Put(key, nxt)
      }
    } else {
      rbt.Put(key, value)
    }
  }
  for _, x := range sums {
    merge(x+m, 1)
  }
  ans := make([]int, n)
  merge(ans[0], -1)
  ans[0] = rbt.Left().Key.(int)
  for i := 1; i < n; i++ {
    for j := 0; j < 1<<i; j++ {
      if j>>(i-1)&1 == 1 {
        s := 0
        for k := 0; k < i; k++ {
          if j>>k&1 == 1 {
            s += ans[k]
          }
        }
        merge(s, -1)
      }
    }
    ans[i] = rbt.Left().Key.(int)
  }
  for i := 0; i < 1<<n; i++ {
    s := 0
    for j := 0; j < n; j++ {
      if i>>j&1 == 1 {
        s += ans[j]
      }
    }
    if s == m {
      for j := 0; j < n; j++ {
        if i>>j&1 == 1 {
          ans[j] = -ans[j]
        }
      }
      break
    }
  }
  return ans

}

Solution 2

class Solution:
  def recoverArray(self, n: int, sums: List[int]) -> List[int]:
    sums.sort()
    ans = []
    for i in range(n, 0, -1):
      k = 1 << i
      d = sums[k - 1] - sums[k - 2]
      cnt = Counter(sums[:k])
      sums1, sums2 = [], []
      sign = 1
      for s in sums[:k]:
        if not cnt[s]:
          continue
        cnt[s] -= 1
        cnt[s + d] -= 1
        sums1.append(s)
        sums2.append(s + d)
        if s + d == 0:
          sign = -1
      ans.append(sign * d)
      sums = sums1 if sign == 1 else sums2
    return ans

class Solution {
  public int[] recoverArray(int n, int[] sums) {
    Arrays.sort(sums);
    int[] sums1 = new int[1 << n];
    int[] sums2 = new int[1 << n];
    Map<Integer, Integer> cnt = new HashMap<>();
    int[] ans = new int[n];
    for (int i = n; i > 0; --i) {
      int k = 1 << i;
      int d = sums[k - 1] - sums[k - 2];
      cnt.clear();
      for (int j = 0; j < k; ++j) {
        cnt.merge(sums[j], 1, Integer::sum);
      }
      int sign = 1;
      for (int j = 0, p = 0; j < k; ++j) {
        if (cnt.getOrDefault(sums[j], 0) == 0) {
          continue;
        }
        cnt.merge(sums[j], -1, Integer::sum);
        cnt.merge(sums[j] + d, -1, Integer::sum);
        sums1[p] = sums[j];
        sums2[p++] = sums[j] + d;
        if (sums[j] + d == 0) {
          sign = -1;
        }
      }
      ans[i - 1] = sign * d;
      System.arraycopy(sign == 1 ? sums1 : sums2, 0, sums, 0, k / 2);
    }
    return ans;
  }
}

class Solution {
public:
  vector<int> recoverArray(int n, vector<int>& sums) {
    sort(sums.begin(), sums.end());
    vector<int> ans(n);
    unordered_map<int, int> cnt;
    for (int i = n; i; --i) {
      cnt.clear();
      int k = 1 << i;
      int d = sums[k - 1] - sums[k - 2];
      for (int j = 0; j < k; ++j) {
        cnt[sums[j]]++;
      }
      vector<int> sums1, sums2;
      int sign = 1;
      for (int j = 0; j < k; ++j) {
        if (cnt[sums[j]] == 0) {
          continue;
        }
        --cnt[sums[j]];
        --cnt[sums[j] + d];
        sums1.push_back(sums[j]);
        sums2.push_back(sums[j] + d);
        if (sums2.back() == 0) {
          sign = -1;
        }
      }
      ans[i - 1] = sign * d;
      for (int j = 0; j < k / 2; ++j) {
        sums[j] = sign == 1 ? sums1[j] : sums2[j];
      }
    }
    return ans;
  }
};

func recoverArray(n int, sums []int) (ans []int) {
  sort.Ints(sums)
  for i := n; i > 0; i-- {
    k := 1 << i
    d := sums[k-1] - sums[k-2]
    cnt := map[int]int{}
    for _, s := range sums[:k] {
      cnt[s]++
    }
    sums1, sums2 := []int{}, []int{}
    sign := 1
    for _, s := range sums[:k] {
      if cnt[s] == 0 {
        continue
      }
      cnt[s]--
      cnt[s+d]--
      sums1 = append(sums1, s)
      sums2 = append(sums2, s+d)
      if s+d == 0 {
        sign = -1
      }
    }
    ans = append(ans, sign*d)
    if sign == -1 {
      sums1 = sums2
    }
    sums = sums1
  }
  return
}