Create maximize-grid-happiness.cpp

Author: kamyu104

C++/maximize-grid-happiness.cpp

@@ -0,0 +1,123 @@
+// Time:  O(C(m * n, i) * C(m * n - i, e))
+// Space: O(min(m * n, i + e))
+
+class Solution {
+public:
+    int getMaxGridHappiness(int m, int n, int introvertsCount, int extrovertsCount) {
+        return iter_backtracking(m, n, introvertsCount, extrovertsCount);
+    }
+
+private:
+    int iter_backtracking(int m, int n, int i, int e) {
+        int result = 0;
+        vector<int> curr;
+        vector<tuple<int, int, int, int, int>> stk = {{2, i, e, 0, 0}};
+        while (!empty(stk)) {
+            const auto [step, i, e, total, x] = stk.back(); stk.pop_back();
+            if (step == 2) {
+                if ((size(curr) == m * n) || (i == 0 && e == 0)) {
+                    result = max(result, total);
+                    continue;
+                }
+                if (total + (i + e) * 120 < result) {  // pruning
+                    continue;
+                }
+                if (e > 0) {
+                    int new_total = count_total(n, curr, 2, total);
+                    stk.emplace_back(3, 0, 0, 0, 0);
+                    stk.emplace_back(2, i, e - 1, new_total, 0);
+                    stk.emplace_back(1, 0, 0, 0, 2);
+                }
+                if (i > 0) {
+                    int new_total = count_total(n, curr, 1, total);
+                    stk.emplace_back(3, 0, 0, 0, 0);
+                    stk.emplace_back(2, i - 1, e, new_total, 0);
+                    stk.emplace_back(1, 0, 0, 0, 1);
+                }
+                if (left(n, curr) || up(n, curr)) {  // leave unoccupied iff left or up is occupied
+                    stk.emplace_back(3, 0, 0, 0, 0);
+                    stk.emplace_back(2, i, e, total, 0);
+                    stk.emplace_back(1, 0, 0, 0, 0);
+                }
+            } else if (step == 1) {
+                curr.emplace_back(x);
+            } else if (step == 3) {
+                curr.pop_back();
+            }
+        }
+        return result;
+    }
+    
+    int left(int n, const vector<int>& curr) {
+        return (size(curr) % n) ? curr[size(curr) - 1] : 0;
+    }
+
+    int up(int n, const vector<int>& curr) {
+        return (size(curr) >= n) ? curr[size(curr) - n] : 0;
+    }
+
+    int count_total(int n, const vector<int>& curr, int t, int total) {
+        return (total
+	            - 30 * ((left(n, curr) == 1) + (up(n, curr) == 1))
+                + 20 * ((left(n, curr) == 2) + (up(n, curr) == 2))
+                + (120 - 30 * ((left(n, curr) != 0) + (up(n, curr) != 0))) * (t == 1)
+                + ( 40 + 20 * ((left(n, curr) != 0) + (up(n, curr) != 0))) * (t == 2));
+    }
+};
+
+// Time:  O(C(m * n, i) * C(m * n - i, e))
+// Space: O(min(m * n, i + e))
+class Solution2 {
+public:
+    int getMaxGridHappiness(int m, int n, int introvertsCount, int extrovertsCount) {
+        int result = 0;
+        vector<int> curr;
+        backtracking(m, n, introvertsCount, extrovertsCount, 0, &curr, &result);
+        return result;
+    }
+
+private:
+    void backtracking(int m, int n, int i, int e, int total,
+                      vector<int> *curr, int *result) {
+        if ((size(*curr) == m * n) || (i == 0 && e == 0)) {
+            *result = max(*result, total);
+            return;
+        }
+        if (total + (i + e) * 120 < *result) {  // pruning
+            return;
+        }
+        if (left(n, *curr) || up(n, *curr)) {  // leave unoccupied iff left or up is occupied
+            curr->emplace_back(0);
+            backtracking(m, n, i, e, total, curr, result);
+            curr->pop_back();
+        }
+        if (i > 0) {
+            int new_total = count_total(n, *curr, 1, total);
+            curr->emplace_back(1);
+            backtracking(m, n, i - 1, e, new_total, curr, result);
+            curr->pop_back();
+        }
+        if (e > 0) {
+            int new_total = count_total(n, *curr, 2, total);
+            curr->emplace_back(2);
+            backtracking(m, n, i, e - 1, new_total, curr, result);
+            curr->pop_back();
+        }
+    }
+    
+    int left(int n, const vector<int>& curr) {
+        return (size(curr) % n) ? curr[size(curr) - 1] : 0;
+    }
+
+    int up(int n, const vector<int>& curr) {
+        return (size(curr) >= n) ? curr[size(curr) - n] : 0;
+    }
+
+    int count_total(int n, const vector<int>& curr, int t, int total) {
+        return (total
+	            - 30 * ((left(n, curr) == 1) + (up(n, curr) == 1))
+                + 20 * ((left(n, curr) == 2) + (up(n, curr) == 2))
+                + (120 - 30 * ((left(n, curr) != 0) + (up(n, curr) != 0))) * (t == 1)
+                + ( 40 + 20 * ((left(n, curr) != 0) + (up(n, curr) != 0))) * (t == 2));
+    }
+};