Posts tagged as “DFS”

花花酱 LeetCode 399. Evaluate Division

By zxi on December 1, 2017

题目大意：给你一些含有变量名的分式的值，让你计算另外一些分式的值，如果不能计算返回-1。

Problem:

Equations are given in the format A / B = k, where A and B are variables represented as strings, and k is a real number (floating point number). Given some queries, return the answers. If the answer does not exist, return -1.0.

Example:
Given a / b = 2.0, b / c = 3.0.
queries are: a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? .
return [6.0, 0.5, -1.0, 1.0, -1.0 ].

The input is: vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries , where equations.size() == values.size(), and the values are positive. This represents the equations. Return vector<double>.

According to the example above:

equations = [ ["a", "b"], ["b", "c"] ],

values = [2.0, 3.0],

queries = [ ["a", "c"], ["b", "a"], ["a", "e"], ["a", "a"], ["x", "x"] ].

The input is always valid. You may assume that evaluating the queries will result in no division by zero and there is no contradiction.

Solution 1: DFS

C++

// Author: Huahua

// Runtime: 3 ms

class Solution {

public:

vector<double> calcEquation(vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries) {

// g[A][B] = k -> A / B = k

unordered_map<string, unordered_map<string, double>> g;

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

const string& A = equations[i].first;

const string& B = equations[i].second;

const double k = values[i];

g[A][B] = k;

g[B][A] = 1.0 / k;

}

vector<double> ans;

for (const auto& pair : queries) {

const string& X = pair.first;

const string& Y = pair.second;

if (!g.count(X) || !g.count(Y)) {

ans.push_back(-1.0);

continue;

}

unordered_set<string> visited;

ans.push_back(divide(X, Y, g, visited));

}

return ans;

}

private:

// get result of A / B

double divide(const string& A, const string& B,

unordered_map<string, unordered_map<string, double>>& g,

unordered_set<string>& visited) {

if (A == B) return 1.0;

visited.insert(A);

for (const auto& pair : g[A]) {

const string& C = pair.first;

if (visited.count(C)) continue;

double d = divide(C, B, g, visited); // d = C / B

// A / B = C / B * A / C

if (d > 0) return d * g[A][C];

}

return -1.0;

}

};

Java

// Updated: 2020/9/27

// Author: Huahua

// Running time: 1 ms

class Solution {

private Map<String, HashMap<String, Double>> g = new HashMap<>();

public double[] calcEquation(List<List<String>> equations, double[] values, List<List<String>> queries) {

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

String x = equations.get(i).get(0);

String y = equations.get(i).get(1);

double k = values[i];

g.computeIfAbsent(x, l -> new HashMap<String, Double>()).put(y, k);

g.computeIfAbsent(y, l -> new HashMap<String, Double>()).put(x, 1.0 / k);

}

double[] ans = new double[queries.size()];

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

String x = queries.get(i).get(0);

String y = queries.get(i).get(1);

if (!g.containsKey(x) || !g.containsKey(y)) {

ans[i] = -1.0;

} else {

ans[i] = divide(x, y, new HashSet<String>());

}

return ans;

}

private double divide(String x, String y, Set<String> visited) {

if (x.equals(y)) return 1.0;

visited.add(x);

if (!g.containsKey(x)) return -1.0;

for (String n : g.get(x).keySet()) {

if (visited.contains(n)) continue;

visited.add(n);

double d = divide(n, y, visited);

if (d > 0) return d * g.get(x).get(n);

}

return -1.0;

}

Python3

"""

Author: Huahua

Running time: 32 ms (beats 100%)

"""

class Solution:

def calcEquation(self, equations, values, queries):

def divide(x, y, visited):

if x == y: return 1.0

visited.add(x)

for n in g[x]:

if n in visited: continue

visited.add(n)

d = divide(n, y, visited)

if d > 0: return d * g[x][n]

return -1.0

g = collections.defaultdict(dict)

for (x, y), v in zip(equations, values):

g[x][y] = v

g[y][x] = 1.0 / v

ans = [divide(x, y, set()) if x in g and y in g else -1 for x, y in queries]

return ans

Solution 2: Union Find

C++

// Author: Huahua

// Runtime: 3 ms

class Solution {

public:

vector<double> calcEquation(const vector<pair<string, string>>& equations, vector<double>& values, const vector<pair<string, string>>& queries) {

// parents["A"] = {"B", 2.0} -> A = 2.0 * B

// parents["B"] = {"C", 3.0} -> B = 3.0 * C

unordered_map<string, pair<string, double>> parents;

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

const string& A = equations[i].first;

const string& B = equations[i].second;

const double k = values[i];

// Neighter is in the forrest

if (!parents.count(A) && !parents.count(B)) {

parents[A] = {B, k};

parents[B] = {B, 1.0};

