LeetCode 1498: Number of Subsequences That Satisfy the Given Sum Condition Solution

Master LeetCode problem 1498 (Number of Subsequences That Satisfy the Given Sum Condition), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1498. Number of Subsequences That Satisfy the Given Sum Condition

Medium

Array Two Pointers Binary Search Sorting

Problem Explanation

Explanation

To solve this problem, we can use a two-pointer approach along with sorting the input array. We will sort the array nums and then iterate through it using two pointers left and right. We will consider all possible subsequences where nums[left] + nums[right] <= target and count the number of valid subsequences. The total number of valid subsequences will be 2^(right-left) for each pair of left and right.

Time Complexity

The time complexity of this approach is O(N*logN) where N is the length of the input array nums.

Space Complexity

The space complexity is O(1) as we are not using any extra space other than a few variables.

Solution Code

class Solution {
    public int numSubseq(int[] nums, int target) {
        int mod = 1000000007;
        int n = nums.length;
        Arrays.sort(nums);
        
        int left = 0, right = n - 1;
        long res = 0;
        
        int[] pow = new int[n];
        pow[0] = 1;
        for (int i = 1; i < n; i++) {
            pow[i] = (pow[i-1] * 2) % mod;
        }
        
        while (left <= right) {
            if (nums[left] + nums[right] <= target) {
                res = (res + pow[right - left]) % mod;
                left++;
            } else {
                right--;
            }
        }
        
        return (int) res;
    }
}

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