902. Numbers At Most N Given Digit Set

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902. Numbers At Most N Given Digit Set

Description

Given an array of digits which is sorted in non-decreasing order. You can write numbers using each digits[i] as many times as we want. For example, if digits = ['1','3','5'], we may write numbers such as '13', '551', and '1351315'.

Return the number of positive integers that can be generated that are less than or equal to a given integer n.

Example 1:

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Input: digits = ["1","3","5","7"], n = 100
Output: 20
Explanation:
The 20 numbers that can be written are:
1, 3, 5, 7, 11, 13, 15, 17, 31, 33, 35, 37, 51, 53, 55, 57, 71, 73, 75, 77.

Example 2:

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Input: digits = ["1","4","9"], n = 1000000000
Output: 29523
Explanation:
We can write 3 one digit numbers, 9 two digit numbers, 27 three digit numbers,
81 four digit numbers, 243 five digit numbers, 729 six digit numbers,
2187 seven digit numbers, 6561 eight digit numbers, and 19683 nine digit numbers.
In total, this is 29523 integers that can be written using the digits array.

Example 3:

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Input: digits = ["7"], n = 8
Output: 1

Constraints:

  • 1 <= digits.length <= 9
  • digits[i].length == 1
  • digits[i] is a digit from'1'to '9'.
  • All the values indigits are unique .
  • digits is sorted innon-decreasing order.
  • 1 <= n <= 10^9

Hints/Notes

Solution

Language: C++

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class Solution {
public:
    string s;
    vector<int> dp;
    set<int> st;
    int atMostNGivenDigitSet(vector<string>& digits, int n) {
        for (auto& d : digits) {
            st.insert(stoi(d));
        }
        s = to_string(n);
        dp.resize(s.size(), -1);
        int res = dfs(0, true, false);
        return res;
    }

    int dfs(int index, bool isLimit, bool isNum) {
        if (index == s.size()) {
            return isNum;
        }
        if (!isLimit && isNum && dp[index] != -1) {
            return dp[index];
        }
        int res = isNum ? 0 : dfs(index + 1, false, false);
        int up = isLimit ? s[index] - '0' : 9;
        // num can have leading zeroes but cannot have zero between
        // use isNum to capture this
        for (auto& d : st){
            if (d > up) {
                break;
            }
            res += dfs(index + 1, isLimit && d == up, true);
        }
        // check status during read and write memo both
        if (!isLimit && isNum) {
            dp[index] = res;
        }
        return res;
    }
};