#include <bits/stdc++.h>
using namespace std;
vector<pair<long long, int>> factorize(long long n) {
vector<pair<long long, int>> factors;
if (n % 2 == 0) {
int cnt = 0;
while (n % 2 == 0) {
n /= 2;
cnt++;
}
factors.push_back( { 2, cnt });
}
for (long long p = 3; p * p <= n; p += 2) {
if (n % p == 0) {
int cnt = 0;
while (n % p == 0) {
n /= p;
cnt++;
}
factors.push_back( { p, cnt });
}
}
if (n > 1)
factors.push_back( { n, 1 });
return factors;
}
// Pruned generation
void genDivsLimited(int i, long long current,
const vector<pair<long long, int>> &factors,
vector<long long> &divisors, long long maxVal) {
if (current > maxVal)
return;
if (i == (int) factors.size()) {
divisors.push_back(current);
return;
}
long long p = factors[i].first;
int exp = factors[i].second;
for (int e = 0; e <= exp; ++e) {
genDivsLimited(i + 1, current, factors, divisors, maxVal);
// prevent overflow + useless work
if (current > maxVal / p)
break;
current *= p;
}
}
// Main function
vector<long long> getDivisors(long long n, long long maxVal) {
vector<pair<long long, int>> factors = factorize(n);
vector<long long> divisors;
genDivsLimited(0, 1, factors, divisors, maxVal);
// sort descending
sort(divisors.begin(), divisors.end(), greater<long long>());
return divisors;
}
bool checkIfMatching1(const long long int hLength,
vector<long long int> amounts, const int start,
long long int totalSum) {
const int S = amounts.size();
int firstNonZero = start;
while (true) {
if (firstNonZero + hLength > S) {
return false;
}
long long int h = amounts[firstNonZero];
for (int i = firstNonZero; i < firstNonZero + hLength; i++) {
amounts[i] -= h;
if (amounts[i] < 0) {
return false;
}
totalSum -= h;
}
for (; firstNonZero < S; firstNonZero++) {
if (amounts[firstNonZero] > 0) {
break;
}
}
if (firstNonZero >= S) {
return totalSum == 0;
}
}
return totalSum == 0;
}
bool checkIfMatching(const long long int hLength, vector<long long int> amounts,
const int start, long long int totalSum) {
const int S = amounts.size();
int firstNonZero = start;
deque<long long int> stairs;
while (true) {
if (firstNonZero + hLength > S) {
return false;
}
stairs.clear();
stairs.push_back(0);
long long int h = amounts[firstNonZero];
int i = firstNonZero;
const int maxIExc = firstNonZero + hLength;
for (; i < maxIExc; i++) {
if (amounts[i] >= stairs.back()) {
h = amounts[i];
stairs.push_back(h);
amounts[i] -= h;
if (amounts[i] < 0) {
return false;
}
totalSum -= h;
} else {
return false;
}
}
stairs.pop_front();
while (stairs.back() == h) {
stairs.pop_back();
}
int STEPS = stairs.size();
if ((i + (int) STEPS) > S) {
return false;
}
for (int s = 0; s < STEPS; s++, i++) {
long long int d = (h - stairs[s]);
amounts[i] -= d;
if (amounts[i] < 0) {
return false;
}
totalSum -= d;
}
firstNonZero += hLength;
for (; firstNonZero < S; firstNonZero++) {
if (amounts[firstNonZero] > 0) {
break;
}
}
if (firstNonZero >= S) {
return totalSum == 0;
}
}
return totalSum == 0;
}
int findMaxWaveWidth(const vector<long long int> &numbers) {
int maxWidth = 0;
int currentWidth = 0;
for (long long int num : numbers) {
if (num != 0) {
currentWidth++; // extend current wave
if (currentWidth > maxWidth) {
maxWidth = currentWidth; // update max
}
} else {
currentWidth = 0; // reset on zero
}
}
return maxWidth;
}
int main() {
cin.tie(NULL);
cout.tie(NULL);
ios_base::sync_with_stdio(false);
int n;
cin >> n;
vector<long long int> amounts(n);
long long int a;
long long int totalSum = 0;
for (int i = 0; i < n; i++) {
cin >> a;
totalSum += a;
amounts[i] = a;
}
int start_ = -1;
for (int i = 0; i < n; i++) {
if (amounts[i] > 0) {
start_ = i;
break;
}
}
const int start = start_;
const int maxVal = findMaxWaveWidth(amounts);
vector<long long int> divisors = getDivisors(totalSum, maxVal);
for (unsigned int i = 0; i < divisors.size(); i++) {
const long long int divisor = divisors[i];
const bool match = checkIfMatching(divisor, amounts, start, totalSum);
if (match) {
cout << divisors[i] << endl;
break;
}
}
}
