求最大子串

Posted 2020-08-29

int n, a[maxn];
int maxSubstr() {
    int sum = 0, minsum = 0, answer = 0;
    for (int i = 1; i <= n; ++ i) {
        sum += a[i];
        minsum = min(sum, minsum);
        answer = max(answer, sum - minsum);
    }
    return answer;
}

 进阶版

/*二、给你两列数 A; B, 定义一个子串 [l; r] 的权值为
   ∑r i=l Ai
k= ___________
   ∑r i=l Bi
问权值最大的子串.*/
const double inf = 1e32;
int n, a[maxn], b[maxn];
double c[maxn];
double maxSubstr() {
    double sum = 0, minsum = inf, answer = -inf;
    for (int i = 1; i <= n; ++ i) {
        sum += c[i];
        answer = max(answer, sum - minsum);
        minsum = min(sum, minsum);
    }
    return answer;
}
double erfen() {
    double l(-inf), r(inf);
    while (l + 1e-10 < r) { 
        double mid = (l + r)/ 2;
        for (int i = 1; i <= n; ++ i) {
            c[i] = a[i] - mid * b[i];
        }
        if (maxSubstr() >= 0) {
            l = mid;
        } else {
            r = mid - 1e-10;
        }
} //把分母乘过去二分答案