DP 之 CODE[VS] 1048 石子归并 （两种实现方式：递归，循环）

dp[i][j] : i到j，最小代价
dp[i][j] = min(dp[i][j], dp[i][k] + dp[k+1][j] + sum[i][j])
(注：i < k < j)

方式一：

// 递归（好理解）
#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <locale>
#include <cmath>
using namespace std;
const int INF = 0x3f3f3f3f;
const int MaxN = 105;

int N, dp[MaxN][MaxN], sum[MaxN][MaxN];


int Solve(int tbegin, int tend) {
    if (dp[tbegin][tend] != INF) return dp[tbegin][tend];
    for (int k = 0; (tbegin + k) < tend; ++k)
    {
        dp[tbegin][tend] = min(dp[tbegin][tend],
            Solve(tbegin, tbegin + k) + Solve(tbegin + k + 1, tend) + sum[tbegin][tend]);
    }
    //cout << tbegin << "-->" << tend << " : " << dp[tbegin][tend] << endl;
    return dp[tbegin][tend];
}

int main() {
    
    cin >> N;
    for (int i = 0; i < N; ++i)
    {
        cin >> sum[i][i];
        for (int j = 0; j < i; ++j)
        {
            sum[j][i] = sum[j][i - 1] + sum[i][i];
        }
    }
    for (int i = 0; i < N; ++i)
    {
        for (int j = 0; j < N; ++j)
        {
            if (i == j) dp[i][j] = 0;
            else dp[i][j] = INF;
        }
    }
    cout << Solve(0, N-1) << endl;


#ifdef HOME
    cerr << "Time elapsed: " << clock() / CLOCKS_PER_SEC << " ms" << endl;
#endif
    return 0;
}

方式二：

// 循环
#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <locale>
#include <cmath>
using namespace std;
const int INF = 0x3f3f3f3f;
const int MaxN = 105;



int N, dp[MaxN][MaxN], sum[MaxN][MaxN];


void Solve() {
    if (N == 1)
    {
        cout << sum[0][0] << endl;
        return;
    }

    for (int i = 0; i < N; ++i)
    {
        for (int j = 0; j < N; ++j)
        {
            if (i == j) dp[i][j] = 0;
            else dp[i][j] = INF;
        }
    }

    for (int k = 1; k < N; ++k)
    {
        for (int i = 0; (i + k) < N; ++i)
        {
            for (int j = i; j < i + k; ++j)
            {
                dp[i][i + k] = min(dp[i][i + k], dp[i][j] + dp[j + 1][i + k] + sum[i][i+k]);
                //cout << i << "-->" << i + k << " : " << dp[i][i + k] << endl;
            }
        }
    }
    cout << dp[0][N - 1] << endl;
}

int main() {
    
    cin >> N;
    for (int i = 0; i < N; ++i)
    {
        cin >> sum[i][i];
        for (int j = 0; j < i; ++j)
        {
            sum[j][i] = sum[j][i - 1] + sum[i][i];
        }
    }
    Solve();


#ifdef HOME
    cerr << "Time elapsed: " << clock() / CLOCKS_PER_SEC << " ms" << endl;
#endif
    return 0;
}