#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vll = vector<ll>;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define rep(i,b,e) for(int i=(b); i<(e); ++i)
#define each(a,x) for(auto &a : (x))
#define all(x) (x).begin(),(x).end()
#define sz(x) int((x).size())
struct SegmentTree{ // (=,max), (punkt, przedział)
vector<pair<ll,int>> val;
int M=1;
void build(int n){
n+=2;
while(M<=n) M*=2;
val.resize(2*M);
rep(i,M,2*M)
val[i] = {0,i-M};
}
void update(int a, ll v){
val[a+=M].fi = v;
while(a!=1){
a/=2;
if(val[2*a] >= val[2*a+1])
val[a] = val[2*a];
else
val[a] = val[2*a+1];
}
}
pair<ll,int> query(int a, int b){ // -> (maksimum, pierwszy indeks z maksimum)
a += M;
b += M;
pair<ll,int> ans = val[a];
if(val[b].fi > val[a].fi)
ans = val[b];
while(a/2 != b/2){
if(!(a&1) && (val[a+1].fi > ans.fi || (val[a+1].fi == ans.fi && val[a+1].se < ans.se)))
ans = val[a+1];
if((b&1) && (val[b-1].fi > ans.fi || (val[b-1].fi == ans.fi && val[b-1].se < ans.se)))
ans = val[b-1];
a>>=1;
b>>=1;
}
return ans;
}
};
ll sum_vll(const vll &arr){
ll sum = 0;
each(x,arr)
sum += x;
return sum;
}
int main(){
cin.tie(0)->sync_with_stdio(0);
int n,m,k;
cin >> n >> m >> k;
vector<vll> incr,decr;
rep(w,0,n){
vll seq(m);
each(x,seq)
cin >> x;
if(seq.front() <= seq.back()){
rep(i,1,sz(seq)) // od razu aplikujemy s. prefiksowe
seq[i] += seq[i-1];
incr.eb(seq);
}else{
reverse(all(seq));
decr.eb(seq);
}
}
// cerr << "INCR:" << endl;
// each(seq,incr){
// each(elem,seq) cerr << elem << " ";
// cerr << endl;
// }
// cerr << "DECR:" << endl;
// each(seq,decr){
// each(elem,seq) cerr << elem << " ";
// cerr << endl;
// }
// Sklejamy ciągi malejące w jeden długi ciąg
vll decr_flat;
{
priority_queue<pair<ll,ll>> pq;
rep(i,0,sz(decr)){
pq.push({decr[i].back(), i});
decr[i].pop_back();
}
// cerr << "constructing decr_flat..." << endl;
while(!pq.empty()){
auto [val, i] = pq.top();
pq.pop();
if(!decr[i].empty()){
pq.push({decr[i].back(), i});
decr[i].pop_back();
}
decr_flat.eb(val);
}
// Sumy prefiksowe
rep(i,1,sz(decr_flat))
decr_flat[i] += decr_flat[i-1];
}
// Posortuj ciągi rosnące
sort(all(incr), [&](const vll &a, const vll &b){
return a.back() > b.back();
});
// Sumy prefiksowe po sumach ciągach rosnących
vll incr_block_sum(sz(incr));
vll incr_block_prefsum(sz(incr));
rep(i,0,sz(incr)){
incr_block_sum[i] = incr[i].back();
if(i > 0) incr_block_prefsum[i] += incr_block_prefsum[i-1];
incr_block_prefsum[i] += incr[i].back();
}
// cerr << "incr_block_sum: ";
// rep(i,0,sz(incr_block_sum)) cerr << incr_block_sum[i] << " ";
// cerr << endl;
// cerr << "incr_block_prefsum: ";
// rep(i,0,sz(incr_block_sum)) cerr << incr_block_prefsum[i] << " ";
// cerr << endl;
// Tworzymy mnóstwo drzew przedziałowych
vector<SegmentTree> tree(m), tree_reduced(m);
rep(i,0,m){
tree[i] = SegmentTree();
tree[i].build(sz(incr));
tree_reduced[i] = SegmentTree();
tree_reduced[i].build(sz(incr));
}
rep(i,0,sz(incr)){
rep(j,0,m){
tree[j].update(i, incr[i][j]);
tree_reduced[j].update(i, incr[i][j] - incr_block_sum[i]);
}
}
int elems_incr = k, elems_decr = 0;
while(elems_incr > sz(incr) * m){
--elems_incr;
++elems_decr;
}
// cerr << "init ELEMS_INCR:" << elems_incr << endl;
// cerr << "init ELEMS_DECR:" << elems_decr << endl;
// cerr << "INCR:" << endl;
// each(seq,incr){
// each(elem,seq) cerr << elem << " ";
// cerr << endl;
// }
// cerr << "DECR_FLAT:" << endl;
// each(elem,decr_flat){
// cerr << elem << " ";
// }
// cerr << endl;
ll ans = 0;
while(elems_incr >= 0
&& elems_decr <= sz(decr) * m){
