Posts published in “Array”

花花酱 LeetCode 410. Split Array Largest Sum

By zxi on July 3, 2018

Problem

Given an array which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays. Write an algorithm to minimize the largest sum among these m subarrays.

Note:
If n is the length of array, assume the following constraints are satisfied:

1 ≤ n ≤ 1000
1 ≤ m ≤ min(50, n)

Examples:

Input:
nums = [7,2,5,10,8]
m = 2

Output:
18

Explanation:
There are four ways to split nums into two subarrays.
The best way is to split it into [7,2,5] and [10,8],
where the largest sum among the two subarrays is only 18.

Solution: DP

Time complexity: O(n^2*m)

Space complexity: O(n*m)

C++ / Recursion + Memorization

// Author: Huahua

// Running time: 111 ms

class Solution {

public:

int splitArray(vector<int>& nums, int m) {

const int n = nums.size();

sums_ = vector<int>(n);

mem_ = vector<vector<int>>(n, vector<int>(m + 1, INT_MAX));

sums_[0] = nums[0];

for (int i = 1; i < n; ++i)

sums_[i] = sums_[i - 1] + nums[i];

return splitArray(nums, n - 1, m);

}

private:

vector<vector<int>> mem_;

vector<int> sums_;

// min of largest sum of spliting nums[0] ~ nums[k] into m groups

int splitArray(const vector<int>& nums, int k, int m) {

if (m == 1) return sums_[k];

if (m > k + 1) return INT_MAX;

if (mem_[k][m] != INT_MAX) return mem_[k][m];

int ans = INT_MAX;

for (int i = 0; i < k; ++i)

ans = min(ans, max(splitArray(nums, i, m - 1), sums_[k] - sums_[i]));

return mem_[k][m] = ans;

}

};

C++ / DP

// Author: Huahua

// Running time: 90 ms

class Solution {

public:

int splitArray(vector<int>& nums, int m) {

const int n = nums.size();

vector<int> sums(n);

// dp[i][j] := min of largest sum of splitting nums[0] ~ nums[j] into i groups.

vector<vector<int>> dp(m + 1, vector<int>(n, INT_MAX));

sums[0] = nums[0];

for (int i = 1; i < n; ++i)

sums[i] = sums[i - 1] + nums[i];

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

dp[1][i] = sums[i];

for (int i = 2; i <= m; ++i)

for (int j = i - 1; j < n; ++j)

for (int k = 0; k < j; ++k)

dp[i][j] = min(dp[i][j], max(dp[i - 1][k], sums[j] - sums[k]));

return dp[m][n - 1];

}

};

Solution: Binary Search

Time complexity: O(log(sum(nums))*n)

Space complexity: O(1)

// Author: Huahua

// Running time: 3 ms

class Solution {

public:

int splitArray(vector<int>& nums, int m) {

long l = *max_element(begin(nums), end(nums));

long r = accumulate(begin(nums), end(nums), 0L) + 1;

while (l < r) {

long limit = (r - l) / 2 + l;

if (min_groups(nums, limit) > m)

l = limit + 1;

else

r = limit;

}

return l;

}

private:

int min_groups(const vector<int>& nums, long limit) {

long sum = 0;

int groups = 1;

for (int num : nums) {

if (sum + num > limit) {

sum = num;

++groups;

} else {

sum += num;

}

return groups;

}

};

花花酱 LeetCode 605. Can Place Flowers

By zxi on June 28, 2018

Problem

Suppose you have a long flowerbed in which some of the plots are planted and some are not. However, flowers cannot be planted in adjacent plots – they would compete for water and both would die.

Given a flowerbed (represented as an array containing 0 and 1, where 0 means empty and 1 means not empty), and a number n, return if n new flowers can be planted in it without violating the no-adjacent-flowers rule.

Example 1:

Input: flowerbed = [1,0,0,0,1], n = 1
Output: True

Example 2:

Input: flowerbed = [1,0,0,0,1], n = 2
Output: False

Note:

The input array won’t violate no-adjacent-flowers rule.
The input array size is in the range of [1, 20000].
n is a non-negative integer which won’t exceed the input array size.

Solution: Greedy

Time complexity: O(n)

Space complexity: O(1)

C++

// Author: Huahua

// Running time: 21 ms

class Solution {

public:

bool canPlaceFlowers(vector<int>& flowerbed, int n) {

int count = 0;

for (size_t i = 0; i < flowerbed.size() && count < n; ++i) {

if (flowerbed[i]) continue;

bool left = i == 0 ? true : !flowerbed[i - 1];

bool right = i == flowerbed.size() - 1 ? true : !flowerbed[i + 1];

if (left && right) {

flowerbed[i++] = 1;

++count;

}

return count == n;

}

};

花花酱 LeetCode 228. Summary Ranges

By zxi on June 27, 2018

Problem

Given a sorted integer array without duplicates, return the summary of its ranges.

