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Program to find sum of rectangle whose sum at most k in Python
Suppose we have a 2d matrix and another value k, we have to find the largest sum of a rectangle where sum ≤ k.
So, if the input is like
| 5 | −2 |
| 7 | 10 |
and k = 15, then the output will be 12, as we can take the rectangle [5, 7] to get sum of 12 less than 15.
To solve this, we will follow these steps −
n := row count of a
m := column count of a
ans := inf
for i1 in range 0 to n, do
row := a list of size m and fill with 0
for i2 in range i1 to n, do
for j in range 0 to m, do
row[j] := row[j] + a[i2, j]
s := a new set
insert 0 into s
sum := 0
for j in range 0 to m, do
sum := sum + row[j];
temp := a list for all items in s which is larger than (sum − k)
if size of temp > 0, then
u := minimum of temp
ans := maximum of ans and (sum − u)
insert sum into s
return ans
Let us see the following implementation to get better understanding −
Example
class Solution: def solve(self, a, k): n = len(a) if n == 0: return 0; m = len(a[0]) ans = -999999; for i1 in range(n): row = [0]*m; for i2 in range(i1, n): for j in range(m): row[j] += a[i2][j] s = set() s.add(0) sum = 0 for j in range(m): sum += row[j]; temp = [e for e in s if e > (sum − k)] if len(temp) > 0: u = min(temp) ans = max(ans, sum − u) s.add(sum) return ans ob = Solution() matrix = [ [5, −2], [7, 10] ] k = 15 print(ob.solve(matrix, k))
Input
[ [5, −2], [7, 10] ], 15
Output
12
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