// cerr << "ELEMS_INCR:" << elems_incr << endl;
// cerr << "ELEMS_DECR:" << elems_decr << endl;
ll decr_val = elems_decr > 0 ? decr_flat[elems_decr-1] : 0;
ll incr_val = 0;
// cerr << " decr_val: " << decr_val << endl;
const int cnt_whole_blocks = elems_incr / m;
const int rest = elems_incr % m;
// cerr << "rest: " << rest << endl;
// cerr << "cnt_whole_blocks: " << cnt_whole_blocks << endl;
if(rest == 0){
// cerr << "REST = 0" << endl;
incr_val = cnt_whole_blocks > 0 ? incr_block_prefsum[cnt_whole_blocks-1] : 0;
}else{
// cerr << "REST =/= 0" << endl;
// 1. trzeba wywalić jeden z użytych całych bloków
if(cnt_whole_blocks > 0){
ll incr_block_val = cnt_whole_blocks > 0 ? incr_block_prefsum[cnt_whole_blocks-1] : 0;
auto [incr_rest_val, pos] = tree_reduced[rest-1].query(0, cnt_whole_blocks-1);
// incr_block_val -= incr_block_sum[pos];
incr_block_val += incr_block_sum[cnt_whole_blocks];
incr_val = max(incr_val, incr_block_val + incr_rest_val);
// cerr << " incr_val_opt1: " << incr_block_val + incr_rest_val << " = " << incr_block_val << " + " << incr_rest_val << endl;
}
// 2. trzeba dołożyć kawałek nowego bloku
{
ll incr_block_val = cnt_whole_blocks > 0 ? incr_block_prefsum[cnt_whole_blocks-1] : 0;
auto [incr_rest_val, pos] = tree[rest-1].query(cnt_whole_blocks, sz(incr)-1);
incr_val = max(incr_val, incr_block_val + incr_rest_val);
// cerr << " incr_val_opt2: " << incr_block_val + incr_rest_val << " = " << incr_block_val << " + " << incr_rest_val << endl;
}
}
// cerr << " incr_val: " << incr_val << endl;
// cerr << "cur: " << incr_val + decr_val << endl;
// cerr << endl;
ans = max(ans, incr_val + decr_val);
--elems_incr;
++elems_decr;
}
cout << ans;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 | #include <bits/stdc++.h> using namespace std; using ll = long long; using vll = vector<ll>; #define mp make_pair #define pb push_back #define eb emplace_back #define fi first #define se second #define rep(i,b,e) for(int i=(b); i<(e); ++i) #define each(a,x) for(auto &a : (x)) #define all(x) (x).begin(),(x).end() #define sz(x) int((x).size()) struct SegmentTree{ // (=,max), (punkt, przedział) vector<pair<ll,int>> val; int M=1; void build(int n){ n+=2; while(M<=n) M*=2; val.resize(2*M); rep(i,M,2*M) val[i] = {0,i-M}; } void update(int a, ll v){ val[a+=M].fi = v; while(a!=1){ a/=2; if(val[2*a] >= val[2*a+1]) val[a] = val[2*a]; else val[a] = val[2*a+1]; } } pair<ll,int> query(int a, int b){ // -> (maksimum, pierwszy indeks z maksimum) a += M; b += M; pair<ll,int> ans = val[a]; if(val[b].fi > val[a].fi) ans = val[b]; while(a/2 != b/2){ if(!(a&1) && (val[a+1].fi > ans.fi || (val[a+1].fi == ans.fi && val[a+1].se < ans.se))) ans = val[a+1]; if((b&1) && (val[b-1].fi > ans.fi || (val[b-1].fi == ans.fi && val[b-1].se < ans.se))) ans = val[b-1]; a>>=1; b>>=1; } return ans; } }; ll sum_vll(const vll &arr){ ll sum = 0; each(x,arr) sum += x; return sum; } int main(){ cin.tie(0)->sync_with_stdio(0); int n,m,k; cin >> n >> m >> k; vector<vll> incr,decr; rep(w,0,n){ vll seq(m); each(x,seq) cin >> x; if(seq.front() <= seq.back()){ rep(i,1,sz(seq)) // od razu aplikujemy s. prefiksowe seq[i] += seq[i-1]; incr.eb(seq); }else{ reverse(all(seq)); decr.eb(seq); } } // cerr << "INCR:" << endl; // each(seq,incr){ // each(elem,seq) cerr << elem << " "; // cerr << endl; // } // cerr << "DECR:" << endl; // each(seq,decr){ // each(elem,seq) cerr << elem << " "; // cerr << endl; // } // Sklejamy ciągi malejące w jeden długi ciąg vll decr_flat; { priority_queue<pair<ll,ll>> pq; rep(i,0,sz(decr)){ pq.push({decr[i].back(), i}); decr[i].pop_back(); } // cerr << "constructing decr_flat..." << endl; while(!pq.empty()){ auto [val, i] = pq.top(); pq.pop(); if(!decr[i].empty()){ pq.push({decr[i].back(), i}); decr[i].pop_back(); } decr_flat.eb(val); } // Sumy prefiksowe rep(i,1,sz(decr_flat)) decr_flat[i] += decr_flat[i-1]; } // Posortuj ciągi rosnące sort(all(incr), [&](const vll &a, const vll &b){ return a.back() > b.back(); }); // Sumy prefiksowe po sumach ciągach rosnących vll incr_block_sum(sz(incr)); vll incr_block_prefsum(sz(incr)); rep(i,0,sz(incr)){ incr_block_sum[i] = incr[i].back(); if(i > 0) incr_block_prefsum[i] += incr_block_prefsum[i-1]; incr_block_prefsum[i] += incr[i].back(); } // cerr << "incr_block_sum: "; // rep(i,0,sz(incr_block_sum)) cerr << incr_block_sum[i] << " "; // cerr << endl; // cerr << "incr_block_prefsum: "; // rep(i,0,sz(incr_block_sum)) cerr << incr_block_prefsum[i] << " "; // cerr << endl; // Tworzymy mnóstwo drzew przedziałowych vector<SegmentTree> tree(m), tree_reduced(m); rep(i,0,m){ tree[i] = SegmentTree(); tree[i].build(sz(incr)); tree_reduced[i] = SegmentTree(); tree_reduced[i].build(sz(incr)); } rep(i,0,sz(incr)){ rep(j,0,m){ tree[j].update(i, incr[i][j]); tree_reduced[j].update(i, incr[i][j] - incr_block_sum[i]); } } int elems_incr = k, elems_decr = 0; while(elems_incr > sz(incr) * m){ --elems_incr; ++elems_decr; } // cerr << "init ELEMS_INCR:" << elems_incr << endl; // cerr << "init ELEMS_DECR:" << elems_decr << endl; // cerr << "INCR:" << endl; // each(seq,incr){ // each(elem,seq) cerr << elem << " "; // cerr << endl; // } // cerr << "DECR_FLAT:" << endl; // each(elem,decr_flat){ // cerr << elem << " "; // } // cerr << endl; ll ans = 0; while(elems_incr >= 0 && elems_decr <= sz(decr) * m){ // cerr << "ELEMS_INCR:" << elems_incr << endl; // cerr << "ELEMS_DECR:" << elems_decr << endl; ll decr_val = elems_decr > 0 ? decr_flat[elems_decr-1] : 0; ll incr_val = 0; // cerr << " decr_val: " << decr_val << endl; const int cnt_whole_blocks = elems_incr / m; const int rest = elems_incr % m; // cerr << "rest: " << rest << endl; // cerr << "cnt_whole_blocks: " << cnt_whole_blocks << endl; if(rest == 0){ // cerr << "REST = 0" << endl; incr_val = cnt_whole_blocks > 0 ? incr_block_prefsum[cnt_whole_blocks-1] : 0; }else{ // cerr << "REST =/= 0" << endl; // 1. trzeba wywalić jeden z użytych całych bloków if(cnt_whole_blocks > 0){ ll incr_block_val = cnt_whole_blocks > 0 ? incr_block_prefsum[cnt_whole_blocks-1] : 0; auto [incr_rest_val, pos] = tree_reduced[rest-1].query(0, cnt_whole_blocks-1); // incr_block_val -= incr_block_sum[pos]; incr_block_val += incr_block_sum[cnt_whole_blocks]; incr_val = max(incr_val, incr_block_val + incr_rest_val); // cerr << " incr_val_opt1: " << incr_block_val + incr_rest_val << " = " << incr_block_val << " + " << incr_rest_val << endl; } // 2. trzeba dołożyć kawałek nowego bloku { ll incr_block_val = cnt_whole_blocks > 0 ? incr_block_prefsum[cnt_whole_blocks-1] : 0; auto [incr_rest_val, pos] = tree[rest-1].query(cnt_whole_blocks, sz(incr)-1); incr_val = max(incr_val, incr_block_val + incr_rest_val); // cerr << " incr_val_opt2: " << incr_block_val + incr_rest_val << " = " << incr_block_val << " + " << incr_rest_val << endl; } } // cerr << " incr_val: " << incr_val << endl; // cerr << "cur: " << incr_val + decr_val << endl; // cerr << endl; ans = max(ans, incr_val + decr_val); --elems_incr; ++elems_decr; } cout << ans; } |
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