} else if (!parents.count(A)) {

parents[A] = {B, k};

} else if (!parents.count(B)) {

parents[B] = {A, 1.0 / k};

} else {

auto& rA = find(A, parents);

auto& rB = find(B, parents);

parents[rA.first] = {rB.first, k / rA.second * rB.second};

}

vector<double> ans;

for (const auto& pair : queries) {

const string& X = pair.first;

const string& Y = pair.second;

if (!parents.count(X) || !parents.count(Y)) {

ans.push_back(-1.0);

continue;

}

auto& rX = find(X, parents); // {rX, X / rX}

auto& rY = find(Y, parents); // {rY, Y / rY}

if (rX.first != rY.first)

ans.push_back(-1.0);

else // X / Y = (X / rX / (Y / rY))

ans.push_back(rX.second / rY.second);

}

return ans;

}

private:

pair<string, double>& find(const string& C, unordered_map<string, pair<string, double>>& parents) {

if (C != parents[C].first) {

const auto& p = find(parents[C].first, parents);

parents[C].first = p.first;

parents[C].second *= p.second;

}

return parents[C];

}

};

Java

// Updated: 9/27/2020

// Author: Huahua

// Running time: 3 ms

class Solution {

class Node {

public String parent;

public double ratio;

public Node(String parent, double ratio) {

this.parent = parent;

this.ratio = ratio;

}

class UnionFindSet {

private Map<String, Node> parents = new HashMap<>();

public Node find(String s) {

if (!parents.containsKey(s)) return null;

Node n = parents.get(s);

if (!n.parent.equals(s)) {

Node p = find(n.parent);

n.parent = p.parent;

n.ratio *= p.ratio;

}

return n;

}

public void union(String A, String B, double ratio) {

boolean hasA = parents.containsKey(A);

boolean hasB = parents.containsKey(B);

if (!hasA && !hasB) {

parents.put(A, new Node(B, ratio));

parents.put(B, new Node(B, 1.0));

} else if (!hasA) {

parents.put(A, new Node(B, ratio));

} else if (!hasB) {

parents.put(B, new Node(A, 1.0 / ratio));

} else {

Node rA = find(A);

Node rB = find(B);

parents.put(rA.parent,

new Node(rB.parent, ratio / rA.ratio * rB.ratio));

}

public double[] calcEquation(List<List<String>> equations, double[] values, List<List<String>> queries) {

UnionFindSet u = new UnionFindSet();

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

u.union(equations.get(i).get(0), equations.get(i).get(1), values[i]);

double[] ans = new double[queries.size()];

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

Node rx = u.find(queries.get(i).get(0));

Node ry = u.find(queries.get(i).get(1));

if (rx == null || ry == null || !rx.parent.equals(ry.parent))

ans[i] = -1.0;

else

ans[i] = rx.ratio / ry.ratio;

}

return ans;

}

Python3

"""

Author: Huahua

Running time: 32 ms (beats 100%)

"""

class Solution:

def calcEquation(self, equations, values, queries):

def find(x):

if x != U[x][0]:

px, pv = find(U[x][0])

U[x] = (px, U[x][1] * pv)

return U[x]

def divide(x, y):

rx, vx = find(x)

ry, vy = find(y)

if rx != ry: return -1.0

return vx / vy

U = {}

for (x, y), v in zip(equations, values):

if x not in U and y not in U:

U[x] = (y, v)

U[y] = (y, 1.0)

elif x not in U:

U[x] = (y, v)

elif y not in U:

U[y] = (x, 1.0 / v)

else:

rx, vx = find(x)

ry, vy = find(y)

U[rx] = (ry, v / vx * vy)

ans = [divide(x, y) if x in U and y in U else -1 for x, y in queries]

return ans

Related Problems:

花花酱 LeetCode 733. Flood Fill

By zxi on November 28, 2017

Problem:

An image is represented by a 2-D array of integers, each integer representing the pixel value of the image (from 0 to 65535).

Given a coordinate (sr, sc) representing the starting pixel (row and column) of the flood fill, and a pixel value newColor, “flood fill” the image.

To perform a “flood fill”, consider the starting pixel, plus any pixels connected 4-directionally to the starting pixel of the same color as the starting pixel, plus any pixels connected 4-directionally to those pixels (also with the same color as the starting pixel), and so on. Replace the color of all of the aforementioned pixels with the newColor.

At the end, return the modified image.

Example 1:

Input:

image = [[1,1,1],[1,1,0],[1,0,1]]

sr = 1, sc = 1, newColor = 2

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

Explanation:

From the center of the image (with position (sr, sc) = (1, 1)), all pixels connected

by a path of the same color as the starting pixel are colored with the new color.

Note the bottom corner is not colored 2, because it is not 4-directionally connected

to the starting pixel.

