Posts published in “Algorithms”

花花酱 LeetCode 2643. Row With Maximum Ones

By zxi on April 28, 2023

Given a m x n binary matrix mat, find the 0-indexed position of the row that contains the maximum count of ones, and the number of ones in that row.

In case there are multiple rows that have the maximum count of ones, the row with the smallest row number should be selected.

Return an array containing the index of the row, and the number of ones in it.

Example 1:

Input: mat = [[0,1],[1,0]]
Output: [0,1]
Explanation: Both rows have the same number of 1's. So we return the index of the smaller row, 0, and the maximum count of ones (1). So, the answer is [0,1].

Example 2:

Input: mat = [[0,0,0],[0,1,1]]
Output: [1,2]
Explanation: The row indexed 1 has the maximum count of ones (2). So we return its index, 1, and the count. So, the answer is [1,2].

Example 3:

Input: mat = [[0,0],[1,1],[0,0]]
Output: [1,2]
Explanation: The row indexed 1 has the maximum count of ones (2). So the answer is [1,2].

Constraints:

m == mat.length
n == mat[i].length
1 <= m, n <= 100
mat[i][j] is either 0 or 1.

Solution: Counting

Time complexity: O(m*n)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

vector<int> rowAndMaximumOnes(vector<vector<int>>& mat) {

vector<int> ans(2);

for (int i = 0; i < mat.size(); ++i) {

int ones = accumulate(begin(mat[i]), end(mat[i]), 0);

if (ones > ans[1]) {

ans[0] = i;

ans[1] = ones;

}

return ans;

}

};

花花酱 LeetCode 2574. Left and Right Sum Differences

By zxi on February 25, 2023

Given a 0-indexed integer array nums, find a 0-indexed integer array answer where:

answer.length == nums.length.
answer[i] = |leftSum[i] - rightSum[i]|.

Where:

leftSum[i] is the sum of elements to the left of the index i in the array nums. If there is no such element, leftSum[i] = 0.
rightSum[i] is the sum of elements to the right of the index i in the array nums. If there is no such element, rightSum[i] = 0.

Return the array answer.

Example 1:

Input: nums = [10,4,8,3]
Output: [15,1,11,22]
Explanation: The array leftSum is [0,10,14,22] and the array rightSum is [15,11,3,0].
The array answer is [|0 - 15|,|10 - 11|,|14 - 3|,|22 - 0|] = [15,1,11,22].

Example 2:

Input: nums = [1]
Output: [0]
Explanation: The array leftSum is [0] and the array rightSum is [0].
The array answer is [|0 - 0|] = [0].

Constraints:

1 <= nums.length <= 1000
1 <= nums[i] <= 10⁵

Solution: O(1) Space

Pre-compute the sum of all numbers as right sum, and accumulate left sum on the fly then we can achieve O(1) space.

Time complexity: O(n)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

vector<int> leftRigthDifference(vector<int>& nums) {

int right = accumulate(begin(nums), end(nums), 0);

vector<int> ans;

for (int i = 0, left = 0; i < nums.size(); ++i) {

right -= nums[i];

ans.push_back(abs(left - right));

left += nums[i];

}

return ans;

}

};

花花酱 LeetCode 2562. Find the Array Concatenation Value

By zxi on February 12, 2023

You are given a 0-indexed integer array nums.

The concatenation of two numbers is the number formed by concatenating their numerals.

For example, the concatenation of 15, 49 is 1549.

The concatenation value of nums is initially equal to 0. Perform this operation until nums becomes empty:

If there exists more than one number in nums, pick the first element and last element in nums respectively and add the value of their concatenation to the concatenation value of nums, then delete the first and last element from nums.
If one element exists, add its value to the concatenation value of nums, then delete it.

Return the concatenation value of the nums.

Example 1:

Input: nums = [7,52,2,4]
Output: 596
Explanation: Before performing any operation, nums is [7,52,2,4] and concatenation value is 0.
 - In the first operation:
We pick the first element, 7, and the last element, 4.
Their concatenation is 74, and we add it to the concatenation value, so it becomes equal to 74.
Then we delete them from nums, so nums becomes equal to [52,2].
 - In the second operation:
We pick the first element, 52, and the last element, 2.
Their concatenation is 522, and we add it to the concatenation value, so it becomes equal to 596.
Then we delete them from the nums, so nums becomes empty.
Since the concatenation value is 596 so the answer is 596.

Example 2:

Input: nums = [5,14,13,8,12]
Output: 673
Explanation: Before performing any operation, nums is [5,14,13,8,12] and concatenation value is 0.
 - In the first operation:
We pick the first element, 5, and the last element, 12.
Their concatenation is 512, and we add it to the concatenation value, so it becomes equal to 512.
Then we delete them from the nums, so nums becomes equal to [14,13,8].
 - In the second operation:
We pick the first element, 14, and the last element, 8.
Their concatenation is 148, and we add it to the concatenation value, so it becomes equal to 660.
Then we delete them from the nums, so nums becomes equal to [13].
 - In the third operation:
nums has only one element, so we pick 13 and add it to the concatenation value, so it becomes equal to 673.
Then we delete it from nums, so nums become empty.
Since the concatenation value is 673 so the answer is 673.

Constraints:

1 <= nums.length <= 1000
1 <= nums[i] <= 10⁴

Solution: Follow the rules

Time complexity: O(sum(log(nums[i]))
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

long long findTheArrayConcVal(vector<int>& nums) {

long long ans = 0;

const int n = nums.size();

for (int i = 0; i < n / 2; ++i) {

int cur = nums[i];

for (int t = nums[n - i - 1]; t > 0; t /= 10)

cur *= 10;

cur += nums[n - i - 1];

ans += cur;

}

if (n & 1) ans += nums[n / 2];

return ans;

}

};

花花酱 LeetCode 2560. House Robber IV

By zxi on February 4, 2023

There are several consecutive houses along a street, each of which has some money inside. There is also a robber, who wants to steal money from the homes, but he refuses to steal from adjacent homes.

