Run-length encoding is a string compression method that works by replacing consecutive identical characters (repeated 2 or more times) with the concatenation of the character and the number marking the count of the characters (length of the run). For example, to compress the string "aabccc" we replace "aa" by "a2" and replace "ccc" by "c3". Thus the compressed string becomes "a2bc3".

Notice that in this problem, we are not adding '1' after single characters.

Given a string s and an integer k. You need to delete at most k characters from s such that the run-length encoded version of s has minimum length.

Find the minimum length of the run-length encoded version of s after deleting at most k characters.

Example 1:

Input: s = "aaabcccd", k = 2
Output: 4
Explanation: Compressing s without deleting anything will give us "a3bc3d" of length 6. Deleting any of the characters 'a' or 'c' would at most decrease the length of the compressed string to 5, for instance delete 2 'a' then we will have s = "abcccd" which compressed is abc3d. Therefore, the optimal way is to delete 'b' and 'd', then the compressed version of s will be "a3c3" of length 4.

Example 2:

Input: s = "aabbaa", k = 2
Output: 2
Explanation: If we delete both 'b' characters, the resulting compressed string would be "a4" of length 2.

Example 3:

Input: s = "aaaaaaaaaaa", k = 0
Output: 3
Explanation: Since k is zero, we cannot delete anything. The compressed string is "a11" of length 3.

Constraints:

1 <= s.length <= 100
0 <= k <= s.length
s contains only lowercase English letters.

Solution 0: Brute Force DFS (TLE)

Time complexity: O(C(n,k))
Space complexity: O(k)

C++

class Solution {

public:

int getLengthOfOptimalCompression(string s, int k) {

const int n = s.length();

auto encode = [&]() -> int {

char p = '$';

int count = 0;

int len = 0;

for (char c : s) {

if (c == '.') continue;

if (c != p) {

p = c;

count = 0;

}

++count;

if (count <= 2 || count == 10 || count == 100)

++len;

}

return len;

};

function<int(int, int)> dfs = [&](int start, int k) -> int {

if (start == n || k == 0) return encode();

int ans = n;

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

char c = s[i];

s[i] = '.'; // delete

ans = min(ans, dfs(i + 1, k - 1));

s[i] = c;

}

return ans;

};

return dfs(0, k);

}

};

Solution1: DP

State:
i: the start index of the substring
last: last char
len: run-length
k: # of chars that can be deleted.

base case:
1. k < 0: return inf # invalid
2. i >= s.length(): return 0 # done

Transition:
1. if s[i] == last: return carry + dp(i + 1, last, len + 1, k)

2. if s[i] != last:
return min(1 + dp(i + 1, s[i], 1, k, # start a new group with s[i]
dp(i + 1, last, len, k -1) # delete / skip s[i], keep it as is.

Time complexity: O(n^3*26)
Space complexity: O(n^3*26)

C++

int cache[101][27][101][101];

class Solution {

public:

int getLengthOfOptimalCompression(string s, int k) {

memset(cache, -1, sizeof(cache));

// Min length of compressioned string of s[i:]

// 1. last char is |last|

// 2. current run-length is len

// 3. we can delete k chars.

function<int(int, int, int, int)> dp =

[&](int i, int last, int len, int k) {

if (k < 0) return INT_MAX / 2;

if (i >= s.length()) return 0;

int& ans = cache[i][last][len][k];

if (ans != -1) return ans;

if (s[i] - 'a' == last) {

// same as the previous char, no need to delete.

int carry = (len == 1 || len == 9 || len == 99);

ans = carry + dp(i + 1, last, len + 1, k);

} else {

ans = min(1 + dp(i + 1, s[i] - 'a', 1, k), // keep s[i]

dp(i + 1, last, len, k - 1)); // delete s[i]

}

return ans;

};

return dp(0, 26, 0, k);

}

};

State compression

dp[i][k] := min len of s[i:] encoded by deleting at most k charchters.

dp[i][k] = min(dp[i+1][k-1] # delete s[i]
encode_len(s[i~j] == s[i]) + dp(j+1, k – sum(s[i~j])) for j in range(i, n)) # keep

Time complexity: O(n^2*k)
Space complexity: O(n*k)

