Welcome to Subscribe On Youtube

Formatted question description: https://leetcode.ca/all/1766.html

1766. Tree of Coprimes

Level

Hard

Description

There is a tree (i.e., a connected, undirected graph that has no cycles) consisting of n nodes numbered from 0 to n - 1 and exactly n - 1 edges. Each node has a value associated with it, and the root of the tree is node 0.

To represent this tree, you are given an integer array nums and a 2D array edges. Each nums[i] represents the i-th node’s value, and each edges[j] = [u_j, v_j] represents an edge between nodes u_j and v_j in the tree.

Two values x and y are coprime if gcd(x, y) == 1 where gcd(x, y) is the greatest common divisor of x and y.

An ancestor of a node i is any other node on the shortest path from node i to the root. A node is not considered an ancestor of itself.

Return an array ans of size n, where ans[i] is the closest ancestor to node i such that nums[i] and nums[ans[i]] are coprime, or -1 if there is no such ancestor.

Example 1:

Image text

Input: nums = [2,3,3,2], edges = [[0,1],[1,2],[1,3]]

Output: [-1,0,0,1]

Explanation: In the above figure, each node’s value is in parentheses.

  • Node 0 has no coprime ancestors.
  • Node 1 has only one ancestor, node 0. Their values are coprime (gcd(2,3) == 1).
  • Node 2 has two ancestors, nodes 1 and 0. Node 1’s value is not coprime (gcd(3,3) == 3), but node 0’s value is (gcd(2,3) == 1), so node 0 is the closest valid ancestor.
  • Node 3 has two ancestors, nodes 1 and 0. It is coprime with node 1 (gcd(3,2) == 1), so node 1 is its closest valid ancestor.

Example 2:

Image text

Input: nums = [5,6,10,2,3,6,15], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]

Output: [-1,0,-1,0,0,0,-1]

Constraints:

  • nums.length == n
  • 1 <= nums[i] <= 50
  • 1 <= n <= 10^5
  • edges.length == n - 1
  • edges[j].length == 2
  • 0 <= u_j, v_j < n
  • u_j != v_j

Solution

First, store each node’s adjacent nodes. Next, preprocess the numbers from 1 to 50 and find coprimes for each number. Then, do depth first search starting from root node 0 and fimd the nearest coprime node for each node.

  • class Solution {
    int[] ans;
    Map<Integer, List<Integer>> edgesMap = new HashMap<Integer, List<Integer>>();
    Map<Integer, List<Integer>> coprimesMap = new HashMap<Integer, List<Integer>>();
    int[] depths;
    int[] pos = new int[51];

    public int[] getCoprimes(int[] nums, int[][] edges) {
        int n = nums.length;
        ans = new int[n];
        depths = new int[n];
        Arrays.fill(ans, -1);
        Arrays.fill(pos, -1);
        for (int[] edge : edges) {
            int node0 = edge[0], node1 = edge[1];
            List<Integer> list0 = edgesMap.getOrDefault(node0, new ArrayList<Integer>());
            List<Integer> list1 = edgesMap.getOrDefault(node1, new ArrayList<Integer>());
            list0.add(node1);
            list1.add(node0);
            edgesMap.put(node0, list0);
            edgesMap.put(node1, list1);
        }
        for (int i = 1; i <= 50; i++) {
            for (int j = 1; j <= 50; j++) {
                if (gcd(i, j) == 1) {
                    List<Integer> list = coprimesMap.getOrDefault(i, new ArrayList<Integer>());
                    list.add(j);
                    coprimesMap.put(i, list);
                }
            }
        }
        depthFirstSearch(nums, 0, -1);
        return ans;
    }

    public void depthFirstSearch(int[] nums, int u, int form) {
        int t = nums[u];
        for (int v : coprimesMap.get(t)) {
            if (pos[v] != -1) {
                if (ans[u] == -1 || depths[ans[u]] < depths[pos[v]])
                    ans[u] = pos[v];
            }
        }
        int p = pos[t];
        pos[t] = u;
        for (int i : edgesMap.get(u)) {
            if (i != form) {
                depths[i] = depths[u] + 1;
                depthFirstSearch(nums, i, u);
            }
        }
        pos[t] = p;
    }

    public int gcd(int a, int b) {
        while (a != 0 && b != 0) {
            if (a >= b)
                a %= b;
            else
                b %= a;
        }
        return a == 0 ? b : a;
    }
}

