其实特别好理解，我们只要写一个数据结构（线段树）支持一下操作：
1.插入一个数\(x\)。
2.查询当前数据结构中最小的数的插入编号。
3.删除插入编号为\(x\)的数。第一眼看成可持久化了
其实就是一个单点修改，区间（全局）查询的线段树。
zkw线段树在普通线段树的基础上进行了优化（卡常神器）。
我们记录每一个点在线段树中叶子节点的编号。这样修改的时候就不用递归下去找了，直接一个while循环pushup上来就完事。
#include<cstdio> #include<iostream> #include<cmath> #include<algorithm> #include<cstring> #include<cstdlib> #include<cctype> #include<vector> #include<stack> #include<queue> using namespace std; #define enter puts("") #define space putchar(' ') #define Mem(a, x) memset(a, x, sizeof(a)) #define In inline typedef long long ll; typedef double db; const int INF = 0x3f3f3f3f; const db eps = 1e-8; const int maxn = 1e5 + 5; inline ll read() { ll ans = 0; char ch = getchar(), last = ' '; while(!isdigit(ch)) last = ch, ch = getchar(); while(isdigit(ch)) ans = (ans << 1) + (ans << 3) + ch - '0', ch = getchar(); if(last == '-') ans = -ans; return ans; } inline void write(ll x) { if(x < 0) x = -x, putchar('-'); if(x >= 10) write(x / 10); putchar(x % 10 + '0'); } int n, m, s; struct Edge { int nxt, to, w; }e[maxn << 1]; int head[maxn], ecnt = -1; In void addEdge(int x, int y, int w) { e[++ecnt] = (Edge){head[x], y, w}; head[x] = ecnt; } int Min[maxn << 2], id[maxn << 2], pos[maxn << 2]; In void pushup(int now) { if(Min[now << 1] <= Min[now << 1 | 1]) Min[now] = Min[now << 1], id[now] = id[now << 1]; else Min[now] = Min[now << 1 | 1], id[now] = id[now << 1 | 1]; } In void build(int L, int R, int now) { if(L == R) { Min[now] = INF; id[now] = L; pos[L] = now; return; } int mid = (L + R) >> 1; build(L, mid, now << 1), build(mid + 1, R, now << 1 | 1); pushup(now); } In void update(int now, int d) { Min[now] = d; while(now >> 1) pushup(now >> 1), now >>= 1; } bool in[maxn]; int dis[maxn]; In void dijkstra(int s) { Mem(dis, 0x3f), dis[s] = 0; update(pos[s], dis[s]); while(Min[1] ^ INF) { int now = id[1]; update(pos[now], INF); if(in[now]) continue; in[now] = 1; for(int i = head[now], v; ~i; i = e[i].nxt) { if(dis[v = e[i].to] > dis[now] + e[i].w) { dis[v] = dis[now] + e[i].w; update(pos[v], dis[v]); } } } } int main() { Mem(head, -1); n = read(), m = read(), s = read(); build(1, n, 1); for(int i = 1; i <= m; ++i) { int x = read(), y = read(), w = read(); addEdge(x, y, w); } dijkstra(1); for(int i = 1; i <= n; ++i) write(dis[i]), space; enter; return 0; }