C++

// Author: Huahua

class Solution {

public:

int getLengthOfOptimalCompression(string s, int k) {

const int n = s.length();

vector<vector<int>> cache(n, vector<int>(k + 1, -1));

function<int(int, int)> dp = [&](int i, int k) -> int {

if (k < 0) return n;

if (i + k >= n) return 0;

int& ans = cache[i][k];

if (ans != -1) return ans;

ans = dp(i + 1, k - 1); // delete

int len = 0;

int same = 0;

int diff = 0;

for (int j = i; j < n && diff <= k; ++j) {

if (s[j] == s[i] && ++same) {

if (same <= 2 || same == 10 || same == 100) ++len;

} else {

++diff;

}

ans = min(ans, len + dp(j + 1, k - diff));

}

return ans;

};

return dp(0, k);

}

};

Java

// Author: Huahua

class Solution {

private int[][] dp;

private char[] s;

private int n;

public int getLengthOfOptimalCompression(

String s, int k) {

this.s = s.toCharArray();

this.n = s.length();

this.dp = new int[n][k + 1];

for (int[] row : dp)

Arrays.fill(row, -1);

return dp(0, k);

}

private int dp(int i, int k) {

if (k < 0) return this.n;

if (i + k >= n) return 0; // done or delete all.

int ans = dp[i][k];

if (ans != -1) return ans;

ans = dp(i + 1, k - 1); // delete s[i]

int len = 0;

int same = 0;

int diff = 0;

for (int j = i; j < n && diff <= k; ++j) {

if (s[j] == s[i]) {

++same;

if (same <= 2 || same == 10 || same == 100) ++len;

} else {

++diff;

}

ans = Math.min(ans, len + dp(j + 1, k - diff));

}

dp[i][k] = ans;

return ans;

}

Python3

# Author: Huahua

class Solution:

def getLengthOfOptimalCompression(self, s: str, k: int) -> int:

n = len(s)

@functools.lru_cache(maxsize=None)

def dp(i, k):

if k < 0: return n

if i + k >= n: return 0

ans = dp(i + 1, k - 1)

l = 0

same = 0

for j in range(i, n):

if s[j] == s[i]:

same += 1

if same <= 2 or same == 10 or same == 100:

l += 1

diff = j - i + 1 - same

if diff < 0: break

ans = min(ans, l + dp(j + 1, k - diff))

return ans

return dp(0, k)

Problem

题目大意：对一个string进行in-place的run length encoding。

https://leetcode.com/problems/string-compression/description/

Given an array of characters, compress it in-place.

The length after compression must always be smaller than or equal to the original array.

Every element of the array should be a character (not int) of length 1.

After you are done modifying the input array in-place, return the new length of the array.

Follow up:
Could you solve it using only O(1) extra space?

Example 1:

Input:
["a","a","b","b","c","c","c"]

Output:
Return 6, and the first 6 characters of the input array should be: ["a","2","b","2","c","3"]

Explanation:
"aa" is replaced by "a2". "bb" is replaced by "b2". "ccc" is replaced by "c3".

Example 2:

Input:
["a"]

Output:
Return 1, and the first 1 characters of the input array should be: ["a"]

Explanation:
Nothing is replaced.

Example 3:

Input:
["a","b","b","b","b","b","b","b","b","b","b","b","b"]

Output:
Return 4, and the first 4 characters of the input array should be: ["a","b","1","2"].

Explanation:
Since the character "a" does not repeat, it is not compressed. "bbbbbbbbbbbb" is replaced by "b12".
Notice each digit has it's own entry in the array.

Note:

All characters have an ASCII value in [35, 126].
1 <= len(chars) <= 1000.

Solution

Time complexity: O(n)

Space complexity: O(1)

C++

// Author: Huahua

// Running time: 9 ms

class Solution {

public:

int compress(vector<char>& chars) {

const int n = chars.size();

int p = 0;

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

int count = 1;

while (i < n && chars[i] == chars[i - 1]) { ++i; ++count; }

chars[p++] = chars[i - 1];

if (count == 1) continue;

for (char c : to_string(count))

chars[p++] = c;

}

return p;

}

};

Posts tagged as “run length”

花花酱 LeetCode 1531. String Compression II

Solution 0: Brute Force DFS (TLE)

C++

Solution1: DP

C++

State compression

C++

Java

Python3

花花酱 LeetCode 1313. Decompress Run-Length Encoded List

Solution: Simulation

C++

花花酱 LeetCode 443. String Compression

Problem

Solution