Find Smallest Common Element in All Rows

Find Smallest Common Element in All Rows - Problem

Given an m x n matrix mat where every row is sorted in strictly increasing order, return the smallest common element in all rows.

If there is no common element, return -1.

Input & Output

Example 1 — Basic Case

$ Input: mat = [[1,2,3,4,5],[2,4,5,8,10],[3,5,7,9,11]]

› Output: 5

💡 Note: Element 5 appears in all three rows: row 0 at index 4, row 1 at index 2, and row 2 at index 1. It's the smallest such common element.

Example 2 — No Common Element

$ Input: mat = [[1,2,3],[4,5,6],[7,8,9]]

› Output: -1

💡 Note: No element appears in all three rows. Each row has completely different elements, so return -1.

Example 3 — Multiple Common Elements

$ Input: mat = [[1,2,3,4,5],[1,3,5,7,9],[1,4,5,8,9]]

› Output: 1

💡 Note: Elements 1 and 5 appear in all rows, but 1 is smaller than 5, so return 1.

Constraints

1 ≤ m, n ≤ 500
1 ≤ mat[i][j] ≤ 10⁴
mat[i] is sorted in strictly increasing order

Visualization

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Asked in

G Google 25 a Amazon 18 M Microsoft 12

The key insight is to leverage the sorted property of each row. Start with elements from the first row as candidates and efficiently check their presence in other rows using binary search. The binary search approach provides optimal performance with Time: O(n × m × log n), Space: O(1).

Common Approaches

✓ Binary Search Optimization

⏱️ Time: O(n × m × log n) Space: O(1)

Since each row is sorted, we can use binary search to efficiently check if each element from the first row exists in all other rows. This reduces the time complexity significantly.

Brute Force - Check Each Element

⏱️ Time: O(m × n²) Space: O(1)

Iterate through each element in the first row, then for each element, check if it appears in all other rows by scanning each row linearly.

Frequency Count with Hash Map

⏱️ Time: O(m × n) Space: O(m × n)

Use a hash map to count how many rows each element appears in. The first element (when iterating in sorted order) that appears in all m rows is our answer.

Binary Search Optimization — Algorithm Steps

Take each element from first row as candidate
Use binary search to check existence in each other row
Return first element found in all rows

Visualization

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Step-by-Step Walkthrough

Pick Candidate

Take element from first row

Binary Search

Use binary search in each other row

Found or Continue

If found in all rows, return; else try next

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

bool binarySearch(int* arr, int size, int target) {
    int left = 0, right = size - 1;
    while (left <= right) {
        int mid = left + (right - left) / 2;
        if (arr[mid] == target) {
            return true;
        } else if (arr[mid] < target) {
            left = mid + 1;
        } else {
            right = mid - 1;
        }
    }
    return false;
}

int solution(int** mat, int matSize, int* matColSize) {
    if (matSize == 0 || matColSize[0] == 0) return -1;
    
    int m = matSize, n = matColSize[0];
    
    // Check each element in first row
    for (int j = 0; j < n; j++) {
        int candidate = mat[0][j];
        bool foundInAll = true;
        
        // Check if this element exists in all other rows using binary search
        for (int i = 1; i < m; i++) {
            if (!binarySearch(mat[i], matColSize[i], candidate)) {
                foundInAll = false;
                break;
            }
        }
        
        if (foundInAll) return candidate;
    }
    
    return -1;
}

int main() {
    // Simplified parsing - assume valid input format
    int mat1[] = {1, 2, 3, 4, 5};
    int mat2[] = {2, 4, 5, 8, 10};
    int mat3[] = {3, 5, 7, 9, 11};
    int* mat[] = {mat1, mat2, mat3};
    int matColSize[] = {5, 5, 5};
    
    printf("%d\n", solution(mat, 3, matColSize));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × m × log n)

For each of n elements in first row, binary search in m-1 other rows takes log n time

⚡ Linearithmic

Space Complexity

O(1)

Only using constant extra variables for binary search

✓ Linear Space

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Medium Frequency

~15 min Avg. Time

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Ln 1, Col 1

Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Binary Search Optimization — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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