From 3204ce5c1e6ebe1b34c5f83854df91742b5349a7 Mon Sep 17 00:00:00 2001
From: Zengtudor <Zengtudor@outlook.com>
Date: Tue, 19 Aug 2025 19:26:00 +0800
Subject: [PATCH] update

---
 src/8/19/segmatrixdp.cpp | 92 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100644 src/8/19/segmatrixdp.cpp

diff --git a/src/8/19/segmatrixdp.cpp b/src/8/19/segmatrixdp.cpp
new file mode 100644
index 0000000..7f6450e
--- /dev/null
+++ b/src/8/19/segmatrixdp.cpp
@@ -0,0 +1,92 @@
+#include <algorithm>
+#include <climits>
+#include <cstdint>
+#include <iostream>
+#include <vector>
+
+using ll = int64_t;
+const ll INF = INT_MAX;
+
+struct M22{
+    std::vector<std::vector<ll>> v{2,std::vector<ll>(2)};
+    M22 operator*(const M22&o){
+        M22 n;
+        n.v[0][0]=std::max(v[0][0]+o.v[0][0],v[0][1]+o.v[1][0]);
+        n.v[0][1]=std::max(v[0][0]+o.v[0][1],v[0][1]+o.v[1][1]);
+        n.v[1][0]=std::max(v[1][0]+o.v[0][0],v[1][1]+o.v[1][0]);
+        n.v[1][1]=std::max(v[1][0]+o.v[0][1],v[1][1]+o.v[1][1]);
+        return n;
+    }
+    M22&operator*=(const M22&o){
+        *this= *this * o;
+        return *this;
+    }
+};
+std::vector<M22> t;
+std::vector<M22> nums;
+
+M22 create(ll l, ll r, ll idx) {
+    if (l == r) {
+        t[idx] = nums[l];
+        return t[idx];
+    }
+    ll mid = (l + r) / 2;
+    t[idx] = create(mid + 1, r, 2 * idx + 2)*create(l, mid, 2 * idx + 1);
+    return t[idx];
+}
+
+void update(ll l, ll r, ll idx, ll pos,const M22&val) {
+    if (l == r) {
+        t[idx] = val;
+        return;
+    }
+    ll mid = (l + r) / 2;
+    if (pos <= mid) {
+        update(l, mid, 2 * idx + 1, pos, val); 
+    } else {
+        update(mid + 1, r, 2 * idx + 2, pos, val);
+    }
+    t[idx] = t[2 * idx + 2]*t[2 * idx + 1];
+}
+
+M22 query(ll cur,ll ql,ll qr,ll l,ll r){
+    if(qr<l || r<ql)return M22{{{0, -INF}, {-INF, 0}}};
+    if(ql<=l && r<=qr)return t[cur];
+    ll mid = (l+r)/2;
+    return query(cur*2+2, ql, qr, mid+1, r)*query(cur*2+1, ql, qr, l, mid);
+}
+
+
+int main(){
+    ll n;
+    std::cin>>n;
+    ll q;
+    std::cin>>q;
+    t.resize(4*n);
+    nums.resize(n);
+    std::vector<ll> a(n),b(n);
+    for(ll i=0; i<n; i++){
+        std::cin>>a[i];
+        std::cin>>b[i];
+    }
+    for(ll i=0;i<n;i++){
+        nums[i].v[0][0]=a[i];
+        nums[i].v[0][1]=b[i];
+        nums[i].v[1][1]=INT_MIN;
+    }
+    create(0, n - 1, 0);
+    const auto output=[&](){
+        M22 nm = query(0, 0, n-1, 0, n-1);
+        std::cout<< std::max(nm.v[0][0] , nm.v[0][1]) <<'\n';
+    };
+    output();
+    while(q--){
+        ll idx;
+        std::cin>>idx;
+        --idx;
+        std::cin>>a[idx]>>b[idx];
+        update(0, n - 1, 0, idx, M22{{{a[idx],b[idx]},{0,INT_MIN}}});
+        output();
+    }
+    std::cin>>q;
+}
\ No newline at end of file