Print all elements in sorted order from row and column wise sorted matrix
Given an n x n matrix, where every row and column is sorted in non-decreasing order. Print all elements of matrix in sorted order.
Example:
Input: mat[][] = { {10, 20, 30, 40},
{15, 25, 35, 45},
{27, 29, 37, 48},
{32, 33, 39, 50},
};
Output:
Elements of matrix in sorted order
10 15 20 25 27 29 30 32 33 35 37 39 40 45 48 50
We can use Young Tableau to solve the above problem. The idea is to consider given 2D array as Young Tableau and call extract minimum O(N)
C++
// A C++ program to Print all elements in sorted order from row and // column wise sorted matrix #include<iostream> #include<climits> using namespace std; #define INF INT_MAX #define N 4 // A utility function to youngify a Young Tableau. This is different // from standard youngify. It assumes that the value at mat[0][0] is // infinite. void youngify(int mat[][N], int i, int j) { // Find the values at down and right sides of mat[i][j] int downVal = (i+1 < N)? mat[i+1][j]: INF; int rightVal = (j+1 < N)? mat[i][j+1]: INF; // If mat[i][j] is the down right corner element, return if (downVal==INF && rightVal==INF) return; // Move the smaller of two values (downVal and rightVal) to // mat[i][j] and recur for smaller value if (downVal < rightVal) { mat[i][j] = downVal; mat[i+1][j] = INF; youngify(mat, i+1, j); } else { mat[i][j] = rightVal; mat[i][j+1] = INF; youngify(mat, i, j+1); } } // A utility function to extract minimum element from Young tableau int extractMin(int mat[][N]) { int ret = mat[0][0]; mat[0][0] = INF; youngify(mat, 0, 0); return ret; } // This function uses extractMin() to print elements in sorted order void printSorted(int mat[][N]) { cout << "Elements of matrix in sorted order n"; for (int i=0; i<N*N; i++) cout << extractMin(mat) << " "; } // driver program to test above function int main() { int mat[N][N] = { {10, 20, 30, 40}, {15, 25, 35, 45}, {27, 29, 37, 48}, {32, 33, 39, 50}, }; printSorted(mat); return 0; } |
chevron_right
filter_none
Java
// A Java program to Print all elements // in sorted order from row and // column wise sorted matrix class GFG { static final int INF = Integer.MAX_VALUE; static final int N = 4; // A utility function to youngify a Young Tableau. // This is different from standard youngify. // It assumes that the value at mat[0][0] is infinite. static void youngify(int mat[][], int i, int j) { // Find the values at down and right sides of mat[i][j] int downVal = (i + 1 < N) ? mat[i + 1][j] : INF; int rightVal = (j + 1 < N) ? mat[i][j + 1] : INF; // If mat[i][j] is the down right corner element, // return if (downVal == INF && rightVal == INF) { return; } // Move the smaller of two values // (downVal and rightVal) to mat[i][j] // and recur for smaller value if (downVal < rightVal) { mat[i][j] = downVal; mat[i + 1][j] = INF; youngify(mat, i + 1, j); } else { mat[i][j] = rightVal; mat[i][j + 1] = INF; youngify(mat, i, j + 1); } } // A utility function to extract // minimum element from Young tableau static int extractMin(int mat[][]) { int ret = mat[0][0]; mat[0][0] = INF; youngify(mat, 0, 0); return ret; } // This function uses extractMin() // to print elements in sorted order static void printSorted(int mat[][]) { System.out.println("Elements of matrix in sorted order n"); for (int i = 0; i < N * N; i++) { System.out.print(extractMin(mat) + " "); } } // Driver Code public static void main(String args[]) { int mat[][] = {{10, 20, 30, 40}, {15, 25, 35, 45}, {27, 29, 37, 48}, {32, 33, 39, 50}}; printSorted(mat); } } // This code is contributed by Rajput-Ji |
chevron_right
filter_none
Python 3
# Python 3 program to Print all elements # in sorted order from row and column # wise sorted matrix import sys INF = sys.maxsize N = 4 # A utility function to youngify a Young # Tableau. This is different from standard # youngify. It assumes that the value at # mat[0][0] is infinite. def youngify(mat, i, j): # Find the values at down and # right sides of mat[i][j] downVal = mat[i + 1][j] if (i + 1 < N) else INF rightVal = mat[i][j + 1] if (j + 1 < N) else INF # If mat[i][j] is the down right # corner element, return if (downVal == INF and rightVal == INF): return # Move the smaller of two values # (downVal and rightVal) to mat[i][j] # and recur for smaller value if (downVal < rightVal): mat[i][j] = downVal mat[i + 1][j] = INF youngify(mat, i + 1, j) else: mat[i][j] = rightVal mat[i][j + 1] = INF youngify(mat, i, j + 1) # A utility function to extract minimum # element from Young tableau def extractMin(mat): ret = mat[0][0] mat[0][0] = INF youngify(mat, 0, 0) return ret # This function uses extractMin() to # print elements in sorted order def printSorted(mat): print("Elements of matrix in sorted order n") i = 0 while i < N * N: print(extractMin(mat), end = " ") i += 1 # Driver Code if __name__ == "__main__": mat = [[10, 20, 30, 40], [15, 25, 35, 45], [27, 29, 37, 48], [32, 33, 39, 50]] printSorted(mat) # This code is contributed by ita_c |
chevron_right
filter_none
C#
