PAT 1068. Find More Coins

#include <cstdio>
#include <cstdlib>
#include <vector>
#include <algorithm>

using namespace std;
const int ROWS = 10002;
const int COLS = 102;

char dp[ROWS][COLS];

bool dfs(vector<int> &coins, vector<int> &path, int idx, int target) {
    if (dp[idx][target] != -1) {
        return dp[idx][target];
    }
    if (idx >= coins.size()) return false;// should not happen
    if (coins[idx] == target) {
        // we found one
        path.push_back(idx);
        return true;
    }
    if (idx == coins.size() - 1) {
        // no more coins to try
        return false;
    }
    path.push_back(idx);
    // try use current idx coin
    if (coins[idx] < target) {
        if (dfs(coins, path, idx + 1, target - coins[idx])) {
            return true;
        }
    }
    path.pop_back();
    // try not use current idx coin
    if (dfs(coins, path, idx + 1, target)) {
        return true;
    }
    dp[idx][target] = false;
    return dp[idx][target];
}

int main() {
    int N, M;
    scanf("%d%d", &N, &M);
    
    vector<int> coins(N);
    
    for (int i=0; i<N; i++) {
        scanf("%d", &coins[i]);
    }
    sort(coins.begin(), coins.end());
    
    for (int i=0; i<ROWS; i++) {
        for (int j=0; j<COLS; j++) {
            dp[i][j] = -1;
        }
    }
    
    // use current st. j-coins>=0
    //dp[i][j] = dp[i-1][j-coins[i]]
    // not use current
    //dp[i][j] = dp[i-1][j];
    vector<int> path;
    bool res = dfs(coins, path, 0, M);
    int len = path.size();
    if (res) {
        if (len > 0) {
            printf("%d", coins[path[0]]);
        }
        for (int i=1; i<len; i++) {
            printf(" %d", coins[path[i]]);
        }
    } else {
        printf("No Solution");
    }
    return 0;
}