CodeForces

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>using namespace std;typedef long long ll;const int maxn = 2005;struct Edge {    int from, to, cost;    bool operator < (const Edge &temp) const {        return cost < temp.cost;    }}edge[maxn*maxn];int n, a[maxn][maxn], tot, head[maxn];struct E { int to, cost, next; } e[maxn*maxn];void init() { tot = 0; memset(head, -1, sizeof(head)); }void addedge(int u, int v, int cost) {    e[++tot].to = v; e[tot].cost = cost; e[tot].next = head[u];    head[u] = tot;}int par[maxn], ran[maxn];int query(int x) { return par[x] == x ? x : par[x] = query(par[x]); }bool unite(int x, int y) {    x = query(x), y = query(y);    if (x == y) return false;    if (ran[x] < ran[y]) par[x] = y;    else {        par[y] = x;        if (ran[x] == ran[y]) ran[x]++;    }    return true;}ll dis[maxn];void dfs(int u, int f, ll d) {    dis[u] = d;    for (int i = head[u]; ~i; i = e[i].next) {        int v = e[i].to, cost = e[i].cost;        if (v == f) continue;        dfs(v, u, d + cost);    }}int iabs(int x) { return x > 0 ? x : -x; }int main() {    scanf("%d", &n);    for (int i = 1; i <= n; i++) {        for (int j = 1; j <= n; j++) {            scanf("%d", &a[i][j]);        }    }    bool ok = true;    int cnt = 0;    for (int i = 1; i <= n; i++) {        for (int j = i; j <= n; j++) {            if (i == j && a[i][j] != 0) { ok = false; i = n + 1; break; }            if (a[i][j] != a[j][i]) { ok = false; i = n + 1; break; }            if (a[i][j] == 0) continue;            edge[++cnt].from = i;            edge[cnt].to = j;            edge[cnt].cost = a[i][j];        }    }    if (!ok) { printf("NO\n"); return 0; }    sort(edge+1, edge+1+cnt);    init();    for (int i = 1; i <= n; i++) par[i] = i, ran[i] = 0;    int num = 0;    for (int i = 1; i <= cnt && num < n - 1; i++) {        int u = edge[i].from, v = edge[i].to, cost = edge[i].cost;        if (unite(u, v)) {            ++num;            addedge(u, v, cost); addedge(v, u, cost);        }    }    if (num != n - 1) { printf("NO\n"); return 0; }    for (int i = 1; i <= n; i++) {        memset(dis, 0, sizeof(dis));        dfs(i, -1, 0);        for (int j = 1; j <= n; j++) {            if (i == j) continue;            if (dis[j] != a[i][j]) { ok = false; i = n + 1; break; }        }    }    if (ok) printf("YES\n");    else printf("NO\n");    return 0;}