cpp: add «368. Largest Divisible Subset»

Signed-off-by: Matej Focko <me@mfocko.xyz>

cpp/largest-divisble-subset.cpp

@@ -0,0 +1,61 @@
+#include <algorithm>
+#include <cassert>
+#include <vector>
+
+struct Solution {
+    std::vector<int> largestDivisibleSubset(std::vector<int> nums) {
+        std::sort(nums.begin(), nums.end());
+
+        solver s(nums);
+        s.solve();
+        return s.result;
+    }
+
+  private:
+    struct solver {
+        const std::vector<int> &nums;
+        int n;
+        std::vector<std::size_t> dp;
+        std::vector<int> tmp;
+        std::vector<int> result;
+
+        solver(const std::vector<int> &nums)
+            : nums(nums), n(nums.size()), dp(nums.size() + 1, 0) {}
+
+        void solve() { solve(0); }
+
+        void solve(int i) {
+            if (i >= n) {
+                if (tmp.size() > result.size()) {
+                    result = tmp;
+                }
+
+                return;
+            }
+
+            if (tmp.empty() ||
+                (tmp.size() > dp[i] && nums[i] % tmp.back() == 0)) {
+                dp[i] = std::max(dp[i], tmp.size());
+
+                tmp.push_back(nums[i]);
+                solve(i + 1);
+                tmp.pop_back();
+            }
+
+            solve(i + 1);
+        }
+    };
+};
+
+int main() {
+    Solution s;
+
+    assert(
+        (s.largestDivisibleSubset(std::vector{1, 2, 3}) == std::vector{1, 2}));
+    assert((s.largestDivisibleSubset(std::vector{1, 2, 4, 8}) ==
+            std::vector{1, 2, 4, 8}));
+    assert((s.largestDivisibleSubset(std::vector{3, 4, 16, 8}) ==
+            std::vector{4, 8, 16}));
+
+    return 0;
+}