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2081. Sum of k-Mirror Numbers

Description

A k-mirror number is a positive integer without leading zeros that reads the same both forward and backward in base-10 as well as in base-k.

  • For example, 9 is a 2-mirror number. The representation of 9 in base-10 and base-2 are 9 and 1001 respectively, which read the same both forward and backward.
  • On the contrary, 4 is not a 2-mirror number. The representation of 4 in base-2 is 100, which does not read the same both forward and backward.

Given the base k and the number n, return the sum of the n smallest k-mirror numbers.

 

Example 1:

Input: k = 2, n = 5
Output: 25
Explanation:
The 5 smallest 2-mirror numbers and their representations in base-2 are listed as follows:
  base-10    base-2
    1          1
    3          11
    5          101
    7          111
    9          1001
Their sum = 1 + 3 + 5 + 7 + 9 = 25.

Example 2:

Input: k = 3, n = 7
Output: 499
Explanation:
The 7 smallest 3-mirror numbers are and their representations in base-3 are listed as follows:
  base-10    base-3
    1          1
    2          2
    4          11
    8          22
    121        11111
    151        12121
    212        21212
Their sum = 1 + 2 + 4 + 8 + 121 + 151 + 212 = 499.

Example 3:

Input: k = 7, n = 17
Output: 20379000
Explanation: The 17 smallest 7-mirror numbers are:
1, 2, 3, 4, 5, 6, 8, 121, 171, 242, 292, 16561, 65656, 2137312, 4602064, 6597956, 6958596

 

Constraints:

  • 2 <= k <= 9
  • 1 <= n <= 30

Solutions

  • class Solution {
    public long kMirror(int k, int n) {
        long ans = 0;
        for (int l = 1;; ++l) {
            int x = (int) Math.pow(10, (l - 1) / 2);
            int y = (int) Math.pow(10, (l + 1) / 2);
            for (int i = x; i < y; i++) {
                long v = i;
                for (int j = l % 2 == 0 ? i : i / 10; j > 0; j /= 10) {
                    v = v * 10 + j % 10;
                }
                String ss = Long.toString(v, k);
                if (check(ss.toCharArray())) {
                    ans += v;
                    if (--n == 0) {
                        return ans;
                    }
                }
            }
        }
    }

    private boolean check(char[] c) {
        for (int i = 0, j = c.length - 1; i < j; i++, j--) {
            if (c[i] != c[j]) {
                return false;
            }
        }
        return true;
    }
}

  • class Solution {
public:
    long long kMirror(int k, int n) {
        long long ans = 0;
        for (int l = 1;; ++l) {
            int x = pow(10, (l - 1) / 2);
            int y = pow(10, (l + 1) / 2);
            for (int i = x; i < y; ++i) {
                long long v = i;
                int j = (l % 2 == 0) ? i : i / 10;
                while (j > 0) {
                    v = v * 10 + j % 10;
                    j /= 10;
                }
                if (check(v, k)) {
                    ans += v;
                    if (--n == 0) {
                        return ans;
                    }
                }
            }
        }
    }

private:
    bool check(long long x, int k) {
        vector<int> s;
        while (x > 0) {
            s.push_back(x % k);
            x /= k;
        }
        for (int i = 0, j = s.size() - 1; i < j; ++i, --j) {
            if (s[i] != s[j]) {
                return false;
            }
        }
        return true;
    }
};


  • class Solution:
    def kMirror(self, k: int, n: int) -> int:
        def check(x: int, k: int) -> bool:
            s = []
            while x:
                s.append(x % k)
                x //= k
            return s == s[::-1]

        ans = 0
        for l in count(1):
            x = 10 ** ((l - 1) // 2)
            y = 10 ** ((l + 1) // 2)
            for i in range(x, y):
                v = i
                j = i if l % 2 == 0 else i // 10
                while j > 0:
                    v = v * 10 + j % 10
                    j //= 10
                if check(v, k):
                    ans += v
                    n -= 1
                    if n == 0:
                        return ans


  • func kMirror(k int, n int) int64 {
	check := func(x int64, k int) bool {
		s := []int{}
		for x > 0 {
			s = append(s, int(x%int64(k)))
			x /= int64(k)
		}
		for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
			if s[i] != s[j] {
				return false
			}
		}
		return true
	}

	var ans int64 = 0
	for l := 1; ; l++ {
		x := pow10((l - 1) / 2)
		y := pow10((l + 1) / 2)
		for i := x; i < y; i++ {
			v := int64(i)
			j := i
			if l%2 != 0 {
				j = i / 10
			}
			for j > 0 {
				v = v*10 + int64(j%10)
				j /= 10
			}
			if check(v, k) {
				ans += v
				n--
				if n == 0 {
					return ans
				}
			}
		}
	}
}

func pow10(exp int) int {
	res := 1
	for i := 0; i < exp; i++ {
		res *= 10
	}
	return res
}


  • function kMirror(k: number, n: number): number {
    function check(x: number, k: number): boolean {
        const s: number[] = [];
        while (x > 0) {
            s.push(x % k);
            x = Math.floor(x / k);
        }
        for (let i = 0, j = s.length - 1; i < j; i++, j--) {
            if (s[i] !== s[j]) {
                return false;
            }
        }
        return true;
    }

    let ans = 0;
    for (let l = 1; ; l++) {
        const x = Math.pow(10, Math.floor((l - 1) / 2));
        const y = Math.pow(10, Math.floor((l + 1) / 2));
        for (let i = x; i < y; i++) {
            let v = i;
            let j = l % 2 === 0 ? i : Math.floor(i / 10);
            while (j > 0) {
                v = v * 10 + (j % 10);
                j = Math.floor(j / 10);
            }
            if (check(v, k)) {
                ans += v;
                n--;
                if (n === 0) {
                    return ans;
                }
            }
        }
    }
}

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