2023-05-06 Daily Challenge

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In: DailyChallenge

Today I have done leetcode's May LeetCoding Challenge with cpp.

May LeetCoding Challenge 6

Description

Number of Subsequences That Satisfy the Given Sum Condition

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 109 + 7.

 

Example 1:

Input: nums = [3,5,6,7], target = 9
Output: 4
Explanation: There are 4 subsequences that satisfy the condition.
[3] -> Min value + max value <= target (3 + 3 <= 9)
[3,5] -> (3 + 5 <= 9)
[3,5,6] -> (3 + 6 <= 9)
[3,6] -> (3 + 6 <= 9)

Example 2:

Input: nums = [3,3,6,8], target = 10
Output: 6
Explanation: There are 6 subsequences that satisfy the condition. (nums can have repeated numbers).
[3] , [3] , [3,3], [3,6] , [3,6] , [3,3,6]

Example 3:

Input: nums = [2,3,3,4,6,7], target = 12
Output: 61
Explanation: There are 63 non-empty subsequences, two of them do not satisfy the condition ([6,7], [7]).
Number of valid subsequences (63 - 2 = 61).

 

Constraints:

  • 1 <= nums.length <= 105
  • 1 <= nums[i] <= 106
  • 1 <= target <= 106

Solution

auto speedup = [](){
  cin.tie(nullptr);
  cout.tie(nullptr);
  ios::sync_with_stdio(false);
  return 0;
}();
const int MOD = 1e9 + 7;
int qpow(int b, int e) {
  int result = 1;
  while(e) {
    if(e & 1) {
      result = 1LL * result * b % MOD;
    }
    b = 1LL * b * b % MOD;
    e >>= 1;
  }
  return result;
}
class Solution {
public:
  int numSubseq(vector<int>& nums, int target) {
    sort(nums.begin(), nums.end());
    int left = 0;
    int right = nums.size() - 1;
    int answer = 0;
    while(left <= right && left < nums.size()) {
      while(right >= 0 && left <= right && nums[left] + nums[right] > target) {
        right -= 1;
      }
      if(right < 0) break;
      if(left < right) {
        answer += qpow(2, right - left);
      } else if (nums[left] * 2 <= target) {
        answer += 1;
      }
      answer %= MOD;
      left += 1;
    }

    return answer;
  }
};

// Accepted
// 62/62 cases passed (126 ms)
// Your runtime beats 89.87 % of cpp submissions
// Your memory usage beats 93.20 % of cpp submissions (47.6 MB)
Algorithm