605 [CF 609E] Minimum spanning tree for each edge

// 605 [CF 609E] Minimum spanning tree for each edge.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
//

/*
http://oj.daimayuan.top/course/22/problem/981

给定一张 n个顶点 m 条边的带权无向简单图，顶点编号从 1 到 n
，对于每一条边请求出包含这条边的生成树的最小边权和。

输入格式
第一行两个数 n,m，表示顶点数和边数。

接下来 m行，每行三个整数 u,v,w
，表示 u 号点和 v号点之间有一条边权为 w的边。

输出格式
输出共 m 行，第 i 行一个整数表示包含第 i 条边的生成树的最小边权和。

样例输入
5 7
1 2 3
1 3 1
1 4 5
2 3 2
2 5 3
3 4 2
4 5 4
样例输出
9
8
11
8
8
8
9
数据规模
对于 100% 的数据，保证 1≤n≤2×105,n−1≤m≤2×105,1≤u,v≤n,1≤w≤109，数据保证图连通。
*/

#include <iostream>
#include <algorithm>
#include <cstring>

using namespace std;

const int N = 200010;
int f[N], deepth[N];
int n, m;
int jlen[N][21];
int jpoint[N][21];
long long q[N];
int h[N], e[2*N], w[2*N], ne[2*N], idx;

struct Edge {
	int a, b, w; int idx;
	bool operator<(const Edge& W)const {
		return w < W.w;
	}
}edges[N];

int find(int x) {
	if (x != f[x]) {
		f[x] = find(f[x]);
	}

	return f[x];
}

void init() {
	memset(h, -1, sizeof h);
	for (int i = 1; i < N; i++) f[i] = i;
}

void add(int a, int b, int c) {
	e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx++;
}


void dfs(int x) {
	for (int i = h[x]; i != -1; i = ne[i]) {
		int j = e[i]; int currlen = w[i];
		if (deepth[j] == 0) {
			deepth[j] = deepth[x] + 1;
			jpoint[j][0] = x;
			jlen[j][0] = max(jlen[j][0], currlen);
			dfs(j);
		}
	}
}

int main() {
	init();
	//cin >> n >> m;
	scanf("%d%d",&n,&m);
	for (int i = 1; i <= m; i++) {
		int a, b, c; 
		//cin >> a >> b >> c;
		scanf("%d%d%d",&a,&b,&c);
		edges[i] = { a,b,c };
		edges[i].idx = i;
	}
	sort(edges+1, edges+m+1);

	long long res = 0, cnt = 0;
	for (int i = 1; i <= m; i++) {
		int a = edges[i].a, b = edges[i].b, w = edges[i].w;
		a = find(a); b = find(b);
		if (a != b) {
			add(edges[i].a, edges[i].b, w); add(edges[i].b, edges[i].a, w);
			f[a] = b;
			res += w;
			cnt++;
		}
	}

	deepth[1] = 1;
	dfs(1);

	for (int i = 1; i <= 20; i++) {
		for (int j = 1; j <= n; j++) {
			jpoint[j][i] = jpoint[jpoint[j][i - 1]][i - 1];
			jlen[j][i] = max(jlen[j][i - 1], jlen[jpoint[j][i - 1]][i - 1]);
		}
	}
	memset(q, 0, sizeof q);
	for (int i = 1; i <= m; i++) {
		int a = edges[i].a, b = edges[i].b, w = edges[i].w, idx = edges[i].idx;
		if (deepth[a] < deepth[b]) swap(a, b);
		int z = deepth[a] - deepth[b];
		int ans = 0;
		for (int i = 0; z; z /= 2, i++) {
			if (z & 1) {
				ans = max(ans, jlen[a][i]);
				a = jpoint[a][i];
			}
		}
		if (a != b) {
			for (int i = 20; i >= 0; i--) {
				if (jpoint[a][i] != jpoint[b][i]) {
					ans = max(ans, jlen[a][i]);
					ans = max(ans, jlen[b][i]);
					a = jpoint[a][i];
					b = jpoint[b][i];
				}
				ans = max(ans, jlen[a][0]);
				ans = max(ans, jlen[b][0]);
			}
		}
		q[idx] = res - ans + w;
	}

	for (int i = 1; i <= m; i++) {
		//cout << q[i] << endl;
		printf("%lld\n", q[i]);
	}

	return 0;
}