Problem
Return the number of permutations of 1 to n so that prime numbers are at prime indices (1-indexed.)
(Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.)
Since the answer may be large, return the answer modulo 10^9 + 7.
Example 1:
Input: n = 5
Output: 12
Explanation: For example [1,2,5,4,3] is a valid permutation, but [5,2,3,4,1] is not because the prime number 5 is at index 1.
Example 2:
Input: n = 100
Output: 682289015
Constraints:
1 <= n <= 100
Solution (Java)
class Solution {
public int numPrimeArrangements(int n) {
int[] a = {
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
89, 97
};
int c = 0;
while (c < 25 && n >= a[c]) {
c++;
}
int m = 1000000007;
long res = 1L;
while ((n - c) > 0) {
res *= (n - c);
res %= m;
n--;
}
while (c > 0) {
res *= c;
res %= m;
c--;
}
return (int) res;
}
}
Explain:
nope.
Complexity:
- Time complexity : O(n).
- Space complexity : O(n).