1498. Number of Subsequences That Satisfy the Given Sum Condition

Medium

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 <= 10^5

• 1 <= nums[i] <= 10^6

• 1 <= target <= 10^6

解題

這題一直過不了，後來發現是直接使用 math.Pow(float64(x), float64(y)) 的話會 overflow！

可以執行下面程式看看，會發現到某個數之後，印出來的都是 -9223372036854775808

package main

import (
	"fmt"
	"math"
)

func main() {
	for i := 0; i < 10000; i++ { //題目 nums 長度最大 10000
		fmt.Println(powInt(2, i))
	}
}

func powInt(x, y int) int {
	return int(math.Pow(float64(x), float64(y)))
}

func numSubseq(nums []int, target int) int {
    sort.Ints(nums)
    left, right := 0, len(nums)-1

    ans := 0
    
    pow2 := make([]int, len(nums)+1)
	pow2[0] = 1
	for i := 1; i <= len(nums); i++ {
		pow2[i] = (pow2[i-1] * 2)  % 1000000007
	}

    
	for left <= right {
		if nums[left] + nums[right] <= target {
			ans += pow2[right-left]
			left++
		} else {
			right--
		}
	}

    return ans % 1000000007
}