940. Distinct Subsequences II

Description

Given a string s, return the number of distinct non-empty subsequences of s. Since the answer may be very large, return it modulo 109 + 7.

A subsequence of a string is a new string that is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (i.e., "ace" is a subsequence of "abcde" while "aec" is not.

 

Example 1:

Input: s = "abc"
Output: 7
Explanation: The 7 distinct subsequences are "a", "b", "c", "ab", "ac", "bc", and "abc".

Example 2:

Input: s = "aba"
Output: 6
Explanation: The 6 distinct subsequences are "a", "b", "ab", "aa", "ba", and "aba".

Example 3:

Input: s = "aaa"
Output: 3
Explanation: The 3 distinct subsequences are "a", "aa" and "aaa".

 

Constraints:

  • 1 <= s.length <= 2000
  • s consists of lowercase English letters.

Solutions

Solution 1

Python Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13

class Solution:
    def distinctSubseqII(self, s: str) -> int:
        mod = 10**9 + 7
        n = len(s)
        dp = [[0] * 26 for _ in range(n + 1)]
        for i, c in enumerate(s, 1):
            k = ord(c) - ord('a')
            for j in range(26):
                if j == k:
                    dp[i][j] = sum(dp[i - 1]) % mod + 1
                else:
                    dp[i][j] = dp[i - 1][j]
        return sum(dp[-1]) % mod

Java Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20

class Solution {
    private static final int MOD = (int) 1e9 + 7;

    public int distinctSubseqII(String s) {
        int[] dp = new int[26];
        for (int i = 0; i < s.length(); ++i) {
            int j = s.charAt(i) - 'a';
            dp[j] = sum(dp) + 1;
        }
        return sum(dp);
    }

    private int sum(int[] arr) {
        int x = 0;
        for (int v : arr) {
            x = (x + v) % MOD;
        }
        return x;
    }
}

C++ Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13

class Solution {
public:
    const int mod = 1e9 + 7;

    int distinctSubseqII(string s) {
        vector<long> dp(26);
        for (char& c : s) {
            int i = c - 'a';
            dp[i] = accumulate(dp.begin(), dp.end(), 1l) % mod;
        }
        return accumulate(dp.begin(), dp.end(), 0l) % mod;
    }
};

Go Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17

func distinctSubseqII(s string) int {
	const mod int = 1e9 + 7
	sum := func(arr []int) int {
		x := 0
		for _, v := range arr {
			x = (x + v) % mod
		}
		return x
	}

	dp := make([]int, 26)
	for _, c := range s {
		c -= 'a'
		dp[c] = sum(dp) + 1
	}
	return sum(dp)
}

TypeScript Code
1
2
3
4
5
6
7
8

function distinctSubseqII(s: string): number {
    const mod = 1e9 + 7;
    const dp = new Array(26).fill(0);
    for (const c of s) {
        dp[c.charCodeAt(0) - 'a'.charCodeAt(0)] = dp.reduce((r, v) => (r + v) % mod, 0) + 1;
    }
    return dp.reduce((r, v) => (r + v) % mod, 0);
}

Rust Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22

impl Solution {
    pub fn distinct_subseq_ii(s: String) -> i32 {
        const MOD: i32 = (1e9 as i32) + 7;
        let mut dp = [0; 26];
        for u in s.as_bytes() {
            let i = (u - &b'a') as usize;
            dp[i] =
                ({
                    let mut sum = 0;
                    dp.iter().for_each(|&v| {
                        sum = (sum + v) % MOD;
                    });
                    sum
                }) + 1;
        }
        let mut res = 0;
        dp.iter().for_each(|&v| {
            res = (res + v) % MOD;
        });
        res
    }
}

C Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17

int distinctSubseqII(char* s) {
    int mod = 1e9 + 7;
    int n = strlen(s);
    int dp[26] = {0};
    for (int i = 0; i < n; i++) {
        int sum = 0;
        for (int j = 0; j < 26; j++) {
            sum = (sum + dp[j]) % mod;
        }
        dp[s[i] - 'a'] = sum + 1;
    }
    int res = 0;
    for (int i = 0; i < 26; i++) {
        res = (res + dp[i]) % mod;
    }
    return res;
}

Solution 2

Python Code
1
2
3
4
5
6
7
8

class Solution:
    def distinctSubseqII(self, s: str) -> int:
        mod = 10**9 + 7
        dp = [0] * 26
        for c in s:
            i = ord(c) - ord('a')
            dp[i] = sum(dp) % mod + 1
        return sum(dp) % mod

Java Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15

class Solution {
    private static final int MOD = (int) 1e9 + 7;

    public int distinctSubseqII(String s) {
        int[] dp = new int[26];
        int ans = 0;
        for (int i = 0; i < s.length(); ++i) {
            int j = s.charAt(i) - 'a';
            int add = (ans - dp[j] + 1) % MOD;
            ans = (ans + add) % MOD;
            dp[j] = (dp[j] + add) % MOD;
        }
        return (ans + MOD) % MOD;
    }
}

C++ Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16

class Solution {
public:
    const int mod = 1e9 + 7;

    int distinctSubseqII(string s) {
        vector<long> dp(26);
        long ans = 0;
        for (char& c : s) {
            int i = c - 'a';
            long add = ans - dp[i] + 1;
            ans = (ans + add + mod) % mod;
            dp[i] = (dp[i] + add) % mod;
        }
        return ans;
    }
};

Go Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

func distinctSubseqII(s string) int {
	const mod int = 1e9 + 7
	dp := make([]int, 26)
	ans := 0
	for _, c := range s {
		c -= 'a'
		add := ans - dp[c] + 1
		ans = (ans + add) % mod
		dp[c] = (dp[c] + add) % mod
	}
	return (ans + mod) % mod
}

Solution 3

Python Code
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11

class Solution:
    def distinctSubseqII(self, s: str) -> int:
        mod = 10**9 + 7
        dp = [0] * 26
        ans = 0
        for c in s:
            i = ord(c) - ord('a')
            add = ans - dp[i] + 1
            ans = (ans + add) % mod
            dp[i] += add
        return ans