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Maximum Side Length of a Square with Sum Less than or Equal to Threshold in C++
Suppose we have a m x n matrix mat and an integer threshold. We have to the maximum side-length of a square with a sum less than or equal to the given threshold or return 0 if there is no such square. So if the input is like −
1 | 1 | 3 | 2 | 4 | 3 | 2 |
1 | 1 | 3 | 2 | 4 | 3 | 2 |
1 | 1 | 3 | 2 | 4 | 3 | 2 |
1 | 1 | 3 | 2 | 4 | 3 | 2 |
1 | 1 | 3 | 2 | 4 | 3 | 2 |
1 | 1 | 3 | 2 | 4 | 3 | 2 |
And threshold is 4, then output will be 2, as there are two squares of side length 2, so max is 2
To solve this, we will follow these steps −
- Define a method called ok, this will take x and matrix m and threshold th
- set curr := 0
- for i in range x – 1 to number of rows of mat – 1
- for c in range x – 1 to number of cols of mat – 1
- curr := mat[r, c]
- if c – x >= 0, then decrease curr by mat[r, c – x]
- if r – x >= 0, then decrease curr by mat[r - x, c]
- if c – x >= 0 and r – x >= 0, then increase curr by mat[r – x, c - x]
- if curr <= th, then return true
- for c in range x – 1 to number of cols of mat – 1
- return false
- In the main method, it will take matrix and threshold
- r := number of rows, c := number of columns, low := 1, high := min of r and c, ans := 0
- for i in range 1 to c – 1
- for j in range 0 to c – 1
- increase mat[j, i] by mat[j, i - 1]
- for j in range 0 to c – 1
- for i in range 1 to r – 1
- for j in range 0 to c – 1
- increase mat[j, i] by mat[ i - 1,j]
- for j in range 0 to c – 1
- while low <= high:
- mid := low + (high - low) / 2
- if of(mid, mat, th), then ans := mid and low := mid + 1, otherwise high := mid – 1
- return ans
Example(C++)
Let us see the following implementation to get a better understanding −
#include <bits/stdc++.h> using namespace std; typedef long long int lli; class Solution { public: bool ok(int x, vector < vector<int> >& mat, int th){ lli current = 0; for(int r = x - 1; r < mat.size(); r++){ for(int c = x - 1; c < mat[0].size(); c++){ current = mat[r][c]; if(c - x >= 0)current -= mat[r][c-x]; if(r -x >= 0)current -= mat[r - x][c]; if(c - x >= 0 && r - x >= 0)current += mat[r-x][c-x]; if(current <= th)return true; } } return false; } int maxSideLength(vector<vector<int>>& mat, int th) { int r = mat.size(); int c = mat[0].size(); int low = 1; int high = min(r, c); int ans = 0; for(int i = 1; i < c; i++){ for(int j = 0; j < r; j++){ mat[j][i] += mat[j][i - 1]; } } for(int i = 1; i < r; i++){ for(int j = 0; j < c; j++){ mat[i][j] += mat[i - 1][j]; } } while(low <= high){ int mid = low + ( high - low ) / 2; if(ok(mid, mat, th)){ ans = mid; low = mid + 1; } else{ high = mid - 1; } } return ans; } }; main(){ vector<vector<int>> v = {{1,1,3,2,4,3,2},{1,1,3,2,4,3,2},{1,1,3,2,4,3,2}}; Solution ob; cout << (ob.maxSideLength(v, 4)); }
Input
[[1,1,3,2,4,3,2],[1,1,3,2,4,3,2],[1,1,3,2,4,3,2]] 4
Output
2
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