CF1692G 2^Sort

Given an array $ a $ of length $ n $ and an integer $ k $ , find the number of indices $ 1 \leq i \leq n - k $ such that the subarray $ [a_i, \dots, a_{i+k}] $ with length $ k+1 $ (not with length $ k $ ) has the following property: - If you multiply the first element by $ 2^0 $ , the second element by $ 2^1 $ , ..., and the ( $ k+1 $ )-st element by $ 2^k $ , then this subarray is sorted in strictly increasing order. More formally, count the number of indices $ 1 \leq i \leq n - k $ such that $ $$$2^0 \cdot a_i < 2^1 \cdot a_{i+1} < 2^2 \cdot a_{i+2} < \dots < 2^k \cdot a_{i+k}. $ $$$

N/A

N/A

In the first test case, both subarrays satisfy the condition: - $ i=1 $ : the subarray $ [a_1,a_2,a_3] = [20,22,19] $ , and $ 1 \cdot 20 < 2 \cdot 22 < 4 \cdot 19 $ . - $ i=2 $ : the subarray $ [a_2,a_3,a_4] = [22,19,84] $ , and $ 1 \cdot 22 < 2 \cdot 19 < 4 \cdot 84 $ . In the second test case, three subarrays satisfy the condition: - $ i=1 $ : the subarray $ [a_1,a_2] = [9,5] $ , and $ 1 \cdot 9 < 2 \cdot 5 $ . - $ i=2 $ : the subarray $ [a_2,a_3] = [5,3] $ , and $ 1 \cdot 5 < 2 \cdot 3 $ . - $ i=3 $ : the subarray $ [a_3,a_4] = [3,2] $ , and $ 1 \cdot 3 < 2 \cdot 2 $ . - $ i=4 $ : the subarray $ [a_4,a_5] = [2,1] $ , but $ 1 \cdot 2 = 2 \cdot 1 $ , so this subarray doesn't satisfy the condition.