Number of subsequences that satisfy the given sum condition

Array Two Pointers Binary Search Sorting

49.3% acceptance

Feb 25, 2026

4650

435

You are given an array of integers nums and an integer target. Return the number of non-empty subsequences of nums such that the sum of the minimum and maximum element on it is less or equal to target. Since the answer may be too large, return it modulo 10^9 + 7.

Solution

Rust

Time O(n log n)

Space O(n)

LeetCode

solution.rs

impl Solution {
  pub fn num_subseq(mut nums: Vec<i32>, target: i32) -> i32 {
    const MOD: i64 = 1_000_000_007;
    nums.sort_unstable();
    let n = nums.len();
    let mut pow2 = vec![1i64; n + 1];
    for i in 1..=n { pow2[i] = pow2[i - 1] * 2 % MOD; }
    let mut ans = 0i64;
    let (mut l, mut r) = (0usize, n - 1);
    while l <= r {
      if nums[l] + nums[r] <= target {
        ans = (ans + pow2[r - l]) % MOD;
        l += 1;
      } else {
        if r == 0 { break; }
        r -= 1;
      }
    }
    ans as i32
  }
}