Submission #1088686

#	Time	Username	Problem	Language	Result	Execution time	Memory
1088686		xnqs	Divide and conquer (IZhO14_divide)	C++17	100 / 100	22 ms	7040 KiB

divide

#include <iostream>
#include <fstream>
#include <vector>
#include <queue>
#include <utility>
#include <algorithm>
#include <map>
#include <unordered_map>
#include <cstring>

int x;
int diff_coords[100005];
int coords[100005];
int arr1[100005];
int arr2[100005];
int64_t pfx2[100005];
int64_t pfx3[100005];
int64_t pfx_min[100005];

int main() {
	std::ios_base::sync_with_stdio(false);
	std::cin.tie(NULL);
	std::cout.tie(NULL);

	std::cin >> x;
	for (int i = 1; i <= x; i++) {
		int a, b, c;
		std::cin >> a >> b >> c;
		coords[i] = a;
		diff_coords[i-1] = coords[i] - coords[i-1];
		arr1[i] = c;
		arr2[i] = b;
		pfx2[i] = pfx2[i-1] + arr2[i];
	}

	pfx_min[0] = 0x3f3f3f3f3f3f3f3f;
	for (int i = 1; i <= x; i++) {
		pfx3[i] = pfx3[i-1] + arr1[i] - diff_coords[i];
		pfx_min[i] = std::min(pfx_min[i-1], pfx3[i]);
	}

	int64_t ans = 0;
	// case 1: individual elements
	for (int i = 1; i <= x; i++) {
		ans = std::max(ans, (int64_t)arr2[i]);
	}

	// case 2: sequences of two or more elements
	int64_t base_gold = arr2[1];
	int64_t base_diff = arr1[1];
	for (int i = 2; i <= x; i++) {
		base_gold += arr2[i];
		base_diff += arr1[i];
		base_diff -= diff_coords[i-1];

		if (base_diff>=0) {
			ans = std::max(ans, base_gold);
			continue;
		}

		int64_t gold = base_gold;
		int64_t diff = base_diff;

		// binary search for minimum position where sum is <= base_diff
		const auto bs = [&]() {
			int ret = i;
			int l = 1, r = i-1;
			while (l<=r) {
				int m = (l+r)>>1;
				if (pfx_min[m]<=base_diff) {
					ret = m;
					r = m-1;
				}
				else {
					l = m+1;
				}
			}
			return ret;
		};

		int pos = bs();
		if (pos==i) {
			continue;
		}

		gold -= pfx2[pos];
		ans = std::max(ans,gold);
	}

	std::cout << ans << "\n";
}

Compilation message (stderr)

divide.cpp: In function 'int main()':
divide.cpp:62:11: warning: unused variable 'diff' [-Wunused-variable]
   62 |   int64_t diff = base_diff;
      |           ^~~~

• Subtask 1: 17 / 17
• Subtask 2: 31 / 31
• Subtask 3: 52 / 52