# 1868. Product of Two Run-Length Encoded Arrays

## Description

Run-length encoding is a compression algorithm that allows for an integer array nums with many segments of consecutive repeated numbers to be represented by a (generally smaller) 2D array encoded. Each encoded[i] = [vali, freqi] describes the ith segment of repeated numbers in nums where vali is the value that is repeated freqi times.

• For example, nums = [1,1,1,2,2,2,2,2] is represented by the run-length encoded array encoded = [[1,3],[2,5]]. Another way to read this is "three 1's followed by five 2's".

The product of two run-length encoded arrays encoded1 and encoded2 can be calculated using the following steps:

1. Expand both encoded1 and encoded2 into the full arrays nums1 and nums2 respectively.
2. Create a new array prodNums of length nums1.length and set prodNums[i] = nums1[i] * nums2[i].
3. Compress prodNums into a run-length encoded array and return it.

You are given two run-length encoded arrays encoded1 and encoded2 representing full arrays nums1 and nums2 respectively. Both nums1 and nums2 have the same length. Each encoded1[i] = [vali, freqi] describes the ith segment of nums1, and each encoded2[j] = [valj, freqj] describes the jth segment of nums2.

Return the product of encoded1 and encoded2.

Note: Compression should be done such that the run-length encoded array has the minimum possible length.

Example 1:

Input: encoded1 = [[1,3],[2,3]], encoded2 = [[6,3],[3,3]]
Output: [[6,6]]
Explanation: encoded1 expands to [1,1,1,2,2,2] and encoded2 expands to [6,6,6,3,3,3].
prodNums = [6,6,6,6,6,6], which is compressed into the run-length encoded array [[6,6]].


Example 2:

Input: encoded1 = [[1,3],[2,1],[3,2]], encoded2 = [[2,3],[3,3]]
Output: [[2,3],[6,1],[9,2]]
Explanation: encoded1 expands to [1,1,1,2,3,3] and encoded2 expands to [2,2,2,3,3,3].
prodNums = [2,2,2,6,9,9], which is compressed into the run-length encoded array [[2,3],[6,1],[9,2]].


Constraints:

• 1 <= encoded1.length, encoded2.length <= 105
• encoded1[i].length == 2
• encoded2[j].length == 2
• 1 <= vali, freqi <= 104 for each encoded1[i].
• 1 <= valj, freqj <= 104 for each encoded2[j].
• The full arrays that encoded1 and encoded2 represent are the same length.

## Solutions

• class Solution {
public List<List<Integer>> findRLEArray(int[][] encoded1, int[][] encoded2) {
List<List<Integer>> ans = new ArrayList<>();
int j = 0;
for (var e : encoded1) {
int vi = e[0], fi = e[1];
while (fi > 0) {
int f = Math.min(fi, encoded2[j][1]);
int v = vi * encoded2[j][0];
int m = ans.size();
if (m > 0 && ans.get(m - 1).get(0) == v) {
ans.get(m - 1).set(1, ans.get(m - 1).get(1) + f);
} else {
}
fi -= f;
encoded2[j][1] -= f;
if (encoded2[j][1] == 0) {
++j;
}
}
}
return ans;
}
}

• class Solution {
public:
vector<vector<int>> findRLEArray(vector<vector<int>>& encoded1, vector<vector<int>>& encoded2) {
vector<vector<int>> ans;
int j = 0;
for (auto& e : encoded1) {
int vi = e[0], fi = e[1];
while (fi) {
int f = min(fi, encoded2[j][1]);
int v = vi * encoded2[j][0];
if (!ans.empty() && ans.back()[0] == v) {
ans.back()[1] += f;
} else {
ans.push_back({v, f});
}
fi -= f;
encoded2[j][1] -= f;
if (encoded2[j][1] == 0) {
++j;
}
}
}
return ans;
}
};

• class Solution:
def findRLEArray(
self, encoded1: List[List[int]], encoded2: List[List[int]]
) -> List[List[int]]:
ans = []
j = 0
for vi, fi in encoded1:
while fi:
f = min(fi, encoded2[j][1])
v = vi * encoded2[j][0]
if ans and ans[-1][0] == v:
ans[-1][1] += f
else:
ans.append([v, f])
fi -= f
encoded2[j][1] -= f
if encoded2[j][1] == 0:
j += 1
return ans


• func findRLEArray(encoded1 [][]int, encoded2 [][]int) (ans [][]int) {
j := 0
for _, e := range encoded1 {
vi, fi := e[0], e[1]
for fi > 0 {
f := min(fi, encoded2[j][1])
v := vi * encoded2[j][0]
if len(ans) > 0 && ans[len(ans)-1][0] == v {
ans[len(ans)-1][1] += f
} else {
ans = append(ans, []int{v, f})
}
fi -= f
encoded2[j][1] -= f
if encoded2[j][1] == 0 {
j++
}
}
}
return
}