Problem Statement | | |
The level-M weight of a permutation P, denoted W(P,M), is computed by finding the number of cycles of P and then taking that number to the M-th power.
For example, the level-3 weight of a permutation with 5 cycles is 5^3.
The total level-M weight of all permutations on N elements, denoted T(N,M), is computed as the sum of W(P,M) over all N! possible permutations P on N elements.
You are given multiple queries.
These are encoded as two int[]s n and m with the same number of elements.
Return a int[] with the same number of elements as n.
For each valid i, element i of the return value should be the value T( n[i], m[i] ) modulo 1,000,000,007.
| | | Definition | | | | Class: | CyclesNumber | | Method: | getExpectation | | Parameters: | int[], int[] | | Returns: | int[] | | Method signature: | int[] getExpectation(int[] n, int[] m) | | (be sure your method is public) |
| | | | | | Notes | | - | Formally, a permutation on N elements is a bijective function P defined on an N-element set S. | | - | A cycle of a permutation is a sequence c[0], c[1], ..., c[k-1] of distinct elements of S such that for each i, P(c[i]) = c[(i+1) mod k]. | | | Constraints | | - | n and m will contain the same number of elements. | | - | n will contain between 1 and 300 elements, inclusive. | | - | Each element of n will be between 1 and 100,000, inclusive. | | - | Each element of m will be between 0 and 300, inclusive. | | | Examples | | 0) | | | | | Returns: {5 } | | Here are two permutations: (1, 2) and (2, 1). (1, 2) have 2 cycles. (2, 1) has one cycle. So answer is 1 * 1 + 2 * 2 = 5. |
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| | 1) | | | | | Returns: {6 } | | Here answer is just number of permutations, 3! = 6. |
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| | 2) | | | | | Returns: {1, 9, 53 } | | Could be more than one query. |
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| | 3) | | | | | Returns: {586836447, 544389755, 327675273 } | | Do not forget take answers modulo 1,000,000,007. |
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