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
#include <iostream>
#include <vector>
#include <algorithm>
#include <set>

#define REP(x,n) for(int x=0;x<(n);++x)

//#define DEBUG_LEVEL 0

#ifdef DEBUG_LEVEL
    #define DEBUG(level, x) {if (level >= DEBUG_LEVEL) {x}}
#else
    #define DEBUG(level, x)
#endif

using namespace std;

const int MAX_P = 300000;
const int MAX_N = 300000;

long long reversedPancakes[MAX_P];
long long reversedPancakesSum[MAX_P];
int reversedPancakesCount = 0;

vector<long long> normalPancakes[MAX_N];
vector<long long> normalPancakesSum[MAX_N];
int sortedPancakesStacks[MAX_N];



void calculatePrefixSums(long long* array, long long* prefixSums, int count) {
    prefixSums[0] = array[0];
    for(int x=1; x < count; ++x) {
        prefixSums[x] = prefixSums[x-1] + array[x];
    }
}

long long inline subSum(long long* prefixSums, int from, int toExclusive) {
    DEBUG(0, cerr << "  subSum from " << from << " to " << toExclusive << endl;)
    if (from == 0) {
        return prefixSums[toExclusive-1];
    }
    return prefixSums[toExclusive-1] - prefixSums[from-1];
}

bool shouldConsumeStack(int stackIndex, int reversedPancakeIndex, int pancakesToConsider) {
    if (reversedPancakeIndex >= reversedPancakesCount) {
        DEBUG(2, cerr << "  No more reversed pancakes, consuming stack " << stackIndex << endl;)
        return true;
    }
    long long massForNormalStack = *normalPancakesSum[stackIndex].rbegin();
    long long massForReversedStackPiece = subSum(reversedPancakesSum, reversedPancakeIndex, min(reversedPancakesCount, reversedPancakeIndex + pancakesToConsider));
    DEBUG(2, cerr << "  Comparing stack " << stackIndex << " with mass " << massForNormalStack << " and reversed pancakes piece with mass " << massForReversedStackPiece << endl;)

    return massForNormalStack > massForReversedStackPiece;
}

int main() {
    int n,m,k;
    cin >> n >> m >> k;

    long long first, last;
    int index = 0;
    REP(x,n) {
        normalPancakes[index].resize(m);
        REP(y,m) {
            cin >> normalPancakes[index][y];
        }
        first = normalPancakes[index][0];
        last = normalPancakes[index][m-1];
        if (first >= last) {
            // add to reversed pancakes
            DEBUG(0,
                cerr<< "Stack added to reversed: ";
                REP(i,m) {
                    cerr << normalPancakes[index][i] << " ";
                }
                cerr << endl;
            )
            std::copy(normalPancakes[index].begin(), normalPancakes[index].end(), &reversedPancakes[reversedPancakesCount]);
            reversedPancakesCount += m;
        } else {
            DEBUG(0,
                cerr<< "Stack applied normally: ";
                REP(i,m) {
                    cerr << normalPancakes[index][i] << " ";
                }
                cerr << endl;
            )
            normalPancakesSum[index].resize(m);
            calculatePrefixSums(&normalPancakes[index][0], &normalPancakesSum[index][0], m);
            sortedPancakesStacks[index] = index;
            ++index;
        }
    }

    n = index; // only that much stacks are left
    sort(reversedPancakes, reversedPancakes + reversedPancakesCount, greater<long long>());

    DEBUG(1, 
        cerr << "Reversed pancakes: " << endl;
        REP(x, reversedPancakesCount) {
            cerr << reversedPancakes[x] << " ";
        }
        cerr << endl;
    )

    calculatePrefixSums(reversedPancakes, reversedPancakesSum, reversedPancakesCount);

    // for now it makes sense to consume whole stack at once
    sort(sortedPancakesStacks, sortedPancakesStacks + n, [&](int a, int b) {
        return normalPancakesSum[a][m-1] > normalPancakesSum[b][m-1];
    });
    DEBUG(1, 
        cerr << "Normal pancakes stacks sorted by total mass: " << endl;
        REP(x, n) {
            int stackIndex = sortedPancakesStacks[x];
            cerr << "Stack " << stackIndex << " with total mass " << normalPancakesSum[stackIndex][m-1] << " and pancakes: ";
            REP(i, m) {
                cerr << normalPancakes[stackIndex][i] << " ";
            }
            cerr << endl;
        }
    );