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 | #include <bits/stdc++.h> using namespace std; vector<pair<long long, int>> factorize(long long n) { vector<pair<long long, int>> factors; if (n % 2 == 0) { int cnt = 0; while (n % 2 == 0) { n /= 2; cnt++; } factors.push_back( { 2, cnt }); } for (long long p = 3; p * p <= n; p += 2) { if (n % p == 0) { int cnt = 0; while (n % p == 0) { n /= p; cnt++; } factors.push_back( { p, cnt }); } } if (n > 1) factors.push_back( { n, 1 }); return factors; } // Pruned generation void genDivsLimited(int i, long long current, const vector<pair<long long, int>> &factors, vector<long long> &divisors, long long maxVal) { if (current > maxVal) return; if (i == (int) factors.size()) { divisors.push_back(current); return; } long long p = factors[i].first; int exp = factors[i].second; for (int e = 0; e <= exp; ++e) { genDivsLimited(i + 1, current, factors, divisors, maxVal); // prevent overflow + useless work if (current > maxVal / p) break; current *= p; } } // Main function vector<long long> getDivisors(long long n, long long maxVal) { vector<pair<long long, int>> factors = factorize(n); vector<long long> divisors; genDivsLimited(0, 1, factors, divisors, maxVal); // sort descending sort(divisors.begin(), divisors.end(), greater<long long>()); return divisors; } bool checkIfMatching1(const long long int hLength, vector<long long int> amounts, const int start, long long int totalSum) { const int S = amounts.size(); int firstNonZero = start; while (true) { if (firstNonZero + hLength > S) { return false; } long long int h = amounts[firstNonZero]; for (int i = firstNonZero; i < firstNonZero + hLength; i++) { amounts[i] -= h; if (amounts[i] < 0) { return false; } totalSum -= h; } for (; firstNonZero < S; firstNonZero++) { if (amounts[firstNonZero] > 0) { break; } } if (firstNonZero >= S) { return totalSum == 0; } } return totalSum == 0; } bool checkIfMatching(const long long int hLength, vector<long long int> amounts, const int start, long long int totalSum) { const int S = amounts.size(); int firstNonZero = start; deque<long long int> stairs; while (true) { if (firstNonZero + hLength > S) { return false; } stairs.clear(); stairs.push_back(0); long long int h = amounts[firstNonZero]; int i = firstNonZero; const int maxIExc = firstNonZero + hLength; for (; i < maxIExc; i++) { if (amounts[i] >= stairs.back()) { h = amounts[i]; stairs.push_back(h); amounts[i] -= h; if (amounts[i] < 0) { return false; } totalSum -= h; } else { return false; } } stairs.pop_front(); while (stairs.back() == h) { stairs.pop_back(); } int STEPS = stairs.size(); if ((i + (int) STEPS) > S) { return false; } for (int s = 0; s < STEPS; s++, i++) { long long int d = (h - stairs[s]); amounts[i] -= d; if (amounts[i] < 0) { return false; } totalSum -= d; } firstNonZero += hLength; for (; firstNonZero < S; firstNonZero++) { if (amounts[firstNonZero] > 0) { break; } } if (firstNonZero >= S) { return totalSum == 0; } } return totalSum == 0; } int findMaxWaveWidth(const vector<long long int> &numbers) { int maxWidth = 0; int currentWidth = 0; for (long long int num : numbers) { if (num != 0) { currentWidth++; // extend current wave if (currentWidth > maxWidth) { maxWidth = currentWidth; // update max } } else { currentWidth = 0; // reset on zero } } return maxWidth; } int main() { cin.tie(NULL); cout.tie(NULL); ios_base::sync_with_stdio(false); int n; cin >> n; vector<long long int> amounts(n); long long int a; long long int totalSum = 0; for (int i = 0; i < n; i++) { cin >> a; totalSum += a; amounts[i] = a; } int start_ = -1; for (int i = 0; i < n; i++) { if (amounts[i] > 0) { start_ = i; break; } } const int start = start_; const int maxVal = findMaxWaveWidth(amounts); vector<long long int> divisors = getDivisors(totalSum, maxVal); for (unsigned int i = 0; i < divisors.size(); i++) { const long long int divisor = divisors[i]; const bool match = checkIfMatching(divisor, amounts, start, totalSum); if (match) { cout << divisors[i] << endl; break; } } } |
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