// A C# program to Print all elements // in sorted order from row and // column wise sorted matrix using System; class GFG { static int INF = int.MaxValue; static int N = 4; // A utility function to youngify a Young Tableau. // This is different from standard youngify. // It assumes that the value at mat[0][0] is infinite. static void youngify(int [,]mat, int i, int j) { // Find the values at down and right sides of mat[i][j] int downVal = (i + 1 < N) ? mat[i + 1,j] : INF; int rightVal = (j + 1 < N) ? mat[i,j + 1] : INF; // If mat[i][j] is the down right corner element, // return if (downVal == INF && rightVal == INF) { return; } // Move the smaller of two values // (downVal and rightVal) to mat[i][j] // and recur for smaller value if (downVal < rightVal) { mat[i,j] = downVal; mat[i + 1,j] = INF; youngify(mat, i + 1, j); } else { mat[i, j] = rightVal; mat[i, j + 1] = INF; youngify(mat, i, j + 1); } } // A utility function to extract // minimum element from Young tableau static int extractMin(int [,]mat) { int ret = mat[0,0]; mat[0, 0] = INF; youngify(mat, 0, 0); return ret; } // This function uses extractMin() // to print elements in sorted order static void printSorted(int [,]mat) { Console.WriteLine("Elements of matrix in sorted order n"); for (int i = 0; i < N * N; i++) { Console.Write(extractMin(mat) + " "); } } // Driver Code static public void Main () { int [,]mat = {{10, 20, 30, 40}, {15, 25, 35, 45}, {27, 29, 37, 48}, {32, 33, 39, 50}}; printSorted(mat); } } // This code is contributed by ajit. |
chevron_right
filter_none
Output:
Elements of matrix in sorted order 10 15 20 25 27 29 30 32 33 35 37 39 40 45 48 50
Time complexity of extract minimum is O(N) and it is called O(N2) times. Therefore the overall time complexity is O(N3).
A better solution is to use the approach used for merging k sorted arrays. The idea is to use a Min Heap of size N which stores elements of first column. The do extract minimum. In extract minimum, replace the minimum element with the next element of the row from which the element is extracted. Time complexity of this solution is O(N2LogN).
// C++ program to merge k sorted arrays of size n each. #include<iostream> #include<climits> using namespace std; #define N 4 // A min heap node struct MinHeapNode { int element; // The element to be stored int i; // index of the row from which the element is taken int j; // index of the next element to be picked from row }; // Prototype of a utility function to swap two min heap nodes void swap(MinHeapNode *x, MinHeapNode *y); // A class for Min Heap class MinHeap { MinHeapNode *harr; // pointer to array of elements in heap int heap_size; // size of min heap public: // Constructor: creates a min heap of given size MinHeap(MinHeapNode a[], int size); // to heapify a subtree with root at given index void MinHeapify(int ); // to get index of left child of node at index i int left(int i) { return (2*i + 1); } // to get index of right child of node at index i int right(int i) { return (2*i + 2); } // to get the root MinHeapNode getMin() { return harr[0]; } // to replace root with new node x and heapify() new root void replaceMin(MinHeapNode x) { harr[0] = x; MinHeapify(0); } }; // This function prints elements of a given matrix in non-decreasing // order. It assumes that ma[][] is sorted row wise sorted. void printSorted(int mat[][N]) { // Create a min heap with k heap nodes. Every heap node // has first element of an array MinHeapNode *harr = new MinHeapNode[N]; for (int i = 0; i < N; i++) { harr[i].element = mat[i][0]; // Store the first element harr[i].i = i; // index of row harr[i].j = 1; // Index of next element to be stored from row } MinHeap hp(harr, N); // Create the min heap // Now one by one get the minimum element from min // heap and replace it with next element of its array for (int count = 0; count < N*N; count++) { // Get the minimum element and store it in output MinHeapNode root = hp.getMin(); cout << root.element << " "; // Find the next elelement that will replace current // root of heap. The next element belongs to same // array as the current root. if (root.j < N) { root.element = mat[root.i][root.j]; root.j += 1; } // If root was the last element of its array else root.element = INT_MAX; //INT_MAX is for infinite // Replace root with next element of array hp.replaceMin(root); } } // FOLLOWING ARE IMPLEMENTATIONS OF STANDARD MIN HEAP METHODS // FROM CORMEN BOOK // Constructor: Builds a heap from a given array a[] of given size MinHeap::MinHeap(MinHeapNode a[], int size) { heap_size = size; harr = a; // store address of array int i = (heap_size - 1)/2; while (i >= 0) { MinHeapify(i); i--; } } // A recursive method to heapify a subtree with root at given index // This method assumes that the subtrees are already heapified void MinHeap::MinHeapify(int i) { int l = left(i); int r = right(i); int smallest = i; if (l < heap_size && harr[l].element < harr[i].element) smallest = l; if (r < heap_size && harr[r].element < harr[smallest].element) smallest = r; if (smallest != i) { swap(&harr[i], &harr[smallest]); MinHeapify(smallest); } } // A utility function to swap two elements void swap(MinHeapNode *x, MinHeapNode *y) { MinHeapNode temp = *x; *x = *y; *y = temp; } // driver program to test above function int main() { int mat[N][N] = { {10, 20, 30, 40}, {15, 25, 35, 45}, {27, 29, 37, 48}, {32, 33, 39, 50}, }; printSorted(mat); return 0; } |
chevron_right
filter_none
Output:
10 15 20 25 27 29 30 32 33 35 37 39 40 45 48 50
Exercise:
Above solutions work for a square matrix. Extend the above solutions to work for an M*N rectangular matrix.
This article is contributed by Varun. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
