Railway Construction

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define N	200000
#define N_	(1 << 18)	/* N_ = pow2(ceil(log2(N))) */
#define M	300000
#define Q	200000
#define INF	0x3f3f3f3f3f3f3f3fLL

typedef unsigned long long ull;

int ij[M], ww[M], m;
int *eh[N], eo[N], *ei[N], eo_[N], n;

void append(int **eh, int *eo, int i, int h) {
	int o = eo[i]++;

	if (o >= 2 && (o & o - 1) == 0)
		eh[i] = (int *) realloc(eh[i], o * 2 * sizeof *eh[i]);
	eh[i][o] = h;
}

long long dd[N]; int pq[N], iq[1 + N], cnt;

int lt(int i, int j) { return dd[i] < dd[j]; }

int p2(int p) {
	return (p *= 2) > cnt ? 0 : (p < cnt && lt(iq[p + 1], iq[p]) ? p + 1 : p);
}

void pq_up(int i) {
	int p, q, j;

	for (p = pq[i]; (q = p / 2) && lt(i, j = iq[q]); p = q)
		iq[pq[j] = p] = j;
	iq[pq[i] = p] = i;
}

void pq_dn(int i) {
	int p, q, j;

	for (p = pq[i]; (q = p2(p)) && lt(j = iq[q], i); p = q)
		iq[pq[j] = p] = j;
	iq[pq[i] = p] = i;
}

void pq_add_last(int i) {
	iq[pq[i] = ++cnt] = i;
}

int pq_remove_first() {
	int i = iq[1], j = iq[cnt--];

	if (j != i)
		pq[j] = 1, pq_dn(j);
	pq[i] = 0;
	return i;
}

int qu[N];

void dijkstra() {
	int cnt_;

	memset(dd, 0x3f, n * sizeof *dd);
	dd[0] = 0, pq_add_last(0);
	cnt_ = 0;
	while (cnt) {
		int i = pq_remove_first(), o;

		qu[cnt_++] = i;
		for (o = eo[i]; o--; ) {
			int h = eh[i][o], j = i ^ ij[h];
			long long d = dd[i] + ww[h];

			if (dd[j] > d) {
				if (dd[j] == INF)
					pq_add_last(j);
				dd[j] = d, pq_up(j);
			}
		}
	}
}

int query(int p, int r) {
	int lower = -1, upper = eo_[p];

	while (upper - lower > 1) {
		int o = (lower + upper) / 2;

		if (ei[p][o] < r)
			lower = o;
		else
			upper = o;
	}
	return lower + 1;
}

int pp[N], ll[N], cc[N + 1], ii1[N], ii2[N]; ull vv[N], ans_;
int i1_, i2_, l_, r_, i_; ull x_;

void add(int l, int r) {
	int i1, i2;

	if (l != -1) {
		i1 = ii1[l], i2 = ii2[l];
		if (ii1[l] != i_) {
			if (ii1[l] == -1 || vv[ii1[l]] > vv[i_])
				ii2[l] = ii1[l], ii1[l] = i_;
			else if (ii2[l] == -1 || vv[ii2[l]] > vv[i_])
				ii2[l] = i_;
			ii1[r - 1] = ii1[l], ii2[r - 1] = ii2[l];
		}
	} else
		i1 = -1, i2 = -1;
	if (i1_ == -2)
		i1_ = i1, i2_ = i2, l_ = l;
	else if ((l == -1 || i1_ != i1 || i2_ != i2) && (i1_ != i_ || i1 != i_)) {
		int r1 = l == -1 ? r_ : l;

		if (i1_ == i_)
			ans_ -= x_ * (cc[r1] - cc[l_] - (query(i_, r1) - query(i_, l_)));
		else {
			int c;

