Description
You are given an integer array digits, where each element is a digit. The array may contain duplicates.
You need to find all the unique integers that follow the given requirements:
- The integer consists of the concatenation of three elements from
digits in any arbitrary order.
- The integer does not have leading zeros.
- The integer is even.
For example, if the given digits were [1, 2, 3], integers 132 and 312 follow the requirements.
Return a sorted array of the unique integers.
Example 1:
Input: digits = [2,1,3,0]
Output: [102,120,130,132,210,230,302,310,312,320]
Explanation: All the possible integers that follow the requirements are in the output array.
Notice that there are no odd integers or integers with leading zeros.
Example 2:
Input: digits = [2,2,8,8,2]
Output: [222,228,282,288,822,828,882]
Explanation: The same digit can be used as many times as it appears in digits.
In this example, the digit 8 is used twice each time in 288, 828, and 882.
Example 3:
Input: digits = [3,7,5]
Output: []
Explanation: No even integers can be formed using the given digits.
Constraints:
3 <= digits.length <= 1000 <= digits[i] <= 9
Solutions
Solution 1: Counting + Enumeration
First, we count the occurrence of each digit in digits, recording it in an array or hash table cnt.
Then, we enumerate all even numbers in the range [100, 1000), checking if each digit of the even number does not exceed the corresponding digit's count in cnt. If so, we add this even number to the answer array.
Finally, we return the answer array.
The time complexity is O(k × 10k), where k is the number of digits of the target even number, which is 3 in this problem. Ignoring the space consumed by the answer, the space complexity is O(1).
PythonJavaC++GoTypeScriptJavaScript
class Solution:
def findEvenNumbers(self, digits: List[int]) -> List[int]:
cnt = Counter(digits)
ans = []
for x in range(100, 1000, 2):
cnt1 = Counter()
y = x
while y:
y, v = divmod(y, 10)
cnt1[v] += 1
if all(cnt[i] >= cnt1[i] for i in range(10)):
ans.append(x)
return ans(code-box)
class Solution {
public int[] findEvenNumbers(int[] digits) {
int[] cnt = new int[10];
for (int x : digits) {
++cnt[x];
}
List<Integer> ans = new ArrayList<>();
for (int x = 100; x < 1000; x += 2) {
int[] cnt1 = new int[10];
for (int y = x; y > 0; y /= 10) {
++cnt1[y % 10];
}
boolean ok = true;
for (int i = 0; i < 10 && ok; ++i) {
ok = cnt[i] >= cnt1[i];
}
if (ok) {
ans.add(x);
}
}
return ans.stream().mapToInt(i -> i).toArray();
}
}(code-box)
class Solution {
public:
vector<int> findEvenNumbers(vector<int>& digits) {
int cnt[10]{};
for (int x : digits) {
++cnt[x];
}
vector<int> ans;
for (int x = 100; x < 1000; x += 2) {
int cnt1[10]{};
for (int y = x; y; y /= 10) {
++cnt1[y % 10];
}
bool ok = true;
for (int i = 0; i < 10 && ok; ++i) {
ok = cnt[i] >= cnt1[i];
}
if (ok) {
ans.push_back(x);
}
}
return ans;
}
};(code-box)
func findEvenNumbers(digits []int) (ans []int) {
cnt := [10]int{}
for _, x := range digits {
cnt[x]++
}
for x := 100; x < 1000; x += 2 {
cnt1 := [10]int{}
for y := x; y > 0; y /= 10 {
cnt1[y%10]++
}
ok := true
for i := 0; i < 10 && ok; i++ {
ok = cnt[i] >= cnt1[i]
}
if ok {
ans = append(ans, x)
}
}
return
}(code-box)
function findEvenNumbers(digits: number[]): number[] {
const cnt: number[] = Array(10).fill(0);
for (const x of digits) {
++cnt[x];
}
const ans: number[] = [];
for (let x = 100; x < 1000; x += 2) {
const cnt1: number[] = Array(10).fill(0);
for (let y = x; y; y = Math.floor(y / 10)) {
++cnt1[y % 10];
}
let ok = true;
for (let i = 0; i < 10 && ok; ++i) {
ok = cnt[i] >= cnt1[i];
}
if (ok) {
ans.push(x);
}
}
return ans;
}(code-box)
/**
* @param {number[]} digits
* @return {number[]}
*/
var findEvenNumbers = function (digits) {
const cnt = Array(10).fill(0);
for (const x of digits) {
++cnt[x];
}
const ans = [];
for (let x = 100; x < 1000; x += 2) {
const cnt1 = Array(10).fill(0);
for (let y = x; y; y = Math.floor(y / 10)) {
++cnt1[y % 10];
}
let ok = true;
for (let i = 0; i < 10 && ok; ++i) {
ok = cnt[i] >= cnt1[i];
}
if (ok) {
ans.push(x);
}
}
return ans;
};(code-box)