The capability of the robber is the maximum amount of money he steals from one house of all the houses he robbed.

You are given an integer array nums representing how much money is stashed in each house. More formally, the i^th house from the left has nums[i] dollars.

You are also given an integer k, representing the minimum number of houses the robber will steal from. It is always possible to steal at least k houses.

Return the minimum capability of the robber out of all the possible ways to steal at least k houses.

Example 1:

Input: nums = [2,3,5,9], k = 2
Output: 5
Explanation: 
There are three ways to rob at least 2 houses:
- Rob the houses at indices 0 and 2. Capability is max(nums[0], nums[2]) = 5.
- Rob the houses at indices 0 and 3. Capability is max(nums[0], nums[3]) = 9.
- Rob the houses at indices 1 and 3. Capability is max(nums[1], nums[3]) = 9.
Therefore, we return min(5, 9, 9) = 5.

Example 2:

Input: nums = [2,7,9,3,1], k = 2
Output: 2
Explanation: There are 7 ways to rob the houses. The way which leads to minimum capability is to rob the house at index 0 and 4. Return max(nums[0], nums[4]) = 2.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁹
1 <= k <= (nums.length + 1)/2

Solution 1: Binary Search + DP

It’s easy to see that higher capability means more houses we can rob. Thus this can be formulate as a binary search algorithm e.g. find the minimum C s.t. we can rob at least k houses.

Then we can use dp(i) to calculate maximum houses we can rob if starting from the i’th house.
dp(i) = max(1 + dp(i + 2) if nums[i] <= C else 0, dp(i + 1))

Time complexity: O(n log m)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

int minCapability(vector<int>& nums, int k) {

int l = 0;

int r = *max_element(begin(nums), end(nums)) + 1;

vector<int> cache(nums.size(), -1);

function<int(int, int)> rob = [&](int m, int i) -> int {

if (i >= nums.size()) return 0;

if (cache[i] >= 0) return cache[i];

if (nums[i] > m) return rob(m, i + 1);

return cache[i] = max(1 + rob(m, i + 2), rob(m, i + 1));

};

while (l < r) {

int m = l + (r - l) / 2;

fill(begin(cache), end(cache), -1);

if (rob(m, 0) >= k)

r = m;

else

l = m + 1;

}

return l;

}

};

Solution 2: Binary Search + Greedy

From: dp(i) = max(1 + dp(i + 2) if nums[i] <= C else 0, dp(i + 1)) we can see that if we can pick the i-th one, it will be the same or better if we skip and start from dp(i + 1). Thus we can convert this from DP to greedy. As long as we can pick the current one, we pick it first.

Time complexity: O(n log m)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

int minCapability(vector<int>& nums, int k) {

int l = 0;

int r = *max_element(begin(nums), end(nums)) + 1;

auto rob = [&](int m) -> int {

int ans = 0;

for (int i = 0; i < nums.size(); ++i)

if (nums[i] <= m) {

++ans;

++i;

}

return ans;

};

while (l < r) {

int m = l + (r - l) / 2;

if (rob(m) >= k)

r = m;

else

l = m + 1;

}

return l;

}

};

花花酱 LeetCode 2559. Count Vowel Strings in Ranges

By zxi on February 4, 2023

You are given a 0-indexed array of strings words and a 2D array of integers queries.

Each query queries[i] = [l_i, r_i] asks us to find the number of strings present in the range l_i to r_i (both inclusive) of words that start and end with a vowel.

Return an array ans of size queries.length, where ans[i] is the answer to the i^th query.

Note that the vowel letters are 'a', 'e', 'i', 'o', and 'u'.

Example 1:

Input: words = ["aba","bcb","ece","aa","e"], queries = [[0,2],[1,4],[1,1]]
Output: [2,3,0]
Explanation: The strings starting and ending with a vowel are "aba", "ece", "aa" and "e".
The answer to the query [0,2] is 2 (strings "aba" and "ece").
to query [1,4] is 3 (strings "ece", "aa", "e").
to query [1,1] is 0.
We return [2,3,0].

Example 2:

Input: words = ["a","e","i"], queries = [[0,2],[0,1],[2,2]]
Output: [3,2,1]
Explanation: Every string satisfies the conditions, so we return [3,2,1].

Constraints:

1 <= words.length <= 10⁵
1 <= words[i].length <= 40
words[i] consists only of lowercase English letters.
sum(words[i].length) <= 3 * 10⁵
1 <= queries.length <= 10⁵
0 <= l_i <= r_i < words.length

Solution: Prefix Sum

Let sum[i] := number of valid strings in words[0:i]

For each query [l, r], answer will be sum[r + 1] – sum[l]

Time complexity: O(n + q)
Space complexity: O(n)

C++

// Author: Huahua

class Solution {

public:

vector<int> vowelStrings(vector<string>& words, vector<vector<int>>& queries) {

const size_t n = words.size();

vector<int> sum(n + 1);

auto check = [](char c) {

return c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u';

};

for (size_t i = 0; i < n; ++i)

sum[i + 1] = sum[i] +

(check(words[i][0]) && check(words[i][words[i].size() - 1]));

vector<int> ans;

for (const auto& q : queries)

ans.push_back(sum[q[1] + 1] - sum[q[0]]);

return ans;

}

};