花花酱 LeetCode 813. Largest Sum of Averages

By zxi on April 9, 2018

Problem

题目大意：把一个数组分成k个段，求每段平均值和的最大值。

https://leetcode.com/problems/largest-sum-of-averages/description/

We partition a row of numbers A into at most K adjacent (non-empty) groups, then our score is the sum of the average of each group. What is the largest score we can achieve?

Note that our partition must use every number in A, and that scores are not necessarily integers.

Example:
Input: 
A = [9,1,2,3,9]
K = 3
Output: 20
Explanation: 
The best choice is to partition A into [9], [1, 2, 3], [9]. The answer is 9 + (1 + 2 + 3) / 3 + 9 = 20.
We could have also partitioned A into [9, 1], [2], [3, 9], for example.
That partition would lead to a score of 5 + 2 + 6 = 13, which is worse.

Note:

1 <= A.length <= 100.
1 <= A[i] <= 10000.
1 <= K <= A.length.
Answers within 10^-6 of the correct answer will be accepted as correct.

Idea

DP, use dp[k][i] to denote the largest average sum of partitioning first i elements into k groups.

Init

dp[1][i] = sum(a[0] ~ a[i – 1]) / i, for i in 1, 2, … , n.

Transition

dp[k][i] = max(dp[k – 1][j] + sum(a[j] ~ a[i – 1]) / (i – j)) for j in k – 1,…,i-1.

that is find the best j such that maximize dp[k][i]

largest sum of partitioning first j elements (a[0] ~ a[j – 1]) into k – 1 groups (already computed)

+ average of a[j] ~ a[i – 1] (partition a[j] ~ a[i – 1] into 1 group).

Answer

dp[K][n]

Solution 1: DP

Time complexity: O(kn^2)

Space complexity: O(kn)

C++

// Author: Huahua

// Running time: 9 ms

class Solution {

public:

double largestSumOfAverages(vector<int>& A, int K) {

const int n = A.size();

vector<vector<double>> dp(K + 1, vector<double>(n + 1, 0.0));

vector<double> sums(n + 1, 0.0);

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

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

dp[1][i] = static_cast<double>(sums[i]) / i;

}

for (int k = 2; k <= K; ++k)

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

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

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

return dp[K][n];

}

};

C++ O(n) space

// Author: Huahua

// Running time: 8 ms

class Solution {

public:

double largestSumOfAverages(vector<int>& A, int K) {

const int n = A.size();

vector<double> dp(n + 1, 0.0);

vector<double> sums(n + 1, 0.0);

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

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

dp[i] = static_cast<double>(sums[i]) / i;

}

for (int k = 2; k <= K; ++k) {

vector<double> tmp(n + 1, 0.0);

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

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

tmp[i] = max(tmp[i], dp[j] + (sums[i] - sums[j]) / (i - j));

dp.swap(tmp);

}

return dp[n];

}

};

Solution 2: DFS + memoriation

C++

// Author: Huahua

// Running time: 10 ms

class Solution {

public:

double largestSumOfAverages(vector<int>& A, int K) {

const int n = A.size();

m_ = vector<vector<double>>(K + 1, vector<double>(n + 1, 0.0));

sums_ = vector<double>(n + 1, 0.0);

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

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

return LSA(A, n, K);

}

private:

vector<vector<double>> m_;

vector<double> sums_;

// Largest sum of averages for first n elements in A paritioned into k groups

double LSA(const vector<int>& A, int n, int k) {

if (m_[k][n] > 0) return m_[k][n];

if (k == 1) return sums_[n] / n;

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

m_[k][n] = max(m_[k][n], LSA(A, i, k - 1) + (sums_[n] - sums_[i]) / (n - i));

return m_[k][n];

}

};

花花酱 LeetCode 763. Partition Labels

By zxi on January 25, 2018

题目大意：把字符串分割成尽量多的不重叠子串，输出子串的长度数组。要求相同字符只能出现在一个子串中。

Problem:

A string S of lowercase letters is given. We want to partition this string into as many parts as possible so that each letter appears in at most one part, and return a list of integers representing the size of these parts.

Example 1:

Input: S = "ababcbacadefegdehijhklij"

Output: [9,7,8]

Explanation:

The partition is "ababcbaca", "defegde", "hijhklij".

This is a partition so that each letter appears in at most one part.

A partition like "ababcbacadefegde", "hijhklij" is incorrect, because it splits S into less parts.

