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Find the largest area rectangular sub-matrix whose sum is equal to k in C++
Suppose we have a 2D matrix mat and a value K, we have to find the longest rectangular submatrix whose sum is same as K.
So, if the input is like
| 2 | 8 | -5 | 6 |
| -7 | 7 | 8 | -3 |
| 11 | -14 | 4 | 3 |
| -4 | 3 | 1 | 10 |
And K = 9
then the output will be Top-Left point is (1, 0) and Bottom-Right point is (3, 2).
| -7 | 7 | 8 |
| 11 | -14 | 4 |
| -4 | 3 | 1 |
To solve this, we will follow these steps −
MAX := 100
Define a function sum_k(), this will take one array arr, start, end, n, k,
Define one map
sum := 0, maximum_length := 0
for initialize i := 0, when i < n, update (increase i by 1), do −
sum := sum + arr[i]
if sum is same as k, then −
maximum_length := i + 1
start := 0
end := i
if sum is not in map, then −
map[sum] := i
if (sum - k) is in map, then −
if maximum_length < (i - map[sum - k]), then −
maximum_length := i - map[sum - k]
start := map[sum - k] + 1
end := i
return true when maximum_length is not 0
From the main method, do the following −
row := row count of mat, col := column count of mat
Define an array temp of size: row.
Define an array final_point = {0,0,0,0}
maxArea := -inf
for initialize left := 0, when left < col, update (increase left by 1), do −
fill temp with 0
for initialize right := left, when right < col, update (increase right by 1), do −
for initialize i := 0, when i < row, update (increase i by 1), do −
temp[i] := temp[i] + mat[i, right]
sum := sum_k(temp, up, down, row, k)
area := (down - up + 1) * (right - left + 1)
if sum is non-zero and maxArea < area, then −
final_point[0] := up, final_point[1] := down
final_point[2] := left, final_point[3] := right
maxArea := area
if final_point is [0,0,0,0] and mat[0,0] is not k, then
return "No sub - matrix found"
display top-left point (final_point[0], final_point[2])
display bottom-right point (final_point[1], final_point[3])
display mat elements.
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
const int MAX = 100;
bool sum_k(int arr[], int& start, int& end, int n, int k) {
unordered_map<int, int> map;
int sum = 0, maximum_length = 0;
for (int i = 0; i < n; i++) {
sum += arr[i];
if (sum == k) {
maximum_length = i + 1;
start = 0;
end = i;
}
if (map.find(sum) == map.end())
map[sum] = i;
if (map.find(sum - k) != map.end()) {
if (maximum_length < (i - map[sum - k])) {
maximum_length = i - map[sum - k];
start = map[sum - k] + 1;
end = i;
}
}
}
return (maximum_length != 0);
}
void sum_zero(vector<vector<int>> &mat, int k) {
int row = mat.size();
int col = mat[0].size();
int temp[row], area;
bool sum;
int up, down;
vector<int> final_point = {0,0,0,0};
int maxArea = INT_MIN;
for (int left = 0; left < col; left++) {
memset(temp, 0, sizeof(temp));
for (int right = left; right < col; right++) {
for (int i = 0; i < row; i++)
temp[i] += mat[i][right];
sum = sum_k(temp, up, down, row, k);
area = (down - up + 1) * (right - left + 1);
if (sum && maxArea < area) {
final_point[0] = up;
final_point[1] = down;
final_point[2] = left;
final_point[3] = right;
maxArea = area;
}
}
}
if (final_point[0] == 0 && final_point[1] == 0 && final_point[2] == 0 &&
final_point[3] == 0 && mat[0][0] != k) {
cout << "No sub-matrix found";
return;
}
cout << "(Top, Left) Coordinate: " << "(" << final_point[0] << ", " << final_point[2] << ")" << endl;
cout << "(Bottom, Right) Coordinate: " << "(" << final_point[1] << ", " << final_point[3] << ")" << endl;
for (int j = final_point[0]; j <= final_point[1]; j++) {
for (int i = final_point[2]; i <= final_point[3]; i++)
cout << mat[j][i] << " ";
cout << endl;
}
}
main(){
vector<vector<int>> v = {
{ 2, 8, -5, 6 },
{ -7, 7, 8, -3 },
{ 11, -14, 4, 3 },
{ -4, 3, 1, 10 }};
sum_zero(v, 9);
}Input
{{ 2, 8, -5, 6 },
{ -7, 7, 8, -3 },
{ 11, -14, 4, 3 },
{ -4, 3, 1, 10 }},
9Output
(Top, Left) Coordinate: (1, 0) (Bottom, Right) Coordinate: (3, 2) -7 7 8 11 -14 4 -4 3 1
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