			if (i1_ != -1) {
				c = query(i1_, r1) - query(i1_, l_);
				ans_ -= vv[i1_] * (cc[r1] - cc[l_] - c) + (i2_ == -1 ? 0 : (i2_ == i_ ? vv[i2_] + x_ : vv[i2_]) * c);
			}
			if (i1_ == -1 || vv[i1_] > vv[i_])
				i2_ = i1_, i1_ = i_;
			else if (i2_ == -1 || vv[i2_] > vv[i_])
				i2_ = i_;
			c = query(i1_, r1) - query(i1_, l_);
			ans_ += vv[i1_] * (cc[r1] - cc[l_] - c) + (i2_ == -1 ? 0 : vv[i2_] * c);
		}
		i1_ = i1, i2_ = i2, l_ = l;
	}
	r_ = r;
}

void pus(int l, int r) {
	if (ii1[l] == ii1[r - 1] && ii2[l] == ii2[r - 1]) {
		int m = (l + r) / 2;

		ii1[m - 1] = ii1[m] = ii1[l], ii2[m - 1] = ii2[m] = ii2[l];
	}
}

void update(int l, int r) {
	int m;

	if (r <= ll[i_] || ii2[l] != -1 && ii2[l] != i_ && vv[ii2[l]] <= vv[i_])
		return;
	if (ll[i_] <= l && ii1[l] == ii1[r - 1] && (ii1[l] == i_ || ii2[l] == ii2[r - 1])) {
		add(l, r);
		return;
	}
	m = (l + r) / 2;
	pus(l, r), update(l, m), update(m, r);
}

int main() {
	static int ii[Q], xx[Q];
	static ull ans[Q + 1];
	int q, h, i, j, p, o;

	scanf("%d%d%d", &n, &m, &q);
	for (i = 0; i < n; i++) {
		scanf("%llu", &vv[i]);
		eh[i] = (int *) malloc(2 * sizeof *eh[i]);
	}
	for (h = 0; h < m; h++) {
		int w;

		scanf("%d%d%d", &i, &j, &w), i--, j--;
		ij[h] = i ^ j, ww[h] = w;
		append(eh, eo, i, h), append(eh, eo, j, h);
	}
	dijkstra();
	memset(pp, -1, n * sizeof *pp);
	for (j = 0; j < n; j++)
		for (o = eo[j]; o--; ) {
			h = eh[j][o], i = j ^ ij[h];
			if (dd[i] + ww[h] == dd[j])
				pp[j] = pp[j] == -1 ? i : -2;
		}
	pp[0] = -2;
	for (i = 1; i < n; i++)
		if (pp[i] == 0)
			pp[i] = -1;
	for (p = 0; p < n; p++)
		ei[p] = (int *) malloc(2 * sizeof *ei[p]);
	for (i = 0; i < n; i++) {
		p = pp[qu[i]];
		if (p == -2)
			continue;
		cc[i + 1] = 1;
		if (p >= 0)
			append(ei, eo_, p, i);
	}
	for (i = 1; i <= n; i++)
		cc[i] += cc[i - 1];
	for (i = n - 1; i >= 0; i--)
		ll[qu[i]] = i + 1 == n || dd[qu[i]] != dd[qu[i + 1]] ? i + 1 : ll[qu[i + 1]];
	for (h = 0; h < q; h++) {
		scanf("%d%d", &ii[h], &xx[h]), ii[h]--;
		vv[ii[h]] += xx[h];
	}
	ii1[0] = ii2[0] = -1, ii1[n - 1] = ii2[n - 1] = -1;
	for (i = 0; i < n; i++) {
		i_ = i, i1_ = i2_ = -2, l_ = -1, x_ = 0;
		update(0, n), add(-1, -1);
	}
	ans[q] = ans_;
	for (h = q - 1; h >= 0; h--) {
		i_ = ii[h], i1_ = i2_ = -2, l_ = -1, x_ = xx[h], vv[i_] -= x_;
		update(0, n), add(-1, -1);
		ans[h] = ans_;
	}
	for (h = 0; h <= q; h++)
		printf("%llu\n", ans[h]);
	return 0;
}