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GlobalAndLocalInversion.java
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GlobalAndLocalInversion.java
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package Leetcode;
/**
* @author kalpak
*
* We have some permutation A of [0, 1, ..., N - 1], where N is the length of A.
*
* The number of (global) inversions is the number of i < j with 0 <= i < j < N and A[i] > A[j].
*
* The number of local inversions is the number of i with 0 <= i < N and A[i] > A[i+1].
*
* Return true if and only if the number of global inversions is equal to the number of local inversions.
*
* Example 1:
* Input: A = [1,0,2]
* Output: true
* Explanation: There is 1 global inversion, and 1 local inversion.
*
* Example 2:
* Input: A = [1,2,0]
* Output: false
* Explanation: There are 2 global inversions, and 1 local inversion.
* Note:
*
* A will be a permutation of [0, 1, ..., A.length - 1].
* A will have length in range [1, 5000].
* The time limit for this problem has been reduced.
*
*/
public class GlobalAndLocalInversion {
public static boolean isIdealPermutation(int[] A) {
// Local Inversions are part of Global Inversions when j == i + 1.
// Thus, whenever we find inversions that j != i + 1, we return false.
// local inversions are actually swaps between two adjacent elements only.
// So whenever we detect |i - A[i]| > 1, we return false.
for(int i = 0; i < A.length; i++) {
if(Math.abs(i - A[i]) > 1)
return false;
}
return true;
}
public static void main(String[] args) {
System.out.println(isIdealPermutation(new int[]{1, 0, 2}));
System.out.println(isIdealPermutation(new int[]{1, 2, 0}));
}
}