Note:

The length of image and image[0] will be in the range [1, 50].
The given starting pixel will satisfy 0 <= sr < image.length and 0 <= sc < image[0].length.
The value of each color in image[i][j] and newColor will be an integer in [0, 65535].

Idea

DFS

Solution:

C++ / DFS

Time complexity: O(mn)

Space complexity: O(1)

// Author: Huahua

// Runtime: 33 ms

class Solution {

public:

vector<vector<int>> floodFill(vector<vector<int>>& image,

int sr, int sc, int newColor) {

if (image[sr][sc] == newColor) return image;

int m = image.size();

int n = image[0].size();

floodFill(image, sc, sr, n, m, image[sr][sc], newColor);

return image;

}

private:

void floodFill(vector<vector<int>>& image,

int x, int y, int n, int m, int orgColor, int newColor) {

if (x < 0 || x >= n || y < 0 || y >= m) return;

if (image[y][x] != orgColor) return;

image[y][x] = newColor;

floodFill(image, x + 1, y, n, m, orgColor, newColor);

floodFill(image, x - 1, y, n, m, orgColor, newColor);

floodFill(image, x, y + 1, n, m, orgColor, newColor);

floodFill(image, x, y - 1, n, m, orgColor, newColor);

}

};

Related Problems:

花花酱 LeetCode 726. Number of Atoms

By zxi on November 15, 2017

Problem:

Given a chemical formula (given as a string), return the count of each atom.

An atomic element always starts with an uppercase character, then zero or more lowercase letters, representing the name.

1 or more digits representing the count of that element may follow if the count is greater than 1. If the count is 1, no digits will follow. For example, H2O and H2O2 are possible, but H1O2 is impossible.

Two formulas concatenated together produce another formula. For example, H2O2He3Mg4 is also a formula.

A formula placed in parentheses, and a count (optionally added) is also a formula. For example, (H2O2) and (H2O2)3 are formulas.

Given a formula, output the count of all elements as a string in the following form: the first name (in sorted order), followed by its count (if that count is more than 1), followed by the second name (in sorted order), followed by its count (if that count is more than 1), and so on.

Example 1:

Input:

formula = "H2O"

Output: "H2O"

Explanation:

The count of elements are {'H': 2, 'O': 1}.

Example 2:

Input:

formula = "Mg(OH)2"

Output: "H2MgO2"

Explanation:

The count of elements are {'H': 2, 'Mg': 1, 'O': 2}.

Example 3:

Input:

formula = "K4(ON(SO3)2)2"

Output: "K4N2O14S4"

Explanation:

The count of elements are {'K': 4, 'N': 2, 'O': 14, 'S': 4}.

Note:

All atom names consist of lowercase letters, except for the first character which is uppercase.
The length of formula will be in the range [1, 1000].
formula will only consist of letters, digits, and round parentheses, and is a valid formula as defined in the problem.

Idea:

Recursion

Time complexity: O(n)

Space complexity: O(n)

Solution:

C++

// Author: Huahua

// Runtime: 3 ms

class Solution {

public:

string countOfAtoms(const string& formula) {

int i = 0;

string ans;

for (const auto& kv : countOfAtoms(formula, i)) {

ans += kv.first;

if (kv.second > 1) ans += std::to_string(kv.second);

}

return ans;

}

private:

map<string, int> countOfAtoms(const string& formula, int& i) {

map<string, int> counts;

while (i != formula.length()) {

if (formula[i] == '(') {

const auto& tmp_counts = countOfAtoms(formula, ++i);

const int count = getCount(formula, i);

for (const auto& kv : tmp_counts)

counts[kv.first] += kv.second * count;

} else if (formula[i] == ')') {

++i;

return counts;

} else {

const string& name = getName(formula, i);

counts[name] += getCount(formula, i);

}

return counts;

}

string getName(const string& formula, int& i) {

string name;

while (isalpha(formula[i])

&& (name.empty() || islower(formula[i]))) name += formula[i++];

return name;

}

int getCount(const string& formula, int& i) {

string count_str;

while (isdigit(formula[i])) count_str += formula[i++];

return count_str.empty() ? 1 : std::stoi(count_str);

}

};

Java

// Author: Huahua

// Runtime: 13 ms

class Solution {

private int i;

public String countOfAtoms(String formula) {

StringBuilder ans = new StringBuilder();

i = 0;

Map<String, Integer> counts = countOfAtoms(formula.toCharArray());

for (String name: counts.keySet()) {

ans.append(name);

int count = counts.get(name);

if (count > 1) ans.append("" + count);

}

return ans.toString();

}

private Map<String, Integer> countOfAtoms(char[] f) {

Map<String, Integer> ans = new TreeMap<String, Integer>();

while (i != f.length) {

if (f[i] == '(') {

++i;

Map<String, Integer> tmp = countOfAtoms(f);

int count = getCount(f);

for (Map.Entry<String, Integer> entry : tmp.entrySet())

ans.put(entry.getKey(),

ans.getOrDefault(entry.getKey(), 0)

