对于一个排好序的数列nums, nums[i] % nums[j] = 0 且 nums[j] % nums[k] = 0 则有 nums[i] % nums[k] = 0.
因此可以用动态规划:
用maxpos记录该子列的结尾元素下标;
数组num用num[i]记录以nums[i]为结尾元素的满足条件的子列的最大元素个数;
数组index用index[i]记录可以整除nums[i]的最大元素nums[j]的下标j;
则有,若nums[i] % nums[j] = 0, 则 num[i] = num[j] + 1 以及 index[i] = j.
代码如下:
class Solution {
public:
vector<int> largestDivisibleSubset(vector<int>& nums) {
if (nums.size() == 0 || nums.size() == 1) {
return nums;
}
sort(nums.begin(), nums.end());
int max = 1, maxpos = 0;
int *num = new int[nums.size()];
int *index = new int[nums.size()];
num[0] = 1; index[0] = -1;
for (int i = 1; i < nums.size(); i++) {
num[i] = 1; index[i] = -1;
for (int j = 0; j < i; j++) {
if (nums[i] % nums[j] == 0) {
num[i] = num[j] + 1;
index[i] = j;
if (max < num[i]) {
max = num[i];
maxpos = i;
}
}
}
}
vector<int> ans;
int i = maxpos;
while (i != -1) {
ans.push_back(nums[i]);
i = index[i];
}
return ans;
}
};