【分治】JZOJ_5231 序列问题

题意

思路

代码

#include<cstdio>
#include<algorithm>

const int P = 1e9 + 7;
int n;
long long ans;
long long a[500001], minr[500001], maxr[500001];
long long minPre[500001], maxPre[500001], s[500001];

void solve(int l, int r) {
	if (l > r) return;
	if (l == r) {
		ans = (ans + a[l] * a[l]) % P;
		return;
	}
	int mid = l + r >> 1;
	solve(l, mid);
	solve(mid + 1, r);
	minr[mid] = 1000000000;
	s[mid] = maxr[mid] = minPre[mid] = maxPre[mid] = 0;
	for (int i = mid + 1; i <= r; i++) {
		minr[i] = std::min(minr[i - 1], a[i]);
		maxr[i] = std::max(maxr[i - 1], a[i]);
		minPre[i] = minPre[i - 1] + minr[i];
		maxPre[i] = maxPre[i - 1] + maxr[i];
		s[i] = (s[i - 1] + minr[i] * maxr[i]) % P;
	}
	long long minl = 1000000000, maxl = 0;
	int u = mid, v = mid;
	for (int i = mid; i >= l; i--) {
		minl = std::min(minl, a[i]);
		maxl = std::max(maxl, a[i]);
		while (minr[u + 1] >= minl && u < r) u++;
		while (maxr[v + 1] <= maxl && v < r) v++;
		if (u < v) {
			ans = (ans + (u - mid) % P * maxl % P * minl % P) % P;
			ans = (ans + (minPre[v] - minPre[u]) % P * maxl % P) % P;
			ans = (ans + s[r] - s[v]) % P;
		} else {
			ans = (ans + (v - mid) % P * maxl % P * minl % P) % P;
			ans = (ans + (maxPre[u] - maxPre[v]) % P * minl) % P;
			ans = (ans + s[r] - s[u]) % P;
		}
	}
}

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++)
		scanf("%d", &a[i]);
	solve(1, n);
	printf("%lld", ans);
}