+ entry.getValue() * count);

} else if (f[i] == ')') {

++i;

return ans;

} else {

String name = getName(f);

ans.put(name, ans.getOrDefault(name, 0) + getCount(f));

}

return ans;

}

private String getName(char[] f) {

String name = "" + f[i++];

while (i < f.length && 'a' <= f[i] && f[i] <= 'z') name += f[i++];

return name;

}

private int getCount(char[] f) {

int count = 0;

while (i < f.length && '0' <= f[i] && f[i] <= '9') {

count = count * 10 + (f[i] - '0');

++i;

}

return count == 0 ? 1 : count;

}

花花酱 LeetCode 216. Combination Sum III

By zxi on November 3, 2017

题目大意：输出所有用k个数的和为n的组合。可以使用的元素是1到9。

Problem:

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

Example 1:

Input: k = 3, n = 7

Output:

[[1,2,4]]

Example 2:

Input: k = 3, n = 9

Output:

1	[[1,2,6], [1,3,5], [2,3,4]]

Idea:

DFS + backtracking

bit

Solution:

C++

// Author: Huahua

// Runtime: 0 ms

class Solution {

public:

vector<vector<int>> combinationSum3(int k, int n) {

vector<vector<int>> ans;

vector<int> cur;

dfs(k, n, 1, cur, ans);

return ans;

}

private:

// Use k numbers (>= s) to sum up to n

void dfs(int k, int n, int s,

vector<int>& cur, vector<vector<int>>& ans) {

if (k == 0) {

if (n == 0) ans.push_back(cur);

return;

}

for (int i = s; i <= 9; ++i) {

if (i > n) return;

cur.push_back(i);

dfs(k - 1, n - i, i + 1, cur, ans);

cur.pop_back();

}

};

C++ / binary

class Solution {

public:

vector<vector<int>> combinationSum3(int k, int n) {

vector<vector<int>> ans;

// 2^9, generate all combinations of [1 .. 9]

for (int i = 0; i < (1 << 9); ++i) {

vector<int> cur;

int sum = 0;

// Use j if (j - 1)-th bit is 1

for (int j = 1; j <= 9; ++j)

if (i & (1 << (j - 1))) {

sum += j;

cur.push_back(j);

}

if (sum == n && cur.size() == k)

ans.push_back(cur);

}

return ans;

}

};

Python

class Solution:

def combinationSum3(self, k, n):

def dfs(k, n, s, cur, ans):

if k == 0 and n == 0:

ans.append(list(cur))

for i in range(s, min(n + 1, 10)):

dfs(k - 1, n - i, i + 1, cur + [i], ans)

ans = []

dfs(k, n, 1, [], ans)

return ans

Related problems:

花花酱 LeetCode 37. Sudoku Solver

By zxi on October 16, 2017

Problem:

Write a program to solve a Sudoku puzzle by filling the empty cells.

Empty cells are indicated by the character '.'.

You may assume that there will be only one unique solution.

A sudoku puzzle…

…and its solution numbers marked in red.

Idea:

DFS + backtracking

Solution:

C++

// Author: Huahua

// Runtime: 3 ms

class Solution {

public:

void solveSudoku(vector<vector<char>>& board) {

rows_ = vector<vector<int>>(9, vector<int>(10));

cols_ = vector<vector<int>>(9, vector<int>(10));

boxes_ = vector<vector<int>>(9, vector<int>(10));

for(int i = 0; i < 9; i++)

for(int j = 0; j < 9; j++) {

const char c = board[i][j];

if ( c != '.') {

int n = c - '0';

int bx = j / 3;

int by = i / 3;

rows_[i][n] = 1;

cols_[j][n] = 1;

boxes_[by * 3 + bx][n] = 1;

}

fill(board, 0, 0);

}

private:

vector<vector<int>> rows_, cols_, boxes_;

bool fill(vector<vector<char>>& board, int x, int y) {

if (y == 9)

return true;

int nx = (x + 1) % 9;

int ny = (nx == 0) ? y + 1 : y;

if (board[y][x] != '.') return fill(board, nx, ny);

for (int i = 1; i <= 9; i++) {

int bx = x / 3;

int by = y / 3;

int box_key = by * 3 + bx;

if (!rows_[y][i] && !cols_[x][i] && !boxes_[box_key][i]) {

rows_[y][i] = 1;

cols_[x][i] = 1;

boxes_[box_key][i] = 1;

board[y][x] = i + '0';

if (fill(board, nx, ny)) return true;

board[y][x] = '.';

boxes_[box_key][i] = 0;

cols_[x][i] = 0;

rows_[y][i] = 0;

}

return false;

}

};

Related Problems:

[解题报告] LeetCode 51. N-Queens