634. Find the Derangement of An Array
Explanation
To find the derangement of an array, we need to find a permutation of the array where no element appears in its original position. This can be solved using dynamic programming. We can define the derangement of an array of size n as the number of ways to rearrange the elements such that no element appears in its original position.
We can use the principle of inclusion-exclusion to compute the derangement for each element. Let dp[i] represent the number of derangements for an array of size i.
The recursive formula for computing dp[i] is:
dp[i] = (i-1) * (dp[i-1] + dp[i-2])
class Solution {
public int findDerangement(int n) {
if (n <= 1) {
return 0;
}
long dp1 = 0, dp2 = 1;
for (int i = 3; i <= n; i++) {
long dp = (i - 1) * (dp1 + dp2) % 1000000007;
dp1 = dp2;
dp2 = dp;
}
return (int)dp2;
}
}Code Editor (Testing phase)
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