June 8: LC DFS practice [M]

Time: O(N^2)

.clang-format

@@ -1,7 +1,7 @@
 BasedOnStyle: Google
 DerivePointerAlignment: false
 # PointerAlignment: Right
-# ColumnLimit: 120
+ColumnLimit: 120
 
 # Default for clang-8, changed in later clangs. Set explicitly for forwards
 # compatibility for students with modern clangs

daily/June8.cpp

@@ -0,0 +1,69 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+class Solution {
+ public:
+  /**
+   * @brief return the max operations needed to get same score II
+   * This time we have options, first two, last two or first and last
+   * So this is a DFS problem, use cache or dp
+   *
+   * @param nums
+   * @return int
+   */
+  int maxOperations(vector<int>& nums) {
+    int len = nums.size();
+    vector<vector<int>> memo(len, vector<int>(len));
+    auto helper = [&](int i, int j, int target) -> int {
+      for (auto& row : memo) {
+        std::fill(row.begin(), row.end(), -1);
+      }
+      function<int(int, int)> dfs = [&](int i, int j) -> int {
+        if (i >= j) return 0;
+        int& res = memo[i][j];      // reference
+        if (res != -1) return res;  // get this before
+        res = 0;
+        if (nums[i] + nums[i + 1] == target) res = max(res, dfs(i + 2, j) + 1);
+        if (nums[j] + nums[j - 1] == target) res = max(res, dfs(i, j - 2) + 1);
+        if (nums[i] + nums[j] == target) res = max(res, dfs(i + 1, j - 1) + 1);
+        return res;
+      };
+      return dfs(i, j);
+    };
+    int res1 = helper(2, len - 1, nums[0] + nums[1]);              // first two nums
+    int res2 = helper(0, len - 3, nums[len - 1] + nums[len - 2]);  // last two nums
+    int res3 = helper(1, len - 2, nums[0] + nums[len - 1]);        // first and last
+    return max({res1, res2, res3}) + 1;                            // add first op
+  }
+
+  int maxOperationsOp(vector<int>& nums) {
+    int len = nums.size();
+    vector<vector<int>> memo(len, vector<int>(len));
+    bool done = false;  // marker
+    auto helper = [&](int i, int j, int target) -> int {
+      if (done) return 0;
+      for (auto& row : memo) {
+        std::fill(row.begin(), row.end(), -1);  // no get before
+      }
+      function<int(int, int)> dfs = [&](int i, int j) -> int {
+        if (done) return 0;
+        if (i >= j) {
+          done = true;
+          return 0;
+        }
+        int& res = memo[i][j];
+        if (res != -1) return res;  // got before
+        res = 0;
+        if (nums[i] + nums[i + 1] == target) res = max(res, dfs(i + 2, j) + 1);
+        if (nums[j] + nums[j - 1] == target) res = max(res, dfs(i, j - 2) + 1);
+        if (nums[i] + nums[j] == target) res = max(res, dfs(i + 1, j - 1) + 1);
+        return res;
+      };
+      return dfs(i, j);
+    };
+    int res1 = helper(2, len - 1, nums[0] + nums[1]);              // first two
+    int res2 = helper(1, len - 2, nums[0] + nums[len - 1]);        // first and last
+    int res3 = helper(0, len - 3, nums[len - 1] + nums[len - 2]);  // last two
+    return max({res1, res2, res3}) + 1;                            // all max + 1 op
+  }
+};