Solution 0: Brute Force

Time complexity: O(n^2)

Space complexity: O(1)

C++

// Author: Huahua

// Running time: 15 ms

class Solution {

public:

vector<int> partitionLabels(string S) {

vector<int> ans;

size_t start = 0;

size_t end = 0;

for (size_t i = 0; i < S.size(); ++i) {

end = max(end, S.find_last_of(S[i]));

if (i == end) {

ans.push_back(end - start + 1);

start = end + 1;

}

return ans;

}

};

Python

"""

Author: Huahua

Running time : 48 ms

"""

class Solution:

def partitionLabels(self, S):

ans = []

start, end = 0, 0

for i in range(len(S)):

end = max(end, S.rfind(S[i]))

if i == end:

ans.append(end - start + 1)

start = end + 1

return ans

Solution 1: Greedy

Time complexity: O(n)

Space complexity: O(26/128)

C++

// Author: Huahua

// Running time: 6 ms

class Solution {

public:

vector<int> partitionLabels(string S) {

vector<int> last_index(128, 0);

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

last_index[S[i]] = i;

vector<int> ans;

int start = 0;

int end = 0;

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

end = max(end, last_index[S[i]]);

if (i == end) {

ans.push_back(end - start + 1);

start = end + 1;

}

return ans;

}

};

Java

// Author: Huahua

// Running time: 16 ms

class Solution {

public List<Integer> partitionLabels(String S) {

int lastIndex[] = new int[128];

for (int i = 0; i < S.length(); ++i)

lastIndex[(int)S.charAt(i)] = i;

List<Integer> ans = new ArrayList<>();

int start = 0;

int end = 0;

for (int i = 0; i < S.length(); ++i) {

end = Math.max(end, lastIndex[(int)S.charAt(i)]);

if (i == end) {

ans.add(end - start + 1);

start = end + 1;

}

return ans;

}

Python3

"""

Author: Huahua

Running time: 78 ms

"""

class Solution:

def partitionLabels(self, S):

last_index = {}

for i, ch in enumerate(S):

last_index[ch] = i

start = end = 0

ans = []

for i, ch in enumerate(S):

end = max(end, last_index[ch])

if i == end:

ans.append(end - start + 1)

start = end + 1

return ans

花花酱 LeetCode 725. Split Linked List in Parts

By zxi on November 13, 2017

Problem:

Given a (singly) linked list with head node root, write a function to split the linked list into k consecutive linked list “parts”.

The length of each part should be as equal as possible: no two parts should have a size differing by more than 1. This may lead to some parts being null.

The parts should be in order of occurrence in the input list, and parts occurring earlier should always have a size greater than or equal parts occurring later.

Return a List of ListNode’s representing the linked list parts that are formed.

Examples 1->2->3->4, k = 5 // 5 equal parts [ [1], [2], [3], [4], null ]

Example 1:

Input:

root = [1, 2, 3], k = 5

Output: [[1],[2],[3],[],[]]

Explanation:

The input and each element of the output are ListNodes, not arrays.

For example, the input root has root.val = 1, root.next.val = 2, \root.next.next.val = 3, and root.next.next.next = null.

The first element output[0] has output[0].val = 1, output[0].next = null.

The last element output[4] is null, but it's string representation as a ListNode is [].

Example 2:

Input:

root = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], k = 3

Output: [[1, 2, 3, 4], [5, 6, 7], [8, 9, 10]]

Explanation:

The input has been split into consecutive parts with size difference at most 1, and earlier parts are a larger size than the later parts.

Note:

The length of root will be in the range [0, 1000].
Each value of a node in the input will be an integer in the range [0, 999].
k will be an integer in the range [1, 50].

Idea:

List + Simulation

Solution:

C++

// Author: Huahua

// Runtime: 9 ms

class Solution {

public:

vector<ListNode*> splitListToParts(ListNode* root, int k) {

int len = 0;

for (ListNode* head = root; head; head = head->next) ++len;

vector<ListNode*> ans(k, nullptr);

int l = len / k;

int r = len % k;

ListNode* head = root;

ListNode* prev = nullptr;

for (int i = 0; i < k; ++i, --r) {

ans[i] = head;

for (int j = 0; j < l + (r > 0); ++j) {

prev = head;

head = head->next;

}

if (prev) prev->next = nullptr;

}

return ans;

}

};

Java

// Author: Huahua

// Runtime: 4 ms

class Solution {

public ListNode[] splitListToParts(ListNode root, int k) {

ListNode[] ans = new ListNode[k];

int len = 0;

for (ListNode head = root; head != null; head = head.next) ++len;

int l = len / k;

int r = len % k;

ListNode prev = null;

ListNode head = root;

for (int i = 0; i < k; ++i, --r) {

ans[i] = head;

int part_len = l + ((r > 0) ? 1 : 0);

for (int j = 0; j < part_len; ++j) {

prev = head;

head = head.next;

}

if (prev != null) prev.next = null;

}

return ans;

}

Python

"""

Author: Huahua

Runtime: 79 ms

"""

class Solution:

def splitListToParts(self, root, k):

total_len = 0

head = root

while head:

total_len += 1

head = head.next

ans = [None for _ in range(k)]

l, r = total_len // k, total_len % k

prev, head = None, root

for i in range(k):

ans[i] = head

for j in range(l + (1 if r > 0 else 0)):

prev, head = head, head.next

if prev: prev.next = None

r -= 1

return ans

Posts tagged as “partition”

花花酱 LeetCode 813. Largest Sum of Averages

Problem

Idea

Init

Transition

Answer

Solution 1: DP

C++

C++ O(n) space

Solution 2: DFS + memoriation

C++

花花酱 LeetCode 763. Partition Labels

花花酱 LeetCode 725. Split Linked List in Parts