#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <math.h>
#include <stdio.h>
#include <deque>
#include <unordered_map>
#include <cassert>
#include <numeric>
#include <queue>
#include <string>
#include <stack>
#define LL long long
using namespace std;
bool alternate(int a, int b, int c)
{
if (a < b && b > c) return true;
if (a > b && b < c) return true;
return false;
}
int toState(int x, int y)
{
return x * 3 + y;
}
pair<int,int> fromState(int state) {
return make_pair(state/3, state%3);
}
const int SAME = 0;
const int MIN = 1;
const int MAX = 2;
const int MIN_VAL = -10000000;
const int MAX_VAL = 10000000;
int deref(int aRef, int val)
{
if (aRef == SAME) return val;
if (aRef == MIN) return MIN_VAL;
if (aRef == MAX) return MAX_VAL;
assert(false);
return -1;
}
LL solve(vector<int> &v) {
const int n = v.size();
const LL INF = 99999999;
vector<vector<int> > dp(9, vector<int>(n+1));
for (int state=0; state < 9; state++)
{
pair<int, int> p = fromState(state);
int x = p.first;
int y = p.second;
dp[state][0] = (x>0? 1 : 0);
dp[state][1] = (x>0 ? 1 : 0) + ((y>0) ? 1 : 0);
}
for (int i=2; i < n; i++)
{
for (int state=0; state < 9; state++)
{
dp[state][i] = INF;
pair<int, int> current = fromState(state);
for (int halfState=0; halfState < 3; halfState++) {
pair<int, int> prev = {current.second, halfState};
int prevState = toState(prev.first, prev.second);
if (current.second != prev.first) continue;
int diff = (current.first > 0) ? 1 : 0;
if (alternate(
deref(current.first, v[i]),
deref(current.second, v[i-1]),
deref(prev.second, v[i-2]))) {
int res = dp[prevState][i-1] + diff;
if (res < dp[state][i]) {
dp[state][i] = res;
}
}
}
//cerr << "i=" << i << ",dp[" << state << "]=" << dp[state][i] << ",";
}
//cerr << "\n";
}
LL changes = INF;
for (int state=0; state < 9; state++)
{
changes = min((int)changes, dp[state][n-1]);
}
return changes;
}
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(NULL);
int n;
cin >> n;
vector<int> v;
for (int i=0; i < n; i++) {
int x; cin >> x;
v.emplace_back(x);
}
LL res = solve(v);
cout << res << "\n";
}
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 | #include <iostream> #include <vector> #include <algorithm> #include <set> #include <math.h> #include <stdio.h> #include <deque> #include <unordered_map> #include <cassert> #include <numeric> #include <queue> #include <string> #include <stack> #define LL long long using namespace std; bool alternate(int a, int b, int c) { if (a < b && b > c) return true; if (a > b && b < c) return true; return false; } int toState(int x, int y) { return x * 3 + y; } pair<int,int> fromState(int state) { return make_pair(state/3, state%3); } const int SAME = 0; const int MIN = 1; const int MAX = 2; const int MIN_VAL = -10000000; const int MAX_VAL = 10000000; int deref(int aRef, int val) { if (aRef == SAME) return val; if (aRef == MIN) return MIN_VAL; if (aRef == MAX) return MAX_VAL; assert(false); return -1; } LL solve(vector<int> &v) { const int n = v.size(); const LL INF = 99999999; vector<vector<int> > dp(9, vector<int>(n+1)); for (int state=0; state < 9; state++) { pair<int, int> p = fromState(state); int x = p.first; int y = p.second; dp[state][0] = (x>0? 1 : 0); dp[state][1] = (x>0 ? 1 : 0) + ((y>0) ? 1 : 0); } for (int i=2; i < n; i++) { for (int state=0; state < 9; state++) { dp[state][i] = INF; pair<int, int> current = fromState(state); for (int halfState=0; halfState < 3; halfState++) { pair<int, int> prev = {current.second, halfState}; int prevState = toState(prev.first, prev.second); if (current.second != prev.first) continue; int diff = (current.first > 0) ? 1 : 0; if (alternate( deref(current.first, v[i]), deref(current.second, v[i-1]), deref(prev.second, v[i-2]))) { int res = dp[prevState][i-1] + diff; if (res < dp[state][i]) { dp[state][i] = res; } } } //cerr << "i=" << i << ",dp[" << state << "]=" << dp[state][i] << ","; } //cerr << "\n"; } LL changes = INF; for (int state=0; state < 9; state++) { changes = min((int)changes, dp[state][n-1]); } return changes; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(NULL); int n; cin >> n; vector<int> v; for (int i=0; i < n; i++) { int x; cin >> x; v.emplace_back(x); } LL res = solve(v); cout << res << "\n"; } |
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