923. 3Sum With Multiplicity

Given an integer array arr, and an integer target, return the number of tuples i, j, k such that i < j < k and arr[i] + arr[j] + arr[k] == target.

As the answer can be very large, return it modulo 109 + 7.

 

Example 1:

Input: arr = [1,1,2,2,3,3,4,4,5,5], target = 8
Output: 20
Explanation: 
Enumerating by the values (arr[i], arr[j], arr[k]):
(1, 2, 5) occurs 8 times;
(1, 3, 4) occurs 8 times;
(2, 2, 4) occurs 2 times;
(2, 3, 3) occurs 2 times.

Example 2:

Input: arr = [1,1,2,2,2,2], target = 5
Output: 12
Explanation: 
arr[i] = 1, arr[j] = arr[k] = 2 occurs 12 times:
We choose one 1 from [1,1] in 2 ways,
and two 2s from [2,2,2,2] in 6 ways.

 

Constraints:

  • 3 <= arr.length <= 3000
  • 0 <= arr[i] <= 100
  • 0 <= target <= 300

Rust Solution

struct Solution;

const MOD: usize = 1_000_000_007;

impl Solution {
    fn three_sum_multi(a: Vec<i32>, target: i32) -> i32 {
        let mut count = vec![0; 101];
        for x in a {
            count[x as usize] += 1;
        }
        let mut res = 0;
        for x in 0..101 {
            for y in x + 1..101 {
                if x + y >= target as usize {
                    break;
                }
                for z in y + 1..101 {
                    if x + y + z > target as usize {
                        break;
                    }
                    if x + y + z == target as usize {
                        res += count[x] * count[y] * count[z];
                        res %= MOD;
                    }
                }
            }
        }
        for x in 0..101 {
            for y in x + 1..101 {
                if x + x + y != target as usize {
                    continue;
                }
                if count[x] > 1 {
                    res += count[x] * (count[x] - 1) / 2 * count[y];
                    res %= MOD;
                }
            }
        }
        for x in 0..101 {
            for y in x + 1..101 {
                if x + y + y != target as usize {
                    continue;
                }
                if count[y] > 1 {
                    res += count[x] * count[y] * (count[y] - 1) / 2;
                    res %= MOD;
                }
            }
        }
        for x in 0..101 {
            if x + x + x != target as usize {
                continue;
            }
            if count[x] > 2 {
                res += count[x] * (count[x] - 1) * (count[x] - 2) / 6;
                res %= MOD;
            }
        }
        res as i32
    }
}

#[test]
fn test() {
    let a = vec![1, 1, 2, 2, 3, 3, 4, 4, 5, 5];
    let target = 8;
    let res = 20;
    assert_eq!(Solution::three_sum_multi(a, target), res);
    let a = vec![1, 1, 2, 2, 2, 2];
    let target = 5;
    let res = 12;
    assert_eq!(Solution::three_sum_multi(a, target), res);
}

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