Example 1:

Input:  [0,1,2,4,5,7]
Output: ["0->2","4->5","7"]
Explanation: 0,1,2 form a continuous range; 4,5 form a continuous range.

Example 2:

Input:  [0,2,3,4,6,8,9]
Output: ["0","2->4","6","8->9"]
Explanation: 2,3,4 form a continuous range; 8,9 form a continuous range.

Solution

Time complexity: O(n)

Space complexity: O(k)

C++

// Author: Huahua

// Running time: 3 ms

class Solution {

public:

vector<string> summaryRanges(vector<int>& nums) {

int s = 0;

vector<string> ans;

for (size_t i = 1; i <= nums.size(); ++i) {

if (i == nums.size() || nums[i] != nums[i - 1] + 1) {

if (s == i - 1)

ans.push_back(to_string(nums[s]));

else

ans.push_back(to_string(nums[s]) + "->" + to_string(nums[i - 1]));

s = i;

}

return ans;

}

};

花花酱 LeetCode 852. Peak Index in a Mountain Array

By zxi on June 17, 2018

Problem

Let’s call an array A a mountain if the following properties hold:

A.length >= 3
There exists some 0 < i < A.length - 1 such that A[0] < A[1] < ... A[i-1] < A[i] > A[i+1] > ... > A[A.length - 1]

Given an array that is definitely a mountain, return any i such that A[0] < A[1] < ... A[i-1] < A[i] > A[i+1] > ... > A[A.length - 1].

Example 1:

Input: [0,1,0]
Output: 1

Example 2:

Input: [0,2,1,0]
Output: 1

Note:

3 <= A.length <= 10000
0 <= A[i] <= 10^6
A is a mountain, as defined above.

Solution1: Liner Scan

Time complexity: O(n)

Space complexity: O(1)

C++

// Author: Huahua

// Running time: 16 ms

class Solution {

public:

int peakIndexInMountainArray(vector<int>& A) {

for (int i = 1; i < A.size(); ++i)

if (A[i] < A[i - 1]) return i - 1;

}

};

C++/STL

// Author: Huahua

// Running time: 16 ms

class Solution {

public:

int peakIndexInMountainArray(vector<int>& A) {

return max_element(begin(A), end(A)) - begin(A);

}

};

Solution 2: Binary Search

Find the smallest l such that A[l] > A[l + 1].

Time complexity: O(logn)

Space complexity: O(1)

C++

// Author: Huahua

// Running time: 18 ms

class Solution {

public:

int peakIndexInMountainArray(vector<int>& A) {

int l = 0;

int r = A.size();

while (l < r) {

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

if (A[m] > A[m + 1])

r = m;

else

l = m + 1;

}

return l;

}

};

Java

// Author: Huahua, 3 ms

class Solution {

public int peakIndexInMountainArray(int[] A) {

int l = 0;

int r = A.length;

while (l < r) {

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

if (A[m] > A[m + 1])

r = m;

else

l = m + 1;

}

return l;

}

Python3

# Author: Huahua, 40 ms

class Solution:

def peakIndexInMountainArray(self, A):

l, r = 0, len(A)

while l < r:

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

if A[m] > A[m + 1]:

r = m

else:

l = m + 1

return l

花花酱 LeetCode 849. Maximize Distance to Closest Person

By zxi on June 11, 2018

Problem

In a row of seats, 1 represents a person sitting in that seat, and 0 represents that the seat is empty.

There is at least one empty seat, and at least one person sitting.

Alex wants to sit in the seat such that the distance between him and the closest person to him is maximized.

Return that maximum distance to closest person.

Example 1:

Input: [1,0,0,0,1,0,1]
Output: 2
Explanation: 
If Alex sits in the second open seat (seats[2]), then the closest person has distance 2.
If Alex sits in any other open seat, the closest person has distance 1.
Thus, the maximum distance to the closest person is 2.

Example 2:

Input: [1,0,0,0]
Output: 3
Explanation: 
If Alex sits in the last seat, the closest person is 3 seats away.
This is the maximum distance possible, so the answer is 3.

Note:

1 <= seats.length <= 20000
seats contains only 0s or 1s, at least one 0, and at least one 1.

Solution

Time complexity: O(n)

Space complexity: O(1)

// Author: Huahua

// Running time: 15 ms

class Solution {

public:

int maxDistToClosest(vector<int>& seats) {

int n = seats.size();

int prev = -1;

int ans = 0;

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

if (i == n) ans = max(ans, n - prev - 1);

else if (seats[i]) {

if (prev == -1) ans = i;

else ans = max(ans, (i - prev) / 2);

prev = i;

}

return ans;

}

};