805. Split Array With Same Average
In a given integer array A, we must move every element of A to either list B or list C. (B and C initially start empty.)
Return true if and only if after such a move, it is possible that the average value of B is equal to the average value of C, and B and C are both non-empty.
Example :
Input:
[1,2,3,4,5,6,7,8]
Output: true
Explanation: We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have the average of 4.5.
Note:
- The length of
A
will be in the range [1, 30].A[i]
will be in the range of[0, 10000]
.
Approach #1: DP. [Java]
class Solution {
public boolean splitArraySameAverage(int[] A) {
int sum = 0;
for (int num : A) {
sum += num;
} boolean[][] dp = new boolean[sum+1][A.length/2+1];
dp[0][0] = true; for (int num : A) {
for (int i = sum; i >= num; --i) {
for (int j = 1; j <= A.length/2; ++j) {
dp[i][j] = dp[i][j] || dp[i-num][j-1];
}
}
} for (int i = 1; i <= A.length/2; ++i)
if (sum * i % A.length == 0 && dp[sum * i / A.length][i])
return true; return false;
}
}
Approach #2: DFS. [Java]
class Solution {
public boolean check(int[] A, int leftSum, int leftNum, int startIndex) {
if (leftNum == 0) return leftSum == 0;
if ((A[startIndex]) > leftSum / leftNum) return false;
for (int i = startIndex; i < A.length - leftNum + 1; i ++) {
if (i > startIndex && A[i] == A[i - 1]) continue;
if (check(A, leftSum - A[i], leftNum - 1, i + 1)) return true;
}
return false;
} public boolean splitArraySameAverage(int[] A) {
if (A.length == 1) return false;
int sumA = 0;
for (int a: A) sumA += a;
Arrays.sort(A);
for (int lenOfB = 1; lenOfB <= A.length / 2; lenOfB ++) {
if ((sumA * lenOfB) % A.length == 0) {
if (check(A, (sumA * lenOfB) / A.length, lenOfB, 0)) return true;
}
}
return false; }
}
Analysis:
Can't understanding.
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