############

class Solution {
    private List<Integer>[] g;
    private List<Integer>[] f;
    private Deque<int[]>[] stks;
    private int[] nums;
    private int[] ans;

    public int[] getCoprimes(int[] nums, int[][] edges) {
        int n = nums.length;
        g = new List[n];
        Arrays.setAll(g, k -> new ArrayList<>());
        for (var e : edges) {
            int u = e[0], v = e[1];
            g[u].add(v);
            g[v].add(u);
        }
        f = new List[51];
        stks = new Deque[51];
        Arrays.setAll(f, k -> new ArrayList<>());
        Arrays.setAll(stks, k -> new ArrayDeque<>());
        for (int i = 1; i < 51; ++i) {
            for (int j = 1; j < 51; ++j) {
                if (gcd(i, j) == 1) {
                    f[i].add(j);
                }
            }
        }
        this.nums = nums;
        ans = new int[n];
        dfs(0, -1, 0);
        return ans;
    }

    private void dfs(int i, int fa, int depth) {
        int t = -1, k = -1;
        for (int v : f[nums[i]]) {
            var stk = stks[v];
            if (!stk.isEmpty() && stk.peek()[1] > k) {
                t = stk.peek()[0];
                k = stk.peek()[1];
            }
        }
        ans[i] = t;
        for (int j : g[i]) {
            if (j != fa) {
                stks[nums[i]].push(new int[] {i, depth});
                dfs(j, i, depth + 1);
                stks[nums[i]].pop();
            }
        }
    }

    private int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
}

  • class Solution:
    def getCoprimes(self, nums: List[int], edges: List[List[int]]) -> List[int]:
        def dfs(i, fa, depth):
            t = k = -1
            for v in f[nums[i]]:
                stk = stks[v]
                if stk and stk[-1][1] > k:
                    t, k = stk[-1]
            ans[i] = t
            for j in g[i]:
                if j != fa:
                    stks[nums[i]].append((i, depth))
                    dfs(j, i, depth + 1)
                    stks[nums[i]].pop()

        g = defaultdict(list)
        for u, v in edges:
            g[u].append(v)
            g[v].append(u)
        f = defaultdict(list)
        for i in range(1, 51):
            for j in range(1, 51):
                if gcd(i, j) == 1:
                    f[i].append(j)
        stks = defaultdict(list)
        ans = [-1] * len(nums)
        dfs(0, -1, 0)
        return ans



  • class Solution {
public:
    vector<int> getCoprimes(vector<int>& nums, vector<vector<int>>& edges) {
        int n = nums.size();
        vector<vector<int>> g(n);
        vector<vector<int>> f(51);
        vector<stack<pair<int, int>>> stks(51);
        for (auto& e : edges) {
            int u = e[0], v = e[1];
            g[u].emplace_back(v);
            g[v].emplace_back(u);
        }
        for (int i = 1; i < 51; ++i) {
            for (int j = 1; j < 51; ++j) {
                if (__gcd(i, j) == 1) {
                    f[i].emplace_back(j);
                }
            }
        }
        vector<int> ans(n);
        function<void(int, int, int)> dfs = [&](int i, int fa, int depth) {
            int t = -1, k = -1;
            for (int v : f[nums[i]]) {
                auto& stk = stks[v];
                if (!stk.empty() && stk.top().second > k) {
                    t = stk.top().first;
                    k = stk.top().second;
                }
            }
            ans[i] = t;
            for (int j : g[i]) {
                if (j != fa) {
                    stks[nums[i]].push({i, depth});
                    dfs(j, i, depth + 1);
                    stks[nums[i]].pop();
                }
            }
        };
        dfs(0, -1, 0);
        return ans;
    }
};

  • func getCoprimes(nums []int, edges [][]int) []int {
	n := len(nums)
	g := make([][]int, n)
	f := [51][]int{}
	type pair struct{ first, second int }
	stks := [51][]pair{}
	for _, e := range edges {
		u, v := e[0], e[1]
		g[u] = append(g[u], v)
		g[v] = append(g[v], u)
	}
	for i := 1; i < 51; i++ {
		for j := 1; j < 51; j++ {
			if gcd(i, j) == 1 {
				f[i] = append(f[i], j)
			}
		}
	}
	ans := make([]int, n)
	var dfs func(i, fa, depth int)
	dfs = func(i, fa, depth int) {
		t, k := -1, -1
		for _, v := range f[nums[i]] {
			stk := stks[v]
			if len(stk) > 0 && stk[len(stk)-1].second > k {
				t, k = stk[len(stk)-1].first, stk[len(stk)-1].second
			}
		}
		ans[i] = t
		for _, j := range g[i] {
			if j != fa {
				stks[nums[i]] = append(stks[nums[i]], pair{i, depth})
				dfs(j, i, depth+1)
				stks[nums[i]] = stks[nums[i]][:len(stks[nums[i]])-1]
			}
		}
	}
	dfs(0, -1, 0)
	return ans
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

All Problems

All Solutions