634. Find the Derangement of An Array

In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position.

There's originally an array consisting of n integers from 1 to n in ascending order, you need to find the number of derangement it can generate.

Also, since the answer may be very large, you should return the output mod 109 + 7.

Example 1:

Input: 3
Output: 2
Explanation: The original array is [1,2,3]. The two derangements are [2,3,1] and [3,1,2].

Note:
n is in the range of [1, 106].

Rust Solution

struct Solution;

impl Solution {
    fn find_derangement(n: i32) -> i32 {
        let n = n as usize;
        let mut dp = vec![0; n + 1];
        dp[0] = 1;
        dp[1] = 0;
        for i in 2..=n {
            dp[i] = (i - 1) * (dp[i - 1] + dp[i - 2]) % 1_000_000_007;
        }
        dp[n] as i32
    }
}

#[test]
fn test() {
    let n = 3;
    let res = 2;
    assert_eq!(Solution::find_derangement(n), res);
}

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