README_EN.md

399. Evaluate Division

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Description

You are given an array of variable pairs equations and an array of real numbers values, where equations[i] = [Ai, Bi] and values[i] represent the equation Ai / Bi = values[i]. Each Ai or Bi is a string that represents a single variable.

You are also given some queries, where queries[j] = [Cj, Dj] represents the jth query where you must find the answer for Cj / Dj = ?.

Return the answers to all queries. If a single answer cannot be determined, return -1.0.

Note: The input is always valid. You may assume that evaluating the queries will not result in division by zero and that there is no contradiction.

 

Example 1:

Input: equations = [["a","b"],["b","c"]], values = [2.0,3.0], queries = [["a","c"],["b","a"],["a","e"],["a","a"],["x","x"]]
Output: [6.00000,0.50000,-1.00000,1.00000,-1.00000]
Explanation: 
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 ]

Example 2:

Input: equations = [["a","b"],["b","c"],["bc","cd"]], values = [1.5,2.5,5.0], queries = [["a","c"],["c","b"],["bc","cd"],["cd","bc"]]
Output: [3.75000,0.40000,5.00000,0.20000]

Example 3:

Input: equations = [["a","b"]], values = [0.5], queries = [["a","b"],["b","a"],["a","c"],["x","y"]]
Output: [0.50000,2.00000,-1.00000,-1.00000]

 

Constraints:

• 1 <= equations.length <= 20
• equations[i].length == 2
• 1 <= Ai.length, Bi.length <= 5
• values.length == equations.length
• 0.0 < values[i] <= 20.0
• 1 <= queries.length <= 20
• queries[i].length == 2
• 1 <= Cj.length, Dj.length <= 5
• Ai, Bi, Cj, Dj consist of lower case English letters and digits.

Solutions

Union find.

Python3

class Solution:
    def calcEquation(
        self, equations: List[List[str]], values: List[float], queries: List[List[str]]
    ) -> List[float]:
        def find(x):
            if p[x] != x:
                origin = p[x]
                p[x] = find(p[x])
                w[x] *= w[origin]
            return p[x]

        w = defaultdict(lambda: 1)
        p = defaultdict()
        for a, b in equations:
            p[a], p[b] = a, b
        for i, v in enumerate(values):
            a, b = equations[i]
            pa, pb = find(a), find(b)
            if pa == pb:
                continue
            p[pa] = pb
            w[pa] = w[b] * v / w[a]
        return [
            -1 if c not in p or d not in p or find(c) != find(d) else w[c] / w[d]
            for c, d in queries
        ]

Java

class Solution {
    private Map<String, String> p;
    private Map<String, Double> w;

    public double[] calcEquation(
        List<List<String>> equations, double[] values, List<List<String>> queries) {
        int n = equations.size();
        p = new HashMap<>();
        w = new HashMap<>();
        for (List<String> e : equations) {
            p.put(e.get(0), e.get(0));
            p.put(e.get(1), e.get(1));
            w.put(e.get(0), 1.0);
            w.put(e.get(1), 1.0);
        }
        for (int i = 0; i < n; ++i) {
            List<String> e = equations.get(i);
            String a = e.get(0), b = e.get(1);
            String pa = find(a), pb = find(b);
            if (Objects.equals(pa, pb)) {
                continue;
            }
            p.put(pa, pb);
            w.put(pa, w.get(b) * values[i] / w.get(a));
        }
        int m = queries.size();
        double[] ans = new double[m];
        for (int i = 0; i < m; ++i) {
            String c = queries.get(i).get(0), d = queries.get(i).get(1);
            ans[i] = !p.containsKey(c) || !p.containsKey(d) || !Objects.equals(find(c), find(d))
                ? -1.0
                : w.get(c) / w.get(d);
        }
        return ans;
    }

    private String find(String x) {
        if (!Objects.equals(p.get(x), x)) {
            String origin = p.get(x);
            p.put(x, find(p.get(x)));
            w.put(x, w.get(x) * w.get(origin));
        }
        return p.get(x);
    }
}

C++

class Solution {
public:
    unordered_map<string, string> p;
    unordered_map<string, double> w;

    vector<double> calcEquation(vector<vector<string>>& equations, vector<double>& values, vector<vector<string>>& queries) {
        int n = equations.size();
        for (auto e : equations) {
            p[e[0]] = e[0];
            p[e[1]] = e[1];
            w[e[0]] = 1.0;
            w[e[1]] = 1.0;
        }
        for (int i = 0; i < n; ++i) {
            vector<string> e = equations[i];
            string a = e[0], b = e[1];
            string pa = find(a), pb = find(b);
            if (pa == pb) continue;
            p[pa] = pb;
            w[pa] = w[b] * values[i] / w[a];
        }
        int m = queries.size();
        vector<double> ans(m);
        for (int i = 0; i < m; ++i) {
            string c = queries[i][0], d = queries[i][1];
            ans[i] = p.find(c) == p.end() || p.find(d) == p.end() || find(c) != find(d) ? -1.0 : w[c] / w[d];
        }
        return ans;
    }

    string find(string x) {
        if (p[x] != x) {
            string origin = p[x];
            p[x] = find(p[x]);
            w[x] *= w[origin];
        }
        return p[x];
    }
};

Go

func calcEquation(equations [][]string, values []float64, queries [][]string) []float64 {
	p := make(map[string]string)
	w := make(map[string]float64)
	for _, e := range equations {
		a, b := e[0], e[1]
		p[a], p[b] = a, b
		w[a], w[b] = 1.0, 1.0
	}

	var find func(x string) string
	find = func(x string) string {
		if p[x] != x {
			origin := p[x]
			p[x] = find(p[x])
			w[x] *= w[origin]
		}
		return p[x]
	}

	for i, v := range values {
		a, b := equations[i][0], equations[i][1]
		pa, pb := find(a), find(b)
		if pa == pb {
			continue
		}
		p[pa] = pb
		w[pa] = w[b] * v / w[a]
	}
	var ans []float64
	for _, e := range queries {
		c, d := e[0], e[1]
		if p[c] == "" || p[d] == "" || find(c) != find(d) {
			ans = append(ans, -1.0)
		} else {
			ans = append(ans, w[c]/w[d])
		}
	}
	return ans
}

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