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69 lines (62 loc) ยท 1.92 KB
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/**
*
* In graph theory, a tree is an undirected graph
* in which any two vertices are connected by exactly one path,
* or equivalently a connected acyclic undirected graph.
*
*
* ๊ทธ๋ํ๊ฐ valid tree์ธ์ง ํ์ธํ๋ ํจ์
* @param {number} n - ๋
ธ๋์ ์
* @param {number[][]} edges - ๊ฐ์ ์ ์ ๋ณด
* @returns {boolean} - ์ฃผ์ด์ง ๊ฐ์ ์ ๋ณด๋ก ๋ง๋ค์ด์ง ๊ทธ๋ํ๊ฐ ํธ๋ฆฌ์ธ์ง ์ฌ๋ถ
*
* ์๊ฐ ๋ณต์ก๋: O(n)
* - ๋ชจ๋ ๋
ธ๋๋ฅผ ํ ๋ฒ์ฉ ๋ฐฉ๋ฌธํ์ฌ ๊ทธ๋ํ๊ฐ ํธ๋ฆฌ์ธ์ง ํ์ธ
*
* ๊ณต๊ฐ ๋ณต์ก๋: O(n)
* - ์ธ์ ๋ฆฌ์คํธ๋ก ๊ทธ๋ํ, ๋ฐฉ๋ฌธ๋ฐฐ์ด
*/
function validTree(n: number, edges: number[][]): boolean {
// ๋
ธ๋์ ๊ฐ์ ์ ์ ๋น๊ต
if (edges.length !== n-1) {
return false
}
// ์ธ์ ๋ฆฌ์คํธ ํํ๋ก ๊ทธ๋ํ ์์ฑ
const grapph: Map<number, number[]> = new Map()
for (let i = 0; i < n; i++) {
grapph.set(i, []);
};
for (const [a, b] of edges) {
grapph.get(a)?.push(b)
grapph.get(a)?.push(b)
};
// ๋ฐฉ๋ฌธ ๋ฐฐ์ด ์์ฑ
const visited: boolean[] = new Array(n).fill(false);
// DFS ๊น์ด ์ฐ์ ํ์
const dfs = (node:number, parent: number): boolean => {
visited[node] = true;
for (const neighbor of grapph.get(node)!) {
if (!visited[neighbor]) {
if (!dfs(neighbor, node)) {
return false;
}
} else if (neighbor !== parent) {
// ์ด๋ฏธ ๋ฐฉ๋ฌธํ ๋
ธ๋๊ฐ ๋ถ๋ชจ๊ฐ ์๋๋ฉด ์ฌ์ดํด ๋ฐ์
return false;
}
}
return true;
}
// DFS๋ฅผ 0๋ฒ ๋
ธ๋๋ถํฐ ์์
// ์์ ์ง์ ์ -1๋ก ์ค์
if(!dfs(0, -1)) {
return false;
};
// ๋ชจ๋ ๋
ธ๋๊ฐ ๋ฐฉ๋ฌธ๋์๋์ง ํ์ธ
for (const isVisited of visited) {
if (!isVisited) {
return false;
}
}
return true;
}