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1995. 统计特殊四元组

English Version

题目描述

给你一个 下标从 0 开始 的整数数组 nums ，返回满足下述条件的 不同 四元组 (a, b, c, d) 的 数目 ：

• nums[a] + nums[b] + nums[c] == nums[d] ，且
• a < b < c < d

 

示例 1：

输入：nums = [1,2,3,6]
输出：1
解释：满足要求的唯一一个四元组是 (0, 1, 2, 3) 因为 1 + 2 + 3 == 6 。

示例 2：

输入：nums = [3,3,6,4,5]
输出：0
解释：[3,3,6,4,5] 中不存在满足要求的四元组。

示例 3：

输入：nums = [1,1,1,3,5]
输出：4
解释：满足要求的 4 个四元组如下：
- (0, 1, 2, 3): 1 + 1 + 1 == 3
- (0, 1, 3, 4): 1 + 1 + 3 == 5
- (0, 2, 3, 4): 1 + 1 + 3 == 5
- (1, 2, 3, 4): 1 + 1 + 3 == 5

 

提示：

• 4 <= nums.length <= 50
• 1 <= nums[i] <= 100

解法

直接暴力枚举，或者用哈希表实现。

Python3

class Solution:
    def countQuadruplets(self, nums: List[int]) -> int:
        ans, n = 0, len(nums)
        for a in range(n - 3):
            for b in range(a + 1, n - 2):
                for c in range(b + 1, n - 1):
                    for d in range(c + 1, n):
                        if nums[a] + nums[b] + nums[c] == nums[d]:
                            ans += 1
        return ans

class Solution:
    def countQuadruplets(self, nums: List[int]) -> int:
        ans, n = 0, len(nums)
        counter = Counter()
        for c in range(n - 2, 1, -1):
            counter[nums[c + 1]] += 1
            for a in range(c - 1):
                for b in range(a + 1, c):
                    ans += counter[nums[a] + nums[b] + nums[c]]
        return ans

class Solution:
    def countQuadruplets(self, nums: List[int]) -> int:
        ans, n = 0, len(nums)
        counter = Counter()
        for b in range(n - 3, 0, -1):
            c = b + 1
            for d in range(c + 1, n):
                counter[nums[d] - nums[c]] += 1
            for a in range(b):
                ans += counter[nums[a] + nums[b]]
        return ans

Java

class Solution {
    public int countQuadruplets(int[] nums) {
        int ans = 0, n = nums.length;
        for (int a = 0; a < n - 3; ++a) {
            for (int b = a + 1; b < n - 2; ++b) {
                for (int c = b + 1; c < n - 1; ++c) {
                    for (int d = c + 1; d < n; ++d) {
                        if (nums[a] + nums[b] + nums[c] == nums[d]) {
                            ++ans;
                        }
                    }
                }
            }
        }
        return ans;
    }
}

class Solution {
    public int countQuadruplets(int[] nums) {
        int ans = 0, n = nums.length;
        int[] counter = new int[310];
        for (int c = n - 2; c > 1; --c) {
            ++counter[nums[c + 1]];
            for (int a = 0; a < c - 1; ++a) {
                for (int b = a + 1; b < c; ++b) {
                    ans += counter[nums[a] + nums[b] + nums[c]];
                }
            }
        }
        return ans;
    }
}

class Solution {
    public int countQuadruplets(int[] nums) {
        int ans = 0, n = nums.length;
        int[] counter = new int[310];
        for (int b = n - 3; b > 0; --b) {
            int c = b + 1;
            for (int d = c + 1; d < n; ++d) {
                if (nums[d] - nums[c] >= 0) {
                    ++counter[nums[d] - nums[c]];
                }
            }
            for (int a = 0; a < b; ++a) {
                ans += counter[nums[a] + nums[b]];
            }
        }
        return ans;
    }
}

C++

class Solution {
public:
    int countQuadruplets(vector<int>& nums) {
        int ans = 0, n = nums.size();
        for (int a = 0; a < n - 3; ++a)
            for (int b = a + 1; b < n - 2; ++b)
                for (int c = b + 1; c < n - 1; ++c)
                    for (int d = c + 1; d < n; ++d)
                        if (nums[a] + nums[b] + nums[c] == nums[d]) ++ans;
        return ans;
    }
};

class Solution {
public:
    int countQuadruplets(vector<int>& nums) {
        int ans = 0, n = nums.size();
        vector<int> counter(310);
        for (int c = n - 2; c > 1; --c)
        {
            ++counter[nums[c + 1]];
            for (int a = 0; a < c - 1; ++a)
            {
                for (int b = a + 1; b < c; ++b)
                {
                    ans += counter[nums[a] + nums[b] + nums[c]];
                }
            }
        }
        return ans;
    }
};

class Solution {
public:
    int countQuadruplets(vector<int>& nums) {
        int ans = 0, n = nums.size();
        vector<int> counter(310);
        for (int b = n - 3; b > 0; --b)
        {
            int c = b + 1;
            for (int d = c + 1; d < n; ++d)
            {
                if (nums[d] - nums[c] >= 0)
                {
                    ++counter[nums[d] - nums[c]];
                }
            }
            for (int a = 0; a < b; ++a) {
                ans += counter[nums[a] + nums[b]];
            }
        }
        return ans;
    }
};

Go

func countQuadruplets(nums []int) int {
	ans, n := 0, len(nums)
	for a := 0; a < n-3; a++ {
		for b := a + 1; b < n-2; b++ {
			for c := b + 1; c < n-1; c++ {
				for d := c + 1; d < n; d++ {
					if nums[a]+nums[b]+nums[c] == nums[d] {
						ans++
					}
				}
			}
		}
	}
	return ans
}

func countQuadruplets(nums []int) int {
	ans, n := 0, len(nums)
	counter := make([]int, 310)
	for c := n - 2; c > 1; c-- {
		counter[nums[c+1]]++
		for a := 0; a < c-1; a++ {
			for b := a + 1; b < c; b++ {
				ans += counter[nums[a]+nums[b]+nums[c]]
			}
		}
	}
	return ans
}

func countQuadruplets(nums []int) int {
	ans, n := 0, len(nums)
	counter := make([]int, 310)
	for b := n - 3; b > 0; b-- {
		c := b + 1
		for d := c + 1; d < n; d++ {
			if nums[d] >= nums[c] {
				counter[nums[d]-nums[c]]++
			}
		}
		for a := 0; a < b; a++ {
			ans += counter[nums[a]+nums[b]]
		}
	}
	return ans
}

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