从O(n3)的最普通的方法,用数学数列方法优化到O(n2),最后优化到O(n),终于AC了,最后的这个确实不好想。
O(n3):
#include <iostream> #include <cstdio> using namespace std; int a[102400]; int main() { ios::sync_with_stdio(false); int T, kase = 0; cin >> T; while(T--){ int N; cin >> N; for(int i = 1; i <= N; ++i) cin >> a[i]; int best = a[0], l = 1, r = 1; for(int i = 1; i <= N; ++i) for(int j = i; j <= N; ++j){ int sum = 0; for(int k = i; k <= j; ++k) sum += a[k]; if(sum > best){ best = sum; l = i; r = j; } } if(kase) printf(" "); printf("Case %d: ", ++kase); printf("%d %d %d ", best, l, r); } return 0; }
O(n2):
#include <iostream> #include <cstdio> using namespace std; int a[102400]; int s[102400]; int main() { ios::sync_with_stdio(false); int T, kase = 0; cin >> T; while(T--){ int N; cin >> N; s[0] = 0; for(int i = 1; i <= N; ++i){ cin >> a[i]; s[i] = s[i-1] + a[i]; } int best = a[1], l = 1, r = 1; for(int i = 1; i <= N; ++i) for(int j = i; j <= N; ++j){ int sum = s[j] - s[i-1]; if(sum > best){ best = sum; l = i; r = j; } } if(kase) printf(" "); printf("Case %d: ", ++kase); printf("%d %d %d ", best, l, r); } return 0; }
O(n):
#include <iostream> #include <cstdio> using namespace std; int a[102400]; int main() { ios::sync_with_stdio(false); int T, kase = 0; cin >> T; while(T--){ int N, sum = 0, max = INT_MIN, l = 1, r = 1, t = 1; cin >> N; for(int i = 1; i <= N; ++i){ cin >> a[i]; sum += a[i]; if(sum > max) max = sum, l = t, r = i; if(sum < 0) t = i + 1, sum = 0; } if(kase) printf(" "); printf("Case %d: ", ++kase); printf("%d %d %d ", max, l, r); } return 0; }