Create lc363. Max Sum of Rectangle No Larger Than K-dp-hard.md

Author: tmp-coder

leetcode/lc363. Max Sum of Rectangle No Larger Than K-dp-hard.md

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+```cpp
+class Solution {
+public:
+    int maxSum(vector<vector<int>>& matrix, int k){
+        int n = matrix.size();
+        if(n ==0)
+            return 0;
+        int m = matrix[0].size();
+        set<int> lower;
+        
+        vector<int> sum(n+1,0);
+        vector<int> col_sum(n,0);
+        int ans = INT32_MIN /2;
+        for(int l = 0 ; l<m ; ++l){
+            // fill_n(sum.begin(), 0, m+1);
+            // fill_n(col_sum.begin(), 0, m);
+            fill(sum.begin(), sum.end(),0);
+            fill(col_sum.begin(),col_sum.end(),0);
+            // vector<int> sum(m+1,0);
+            // vector<int> col_sum(m,0);
+            // cout << "======== l = "<< l << "=========\n";
+            for(int r = l ;r <m ; ++r){
+                lower.clear();
+                lower.insert(0);
+                // cout << "======== r = "<< r <<"============\n"; 
+                for(int i=0 ; i<n ; ++i){
+                    col_sum[i] +=  matrix[i][r];
+                    sum[i+1] =sum[i] + col_sum[i];
+                    // cout << col_sum[i] << " " <<sum[i+1]<<"\n" ;
+                    int find = sum[i+1] - k;
+                    auto it = lower.lower_bound(find);
+                    if (it != lower.end()){
+                        // cout << *it << " " << r<< " " << i << "\n";
+                        ans = max(ans, sum[i+1] - *it);
+                    }
+                    lower.insert(sum[i+1]);
+                }
+                // cout << "\n";
+            }
+            // cout << "\n";
+        }
+        return ans;
+    }
+    int maxSumSubmatrix(vector<vector<int>>& matrix, int k) {
+        int n = matrix.size();
+        if(n ==0)
+            return 0;
+        int m = matrix[0].size();
+        if(n > m ){
+            return maxSum(matrix,k);
+        }
+        set<int> lower;
+        
+        vector<int> sum(m+1,0);
+        vector<int> col_sum(m,0);
+        int ans = INT32_MIN /2;
+        for(int l = 0 ; l<n ; ++l){
+            // fill_n(sum.begin(), 0, m+1);
+            // fill_n(col_sum.begin(), 0, m);
+            fill(sum.begin(), sum.end(),0);
+            fill(col_sum.begin(),col_sum.end(),0);
+            // vector<int> sum(m+1,0);
+            // vector<int> col_sum(m,0);
+            // cout << "======== l = "<< l << "=========\n";
+            for(int r = l ;r <n ; ++r){
+                lower.clear();
+                lower.insert(0);
+                // cout << "======== r = "<< r <<"============\n"; 
+                for(int i=0 ; i<m ; ++i){
+                    col_sum[i] +=  matrix[r][i];
+                    sum[i+1] =sum[i] + col_sum[i];
+                    // cout << col_sum[i] << " " <<sum[i+1]<<"\n" ;
+                    int find = sum[i+1] - k;
+                    auto it = lower.lower_bound(find);
+                    if (it != lower.end()){
+                        // cout << *it << " " << r<< " " << i << "\n";
+                        ans = max(ans, sum[i+1] - *it);
+                    }
+                    lower.insert(sum[i+1]);
+                }
+            }
+        }
+        return ans;
+    }
+};
+
+```