LeetCode-in-Java
2438. 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 <= 1091 <= queries.length <= 1050 <= starti <= endi < powers.length
Solution
import java.util.ArrayList;
import java.util.List;
public class Solution {
public int[] productQueries(int n, int[][] queries) {
int length = queries.length;
final long mod = (long) (1e9 + 7);
// convert n to binary form
// take the set bit and find the corresponding 2^i
// now answer for the query
int[] powerTracker = new int[32];
List<Long> productTakingPowers = new ArrayList<>();
int[] result = new int[length];
fillPowerTracker(powerTracker, n);
fillProductTakingPowers(productTakingPowers, powerTracker);
int index = 0;
for (int[] query : queries) {
int left = query[0];
int right = query[1];
long product = 1;
for (int i = left; i <= right; i++) {
product = (product * productTakingPowers.get(i)) % mod;
}
result[index++] = (int) (product % mod);
}
return result;
}
private void fillPowerTracker(int[] powerTracker, int n) {
int index = 0;
while (n > 0) {
powerTracker[index++] = n & 1;
n >>= 1;
}
}
private void fillProductTakingPowers(List<Long> productTakingPowers, int[] powerTracker) {
for (int i = 0; i < 32; i++) {
if (powerTracker[i] == 1) {
long power = (long) (Math.pow(2, i));
productTakingPowers.add(power);
}
}
}
}