Bzoj4199:[NOI2015]品酒大会
2018-02-21 22:44
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题面
Bzoj4199Sol
后缀数组显然的暴力就是求\(LCP\)+差分
\(40\)分
# include <bits/stdc++.h> # define RG register # define IL inline # define Fill(a, b) memset(a, b, sizeof(a)) using namespace std; typedef long long ll; const int _(3e5 + 5); IL int Input(){ RG int x = 0, z = 1; RG char c = getchar(); for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1; for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48); return x * z; } int a[_], n, s[_], rk[_], sa[_], height[_], tmp[_], t[_]; ll ans1[_], ans2[_]; int st[20][_], lg[_]; char ss[_]; IL int Cmp(RG int i, RG int j, RG int k){ return tmp[i] == tmp[j] && i + k <= n && j + k <= n && tmp[i + k] == tmp[j + k]; } IL void Suffix_Sort(){ RG int m = 26; for(RG int i = 1; i <= n; ++i) ++t[rk[i] = s[i]]; for(RG int i = 1; i <= m; ++i) t[i] += t[i - 1]; for(RG int i = n; i; --i) sa[t[rk[i]]--] = i; for(RG int k = 1; k <= n; k <<= 1){ RG int l = 0; for(RG int i = n - k + 1; i <= n; ++i) tmp[++l] = i; for(RG int i = 1; i <= n; ++i) if(sa[i] > k) tmp[++l] = sa[i] - k; for(RG int i = 0; i <= m; ++i) t[i] = 0; for(RG int i = 1; i <= n; ++i) ++t[rk[tmp[i]]]; for(RG int i = 1; i <= m; ++i) t[i] += t[i - 1]; for(RG int i = n; i; --i) sa[t[rk[tmp[i]]]--] = tmp[i]; swap(tmp, rk), rk[sa[1]] = l = 1; for(RG int i = 2; i <= n; ++i) rk[sa[i]] = Cmp(sa[i - 1], sa[i], k) ? l : ++l; if(l >= n) break; m = l; } for(RG int i = 1, h = 0; i <= n; ++i){ if(h) --h; while(s[i + h] == s[sa[rk[i] - 1] + h]) ++h; height[rk[i]] = h; } } IL void ST_Prepare(){ for(RG int i = 2; i <= n; ++i) lg[i] = lg[i >> 1] + 1; for(RG int i = 1; i <= n; ++i) st[0][i] = height[i]; for(RG int i = 1; i <= lg ; ++i) for(RG int j = 1; j + (1 << i) - 1 <= n; ++j) st[i][j] = min(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]); } IL int LCP(RG int x, RG int y){ x = rk[x], y = rk[y]; if(x > y) swap(x, y); ++x; RG int len = y - x + 1; return min(st[lg[len]][x], st[lg[len]][y - (1 << lg[len]) + 1]); } int main(RG int argc, RG char* argv[]){ Fill(ans2, -127), n = Input(), scanf(" %s", ss + 1); for(RG int i = 1; i <= n; ++i) s[i] = ss[i] - 'a' + 1, a[i] = Input(); Suffix_Sort(), ST_Prepare(); for(RG int i = 1; i < n; ++i) for(RG int j = i + 1; j <= n; ++j){ RG int lcp = LCP(i, j); ++ans1[0], --ans1[lcp + 1]; ans2[lcp] = max(ans2[lcp], 1LL * a[i] * a[j]); } for(RG int i = 0; i < n; ++i) ans1[i] += ans1[i - 1]; for(RG int i = n - 1; ~i; --i) ans2[i] = max(ans2[i], ans2[i + 1]); for(RG int i = 0; i < n; ++i) printf("%lld %lld\n", ans1[i], ans2[i] == ans2 ? 0 : ans2[i]); return 0; }
正解,把\(height\)从大到小排序
每次合并\(height\)两边的集合,因为从大到小,所以两边集合的\(LCP\)一定就是这个\(height\),因为有负数权值,维护集合的最大值,最小值组合
# include <bits/stdc++.h> # define RG register # define IL inline # define Fill(a, b) memset(a, b, sizeof(a)) using namespace std; typedef long long ll; const int _(3e5 + 5); IL int Input(){ RG int x = 0, z = 1; RG char c = getchar(); for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1; for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48); return x * z; } int a[_], n, s[_], rk[_], sa[_], height[_], tmp[_], t[_]; ll ans1[_], ans2[_]; int fa[_], id[_], size[_], mx[_], mn[_]; char ss[_]; IL int Cmp(RG int i, RG int j, RG int k){ return tmp[i] == tmp[j] && i + k <= n && j + k <= n && tmp[i + k] == tmp[j + k]; } IL int _Cmp(RG int x, RG int y){ return height[x] > height[y]; } IL void Suffix_Sort(){ RG int m = 26; for(RG int i = 1; i <= n; ++i) ++t[rk[i] = s[i]]; for(RG int i = 1; i <= m; ++i) t[i] += t[i - 1]; for(RG int i = n; i; --i) sa[t[rk[i]]--] = i; for(RG int k = 1; k <= n; k <<= 1){ RG int l = 0; for(RG int i = n - k + 1; i <= n; ++i) tmp[++l] = i; for(RG int i = 1; i <= n; ++i) if(sa[i] > k) tmp[++l] = sa[i] - k; for(RG int i = 0; i <= m; ++i) t[i] = 0; for(RG int i = 1; i <= n; ++i) ++t[rk[tmp[i]]]; for(RG int i = 1; i <= m; ++i) t[i] += t[i - 1]; for(RG int i = n; i; --i) sa[t[rk[tmp[i]]]--] = tmp[i]; swap(tmp, rk), rk[sa[1]] = l = 1; for(RG int i = 2; i <= n; ++i) rk[sa[i]] = Cmp(sa[i - 1], sa[i], k) ? l : ++l; if(l >= n) break; m = l; } for(RG int i = 1, h = 0; i <= n; ++i){ if(h) --h; while(s[i + h] == s[sa[rk[i] - 1] + h]) ++h; height[rk[i]] = h; } } IL int Find(RG int x){ return fa[x] == x ? x : fa[x] = Find(fa[x]); } int main(RG int argc, RG char* argv[]){ Fill(ans2, -127), n = Input(), scanf(" %s", ss + 1); for(RG int i = 1; i <= n; ++i) s[i] = ss[i] - 'a' + 1, a[i] = Input(); for(RG int i = 1; i <= n; ++i) fa[i] = id[i] = i, size[i] = 1, mx[i] = mn[i] = a[i]; Suffix_Sort(), sort(id + 2, id + n + 1, _Cmp); for(RG int i = 2; i <= n; ++i){ RG int fx = Find(sa[id[i] - 1]), fy = Find(sa[id[i]]); ans1[height[id[i]]] += 1LL * size[fx] * size[fy]; fa[fy] = fx, size[fx] += size[fy]; ans2[height[id[i]]] = max(ans2[height[id[i]]], max(1LL * mx[fx] * mx[fy], 1LL * mx[fx] * mn[fy])); ans2[height[id[i]]] = max(ans2[height[id[i]]], max(1LL * mn[fx] * mx[fy], 1LL * mn[fx] * mn[fy])); mx[fx] = max(mx[fx], mx[fy]); mn[fx] = min(mn[fx], mn[fy]); } for(RG int i = n - 1; ~i; --i) ans1[i] += ans1[i + 1], ans2[i] = max(ans2[i], ans2[i + 1]); for(RG int i = 0; i < n; ++i) printf("%lld %lld\n", ans1[i], ans2[i] == ans2 ? 0 : ans2[i]); return 0; }
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