    long long consumedMass = 0;
    long long consumedCount = 0;
    int pancakesStackIndex = 0;
    int reversedPancakeIndex = 0;
    DEBUG(1, cerr << "best stack is " << sortedPancakesStacks[pancakesStackIndex] << " with mass " << normalPancakesSum[sortedPancakesStacks[pancakesStackIndex]][m-1] << endl;)
    while (consumedCount + m <= k) {
        if (pancakesStackIndex < n && shouldConsumeStack(sortedPancakesStacks[pancakesStackIndex], reversedPancakeIndex, m)) {
            int stackIndex = sortedPancakesStacks[pancakesStackIndex];
            DEBUG(2, cerr << "consuming stack " << stackIndex << " with " << m << " pancakes and mass " << normalPancakesSum[stackIndex][m-1] << endl;)
            consumedMass += normalPancakesSum[stackIndex][m-1];
            consumedCount += m;
            ++pancakesStackIndex;
            DEBUG(2, cerr << "  new best stack is " << sortedPancakesStacks[pancakesStackIndex] << " with mass " << normalPancakesSum[sortedPancakesStacks[pancakesStackIndex]][m-1] << endl;)
        } else if (reversedPancakeIndex < reversedPancakesCount) {
            DEBUG(2, cerr << "consuming single reversed pancake " << reversedPancakeIndex << " with mass " << reversedPancakes[reversedPancakeIndex] << endl;)
            consumedMass += reversedPancakes[reversedPancakeIndex];
            ++consumedCount;
            ++reversedPancakeIndex;
        } else {
            cerr << "SHOULD NEVER HAPPEN" << endl;
            //should never happen
            break;
        }
    }

    if (pancakesStackIndex == n) {
        // all stacks are consumed, consume reversed pancakes until k
        long long remainingMass = subSum(reversedPancakesSum, reversedPancakeIndex, reversedPancakeIndex + (k - consumedCount));
        consumedMass += remainingMass;
        DEBUG(2, cerr << "consuming " << (k - consumedCount) << " reversed pancakes from " << reversedPancakeIndex << " with total mass " << remainingMass << endl;)

        DEBUG(2, cerr << "Result is " << consumedMass << endl;)
        cout << consumedMass;
        return 0;
    }

    //consume reversed pancakes one by one, until single stack becomes larger (which ends the flow)
    for (int remainingK = k - consumedCount; remainingK > 0; --remainingK) {
        DEBUG(2, cerr << "Remaining pancakes: " << remainingK << endl;)

        //it must always exist, because consuming a stack will end the flow
        int bestStackIndex = *std::max_element(sortedPancakesStacks + pancakesStackIndex, sortedPancakesStacks + n, [&](int a, int b) {
            return normalPancakesSum[a][remainingK-1] < normalPancakesSum[b][remainingK-1];
        });
        DEBUG(0, cerr << "  range is (" << pancakesStackIndex << ", " << n << "), best is " << bestStackIndex << endl;)

        long long bestStackMass = normalPancakesSum[bestStackIndex][remainingK-1];
        long long reversedPancakesMass = subSum(reversedPancakesSum, reversedPancakeIndex, min(reversedPancakeIndex + remainingK, reversedPancakesCount));

        DEBUG(1, cerr << "  Best stack for remaining " << remainingK << " pancakes is " << bestStackIndex << " with mass " << bestStackMass << endl;)
        DEBUG(1, cerr << "  Reversed pancakes for remaining " << remainingK << " pancakes is      " << reversedPancakesMass << endl;)
    
        if (reversedPancakesMass >= bestStackMass) {
            // consume reversed pancake
            DEBUG(2, cerr << "  Consuming single reversed pancake " << reversedPancakeIndex << " with mass " << reversedPancakes[reversedPancakeIndex] << endl;)
            consumedMass += reversedPancakes[reversedPancakeIndex];
            ++consumedCount;
            ++reversedPancakeIndex;
        } else if (reversedPancakes[reversedPancakeIndex] >= normalPancakes[bestStackIndex][remainingK-1]) {
            // consume reversed pancake
            DEBUG(2, cerr << "  Consuming single reversed pancake " << reversedPancakeIndex << " with mass " << reversedPancakes[reversedPancakeIndex] << " even though stack is greater" << endl;)
            consumedMass += reversedPancakes[reversedPancakeIndex];
            ++consumedCount;
            ++reversedPancakeIndex;
        } else {
            // consume stack
            DEBUG(2, cerr << "  Consuming stack " << bestStackIndex << " with mass " << bestStackMass << endl;)
            consumedMass += bestStackMass;
            consumedCount += remainingK;
            break;
        }
    }

    DEBUG(2, cerr << "Result is " << consumedMass << endl;)
    cout << consumedMass;

    return 0;
}