# Diagonal Traverse Problem

## Description

LeetCode Problem 498.

Given an m x n matrix mat, return an array of all the elements of the array in a diagonal order.

Example 1:

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

Example 2:

``````1
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Input: mat = [[1,2],[3,4]]
Output: [1,2,3,4]
``````

Constraints:

• m == mat.length
• n == mat[i].length
• 1 <= m, n <= 10^4
• 1 <= m * n <= 10^4
• -10^5 <= mat[i][j] <= 10^5

## Sample C++ Code

The index sum (say it is i) of each round is from 0 to n+m-1. If the column index is j, then the row index is i-j. We need to ensure that j is in [0, m-1], and i-j is in [0, n-1]. Then j’s value is between min(i, m-1) and max(i-n+1, 0).

``````1
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class Solution {
public:
vector<int> findDiagonalOrder(vector<vector<int>>& matrix) {
if (matrix.empty())
return {};
vector<int>res;
int n = matrix.size(), m = matrix[0].size();
for (int i = 0; i < n + m - 1; i++) {
if (i & 1) {
for (int j = min(i, m - 1); j >= max(i - n + 1, 0); j--)
res.push_back(matrix[i - j][j]);
} else {
for (int j = max(i - n + 1, 0); j <= min(i, m - 1); j++)
res.push_back(matrix[i - j][j]);
}
}
return res;
}
};
``````