Question

377. Combination Sum IV

中文文档

Description

Given an array of distinct integers nums and a target integer target, return _the number of possible combinations that add up to_ target.

The test cases are generated so that the answer can fit in a 32-bit integer.

 

Example 1:

Input: nums = [1,2,3], target = 4
Output: 7
Explanation:
The possible combination ways are:
(1, 1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 3)
(2, 1, 1)
(2, 2)
(3, 1)
Note that different sequences are counted as different combinations.

Example 2:

Input: nums = [9], target = 3
Output: 0

 

Constraints:

• 1 <= nums.length <= 200
• 1 <= nums[i] <= 1000
• All the elements of nums are unique.
• 1 <= target <= 1000

 

Follow up: What if negative numbers are allowed in the given array? How does it change the problem? What limitation we need to add to the question to allow negative numbers?

Solutions

Solution 1

class Solution:
  def combinationSum4(self, nums: List[int], target: int) -> int:
    f = [1] + [0] * target
    for i in range(1, target + 1):
      for x in nums:
        if i >= x:
          f[i] += f[i - x]
    return f[target]

class Solution {
  public int combinationSum4(int[] nums, int target) {
    int[] f = new int[target + 1];
    f[0] = 1;
    for (int i = 1; i <= target; ++i) {
      for (int x : nums) {
        if (i >= x) {
          f[i] += f[i - x];
        }
      }
    }
    return f[target];
  }
}

class Solution {
public:
  int combinationSum4(vector<int>& nums, int target) {
    int f[target + 1];
    memset(f, 0, sizeof(f));
    f[0] = 1;
    for (int i = 1; i <= target; ++i) {
      for (int x : nums) {
        if (i >= x && f[i - x] < INT_MAX - f[i]) {
          f[i] += f[i - x];
        }
      }
    }
    return f[target];
  }
};

func combinationSum4(nums []int, target int) int {
  f := make([]int, target+1)
  f[0] = 1
  for i := 1; i <= target; i++ {
    for _, x := range nums {
      if i >= x {
        f[i] += f[i-x]
      }
    }
  }
  return f[target]
}

function combinationSum4(nums: number[], target: number): number {
  const f: number[] = new Array(target + 1).fill(0);
  f[0] = 1;
  for (let i = 1; i <= target; ++i) {
    for (const x of nums) {
      if (i >= x) {
        f[i] += f[i - x];
      }
    }
  }
  return f[target];
}

/**
 * @param {number[]} nums
 * @param {number} target
 * @return {number}
 */
var combinationSum4 = function (nums, target) {
  const f = new Array(target + 1).fill(0);
  f[0] = 1;
  for (let i = 1; i <= target; ++i) {
    for (const x of nums) {
      if (i >= x) {
        f[i] += f[i - x];
      }
    }
  }
  return f[target];
};

public class Solution {
  public int CombinationSum4(int[] nums, int target) {
    int[] f = new int[target + 1];
    f[0] = 1;
    for (int i = 1; i <= target; ++i) {
      foreach (int x in nums) {
        if (i >= x) {
          f[i] += f[i - x];
        }
      }
    }
    return f[target];
  }
}