problems(cpp): add „363. Max Sum of Rectangle No Larger Than K“

Signed-off-by: Matej Focko <mfocko@redhat.com>

problems/max-sum-of-rectangle-no-larger-than-k.cpp

@@ -0,0 +1,54 @@
+#include <set>
+#include <vector>
+
+class Solution {
+    void row_partial_sums(const std::vector<std::vector<int>>& matrix, std::size_t y, std::vector<int>& partial) const
+    {
+        for (std::size_t x = 0; x < partial.size(); x++) {
+            partial[x] += matrix[y][x];
+        }
+    }
+
+    int find(std::vector<int>& partial_sums, int k) const
+    {
+        int max_sum = INT_MIN;
+
+        std::set<int> prefixes;
+        prefixes.insert(0);
+
+        int running_sum = 0;
+        for (auto partial : partial_sums) {
+            running_sum += partial;
+
+            auto found = prefixes.lower_bound(running_sum - k);
+            if (found != prefixes.end()) {
+                max_sum = std::max(max_sum, running_sum - *found);
+            }
+
+            prefixes.insert(running_sum);
+        }
+
+        return max_sum;
+    }
+
+public:
+    int maxSumSubmatrix(const std::vector<std::vector<int>>& matrix, int k) const
+    {
+        std::size_t rows = matrix.size();
+        std::size_t cols = matrix.front().size();
+
+        int max_sum = INT_MIN;
+
+        for (std::size_t y_min = 0; y_min < rows; y_min++) {
+            std::vector<int> partial_sums(cols, 0);
+
+            for (std::size_t y_max = y_min; y_max < rows; y_max++) {
+                row_partial_sums(matrix, y_max, partial_sums);
+                int maximum = find(partial_sums, k);
+                max_sum = std::max(max_sum, maximum);
+            }
+        }
+
+        return max_sum;
+    }
+};