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2529. Range Product Queries Of Powers

Array Bit Manipulation Prefix Sum

Problem - Range Product Queries Of Powers

Medium

Given a positive integer n, there exists a 0-indexed array called powers, composed of the minimum number of powers of 2 that sum to n. The array is sorted in non-decreasing order, and there is only one way to form the array.

You are also given a 0-indexed 2D integer array queries, where queries[i] = [lefti, righti]. Each queries[i] represents a query where you have to find the product of all powers[j] with lefti <= j <= righti.

Return an array answers, equal in length to queries, where answers[i] is the answer to the ith query. Since the answer to the ith query may be too large, each answers[i] should be returned modulo 109 + 7.

 

Example 1:

Input: n = 15, queries = [[0,1],[2,2],[0,3]]
Output: [2,4,64]
Explanation:
For n = 15, powers = [1,2,4,8]. It can be shown that powers cannot be a smaller size.
Answer to 1st query: powers[0] * powers[1] = 1 * 2 = 2.
Answer to 2nd query: powers[2] = 4.
Answer to 3rd query: powers[0] * powers[1] * powers[2] * powers[3] = 1 * 2 * 4 * 8 = 64.
Each answer modulo 109 + 7 yields the same answer, so [2,4,64] is returned.

Example 2:

Input: n = 2, queries = [[0,0]]
Output: [2]
Explanation:
For n = 2, powers = [2].
The answer to the only query is powers[0] = 2. The answer modulo 109 + 7 is the same, so [2] is returned.

 

Constraints:

  • 1 <= n <= 109
  • 1 <= queries.length <= 105
  • 0 <= starti <= endi < powers.length

Solutions

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class Solution:
    def productQueries(self, n: int, queries: List[List[int]]) -> List[int]:
        powers = []

        while n:
            val = n & -n # Bitwise operation to isolate the rightmost bit
            powers.append(val)
            n -= val

        modulo = 10**9 + 7
        results = []
        for left, right in queries:
            val = 1
            for i in range(left, right + 1):
                val = val * powers[i] % modulo
            results.append(val)
        return results

Submission Stats:

  • Runtime: 213 ms (35.94%)
  • Memory: 48.3 MB (17.38%)