原题链接在这里:https://leetcode.com/problems/3sum-with-multiplicity/

题目:

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

As the answer can be very large, return it modulo 10^9 + 7.

Example 1:

Input: A = [1,1,2,2,3,3,4,4,5,5], target = 8
Output: 20
Explanation:
Enumerating by the values (A[i], A[j], A[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: A = [1,1,2,2,2,2], target = 5
Output: 12
Explanation:
A[i] = 1, A[j] = A[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.

Note:

  1. 3 <= A.length <= 3000
  2. 0 <= A[i] <= 100
  3. 0 <= target <= 300

题解:

Perform 3Sum and find the target.

Here there are 2 cases:

1. A[l] != A[r], count the frequency of A[l] and A[r], possible number of tuples is leftCount*rightCount.

e.g. 2333, A[l] = 2, A[r] = 3, leftCount = 1, rightCount = 3, number of types is 1*3 = 3.

2. A[l] == A[r], number of tupes is count*(count-1)/2.

e.g. 222, A[l] = 2, A[r] = 2, number of tupes 3*2/2 = 3. There are 3 ways to pick 2 elements from it.

Time Compelxity: O(n^2). n = A.length.

Space: O(1).

AC Java:

 class Solution {
public int threeSumMulti(int[] A, int target) {
if(A == null || A.length == 0){
return 0;
} int res = 0;
int M = 1000000000+7;
Arrays.sort(A);
for(int i = 0; i<A.length-2; i++){
int l = i+1;
int r = A.length-1;
while(l<r){
int sum = A[i] + A[l] + A[r];
if(sum < target){
l++;
}else if(sum > target){
r--;
}else if(A[l] != A[r]){
int leftCount = 1;
int rightCount = 1;
while(l+1<r && A[l]==A[l+1]){
leftCount++;
l++;
} while(l+1<r && A[r]==A[r-1]){
rightCount++;
r--;
} res += leftCount*rightCount;
res = res%M;
l++;
r--;
}else{
// A[l] == A[r]
res += (r-l+1)*(r-l)/2;
res = res%M;
break;
}
}
} return res;
}
}

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