321E - Ciel and Gondolas - CodeForces Solution

#include <iostream>
#include <vector>
#include <tuple>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <cmath>
#include <random>
#include <string>
#include <bitset>
#include <cassert>
#include <climits>
#include <algorithm>
#include <unordered_set>
#include <unordered_map>
using namespace std;
 
#define ll long long
#define f first
#define s second
 
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
 
template<typename A> void __print(const A &x);
template<typename A, typename B> void __print(const pair<A, B> &p);
template<typename... A> void __print(const tuple<A...> &t);
template<typename T> void __print(stack<T> s);
template<typename T> void __print(queue<T> q);
template<typename T, typename... U> void __print(priority_queue<T, U...> q);
 
template<typename A> void __print(const A &x) {
    bool first = true;
    cerr << '{';
    for (const auto &i : x) {
        cerr << (first ? "" : ","), __print(i);
        first = false;
    }
    cerr << '}';
}
 
template<typename A, typename B> void __print(const pair<A, B> &p) {
    cerr << '(';
    __print(p.f);
    cerr << ',';
    __print(p.s);
    cerr << ')';
}
 
template<typename... A> void __print(const tuple<A...> &t) {
    bool first = true;
    cerr << '(';
    apply([&first] (const auto &...args) { ((cerr << (first ? "" : ","), __print(args), first = false), ...); }, t);
    cerr << ')';
}
 
template<typename T> void __print(stack<T> s) {
    vector<T> debugVector;
    while (!s.empty()) {
        T t = s.top();
        debugVector.push_back(t);
        s.pop();
    }
    reverse(debugVector.begin(), debugVector.end());
    __print(debugVector);
}
 
template<typename T> void __print(queue<T> q) {
    vector<T> debugVector;
    while (!q.empty()) {
        T t = q.front();
        debugVector.push_back(t);
        q.pop();
    }
    __print(debugVector);
}
 
template<typename T, typename... U> void __print(priority_queue<T, U...> q) {
    vector<T> debugVector;
    while (!q.empty()) {
        T t = q.top();
        debugVector.push_back(t);
        q.pop();
    }
    __print(debugVector);
}
 
void _print() { cerr << "]\n"; }
 
template <typename Head, typename... Tail> void _print(const Head &H, const Tail &...T) {
    __print(H);
    if (sizeof...(T)) cerr << ", ";
    _print(T...);
}
 
#ifdef DEBUG
	#define D(...) cerr << "Line: " << __LINE__ << " [" << #__VA_ARGS__ << "] = ["; _print(__VA_ARGS__)
#else
    #define D(...)
#endif

int read() {
    char ch = getchar();
    int ret = 0;
    for(; ch < '0' || ch > '9'; ch = getchar());
    for(; ch >= '0' && ch <= '9'; ch = getchar()) {
        ret = (ret << 3) + (ret << 1) + ch - '0';
    }
    return ret;
}

int n, k, u[4005][4005], c[4005][4005], tmp1[4005], tmp2[4005];

void dp(int l, int r, int cl, int cr) {
    if (r < l || cr < cl) return;
    int m = (l + r) / 2, idx = cl;
    for (int i = min(m, cr + 1), x; i > cl; i--) {
        x = c[i][m];
        if (tmp2[i - 1] + x < tmp1[m]) {
            tmp1[m] = tmp2[i - 1] + x;
            idx = i - 1;
        }
    }
    dp(l, m - 1, cl, idx);
    dp(m + 1, r, idx, cr);
}

int main() {

    ios_base::sync_with_stdio(false);
    cin.tie(0);

    scanf("%d%d", &n, &k);
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            u[i][j] = read();
            u[i][j] += u[i][j - 1];
        }
    }

    for (int i = 1; i <= n; i++) {
        for (int j = i + 1; j <= n; j++) {
            c[i][j] = c[i][j - 1] + u[j][j] - u[j][i - 1];
        }
    }
    for (int i = 1; i <= n; i++) {
        tmp1[i] = c[1][i];
    }

    for (int i = 2; i <= k; i++) {
        swap(tmp1, tmp2);
        fill(tmp1, tmp1 + 4005, 2e9);
        dp(i, n, i - 1, n - 1);
    }

    printf("%d\n", tmp1[n]);

}