[leetcode-363]Max Sum of Rectangle No Larger Than K(java)

这道题我的想法就是使用暴力搜索，维护两个节点，第一个节点是矩阵的左上角，第二个节点是矩阵的右下角。然后在围起来的矩阵里面去计算面积。
假设矩阵的行为M，矩阵的列为N，那么上述算法的事件复杂度为O(MN*MN*MN)。因此肯定是不可行的。
于是只能采用用空间换取时间的方法，对于每个节点，将(0,0)看做矩阵的左上角，将当前节点看成矩阵的右下角，记录下当前节点对应的行和宽。
但是很不幸，代码TLE，原因在于，在计算面积时还是要有个for循环。

于是又更新了一般，这一版里面维护了以当前节点为右下角，以(0,0)为左上角的矩阵的面积。OK，通过！

代码1：

public class Solution {
    class Node{
        int totalRow;
        int totalCol;
        Node(int rowVal,int colVal){
            totalRow = rowVal;
            totalCol = colVal;
        }
    }
    public int maxSumSubmatrix(int[][] matrix, int k) {
        int row = matrix.length;
        int col = matrix[0].length;

        Node[][] totalMatrix = new Node[row][col];

        initTotalMatrix(matrix,totalMatrix);
        int max = Integer.MIN_VALUE;
        for(int rowUp = 0;rowUpfor(int colUp = 0;colUpfor(int rowDown = rowUp;rowDownfor(int colDown = colUp;colDownint res = getArea(matrix,totalMatrix,rowUp,colUp,rowDown,colDown);
                        if(res <= k){
                            if(res == k)
                                return res;
                            if(res > max)
                                max = res;
                        }
                    }
                }
            }
        }
        return max;
    }
    private int getArea(int[][] matrix,Node[][] totalMatrix,int upRow,int upCol,int downRow,int downCol){
         int col = downCol-upCol;
         int row = downRow-upRow;

         int res = 0;         
         if(col < row){
             for(int i = upCol;i<=downCol;i++){
                res += totalMatrix[downRow][i].totalCol - totalMatrix[upRow][i].totalCol + matrix[upRow][i];      
             }

         }else{
             for(int i = upRow;i<=downRow;i++){
                res += totalMatrix[i][downCol].totalRow - totalMatrix[i][upCol].totalRow + matrix[i][upCol];        
             }
         }
         return res;
    }
    private void initTotalMatrix(int[][] matrix,Node[][] totalMatrix){
        int row = matrix.length;
        int col = matrix[0].length;
        Node tmp;
        for(int i = 0;ifor(int j = 0;jnew Node(matrix[i][j],matrix[i][j]);
                totalMatrix[i][j] = tmp;
                if(i > 0){
                    Node prevRowNode = totalMatrix[i-1][j];
                    tmp.totalCol += prevRowNode.totalCol;
                }
                if(j > 0){
                    Node prevColNode = totalMatrix[i][j-1];
                    tmp.totalRow += prevColNode.totalRow;
                }
            }
        }
    }
}

更新后：

public class Solution {
    class AreaNode{
        int area;
        AreaNode(int area){
            this.area = area;
        }
    }
    class TotalNode{
        int totalRow;
        int totalCol;
        TotalNode(int row,int col){
            totalRow = row;
            totalCol = col;
        }
    }
    public int maxSumSubmatrix(int[][] matrix, int k) {
        int row = matrix.length;
        int col = matrix[0].length;

        AreaNode[][] areaMatrix = new AreaNode[row][col];//保存面积信息
        TotalNode[][] totalMatrix = new TotalNode[row][col];//保存行列信息

        initareaMatrix(matrix,areaMatrix,totalMatrix);
        int max = Integer.MIN_VALUE;
        for(int rowUp = 0;rowUpfor(int colUp = 0;colUpfor(int rowDown = rowUp;rowDownfor(int colDown = colUp;colDownint res = getArea(areaMatrix,totalMatrix,rowUp,colUp,rowDown,colDown) + matrix[rowUp][colUp];
                        if(res <= k){
                            if(res == k)
                                return res;
                            if(res > max)
                                max = res;
                        }
                    }
                }
            }
        }
        return max;
    }
    private int getArea(AreaNode[][] areaMatrix,TotalNode[][] totalMatrix,int upRow,int upCol,int downRow,int downCol){
        return areaMatrix[downRow][downCol].area - areaMatrix[upRow][downCol].area - areaMatrix[downRow][upCol].area
                + areaMatrix[upRow][upCol].area + totalMatrix[upRow][downCol].totalRow - totalMatrix[upRow][upCol].totalRow
                +totalMatrix[downRow][upCol].totalCol - totalMatrix[upRow][upCol].totalCol;
    }
    private void initareaMatrix(int[][] matrix,AreaNode[][] areaMatrix,TotalNode[][] totalMatrix){
        int row = matrix.length;
        int col = matrix[0].length;
        for(int i = 0;ifor(int j = 0;jint res = 0;
                int totalRow = matrix[i][j];
                int totalCol = matrix[i][j];

                if(i > 0){
                    res += areaMatrix[i-1][j].area;
                    totalCol += totalMatrix[i-1][j].totalCol;
                }
                if(j > 0){
                    res += areaMatrix[i][j-1].area;
                    totalRow += totalMatrix[i][j-1].totalRow;
                }
                if(i > 0&&j > 0){
                    res -= areaMatrix[i-1][j-1].area;
                }
                res += matrix[i][j];
                areaMatrix[i][j] = new AreaNode(res);
                totalMatrix[i][j] = new TotalNode(totalRow,totalCol);
            }
        }
    }
}