Skip to content

357. Count Numbers with Unique Digits

Description

Given an integer n, return the count of all numbers with unique digits, x, where 0 <= x < 10n.

 

Example 1:

Input: n = 2
Output: 91
Explanation: The answer should be the total numbers in the range of 0 ≤ x < 100, excluding 11,22,33,44,55,66,77,88,99

Example 2:

Input: n = 0
Output: 1

 

Constraints:

  • 0 <= n <= 8

Solutions

Solution 1

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
class Solution:
    def countNumbersWithUniqueDigits(self, n: int) -> int:
        if n == 0:
            return 1
        if n == 1:
            return 10
        ans, cur = 10, 9
        for i in range(n - 1):
            cur *= 9 - i
            ans += cur
        return ans

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
class Solution {
    public int countNumbersWithUniqueDigits(int n) {
        if (n == 0) {
            return 1;
        }
        if (n == 1) {
            return 10;
        }
        int ans = 10;
        for (int i = 0, cur = 9; i < n - 1; ++i) {
            cur *= (9 - i);
            ans += cur;
        }
        return ans;
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
class Solution {
public:
    int countNumbersWithUniqueDigits(int n) {
        if (n == 0) return 1;
        if (n == 1) return 10;
        int ans = 10;
        for (int i = 0, cur = 9; i < n - 1; ++i) {
            cur *= (9 - i);
            ans += cur;
        }
        return ans;
    }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
func countNumbersWithUniqueDigits(n int) int {
    if n == 0 {
        return 1
    }
    if n == 1 {
        return 10
    }
    ans := 10
    for i, cur := 0, 9; i < n-1; i++ {
        cur *= (9 - i)
        ans += cur
    }
    return ans
}

Solution 2

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
class Solution:
    def countNumbersWithUniqueDigits(self, n: int) -> int:
        @cache
        def dfs(pos, mask, lead):
            if pos <= 0:
                return 1
            ans = 0
            for i in range(10):
                if (mask >> i) & 1:
                    continue
                if i == 0 and lead:
                    ans += dfs(pos - 1, mask, lead)
                else:
                    ans += dfs(pos - 1, mask | (1 << i), False)
            return ans

        return dfs(n, 0, True)

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
class Solution {
    private int[][] dp = new int[10][1 << 11];

    public int countNumbersWithUniqueDigits(int n) {
        for (var e : dp) {
            Arrays.fill(e, -1);
        }
        return dfs(n, 0, true);
    }

    private int dfs(int pos, int mask, boolean lead) {
        if (pos <= 0) {
            return 1;
        }
        if (!lead && dp[pos][mask] != -1) {
            return dp[pos][mask];
        }
        int ans = 0;
        for (int i = 0; i < 10; ++i) {
            if (((mask >> i) & 1) == 1) {
                continue;
            }
            if (i == 0 && lead) {
                ans += dfs(pos - 1, mask, lead);
            } else {
                ans += dfs(pos - 1, mask | (1 << i), false);
            }
        }
        if (!lead) {
            dp[pos][mask] = ans;
        }
        return ans;
    }
}

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
class Solution {
public:
    int dp[10][1 << 11];

    int countNumbersWithUniqueDigits(int n) {
        memset(dp, -1, sizeof dp);
        return dfs(n, 0, true);
    }

    int dfs(int pos, int mask, bool lead) {
        if (pos <= 0) {
            return 1;
        }
        if (!lead && dp[pos][mask] != -1) {
            return dp[pos][mask];
        }
        int ans = 0;
        for (int i = 0; i < 10; ++i) {
            if ((mask >> i) & 1) continue;
            if (i == 0 && lead) {
                ans += dfs(pos - 1, mask, lead);
            } else {
                ans += dfs(pos - 1, mask | 1 << i, false);
            }
        }
        if (!lead) {
            dp[pos][mask] = ans;
        }
        return ans;
    }
};

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
func countNumbersWithUniqueDigits(n int) int {
    dp := make([][]int, 10)
    for i := range dp {
        dp[i] = make([]int, 1<<11)
        for j := range dp[i] {
            dp[i][j] = -1
        }
    }
    var dfs func(int, int, bool) int
    dfs = func(pos, mask int, lead bool) int {
        if pos <= 0 {
            return 1
        }
        if !lead && dp[pos][mask] != -1 {
            return dp[pos][mask]
        }
        ans := 0
        for i := 0; i < 10; i++ {
            if ((mask >> i) & 1) == 1 {
                continue
            }
            if i == 0 && lead {
                ans += dfs(pos-1, mask, lead)
            } else {
                ans += dfs(pos-1, mask|1<<i, false)
            }
        }
        if !lead {
            dp[pos][mask] = ans
        }
        return ans
    }

    return dfs(n, 0, true)
}

Comments