Codeforces 935E Fafa and Ancient Mathematics dp

Fafa and Ancient Mathematics

转换成树上问题dp一下。

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ull unsigned long long

using namespace std;

const int N = 1e4 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

char s[N];
int P, M, n, ans;
int mxdp[N][101], mndp[N][101], cnt[N];
int weight[N];

inline bool chkmax(int &a, int b) {
    return a < b ? a = b, true : false;
}
inline bool chkmin(int &a, int b) {
    return a > b ? a = b, true : false;
}

int getPos(int l, int r) {
    int w = 0, pos = -1;
    int digit = -1;
    for(int i = l; i <= r; i++) {
        if(s[i] == '(') w += 10000;
        else if(s[i] == ')') w -= 10000;
        else if(s[i] == '?') weight[i] = w;
        if(isdigit(s[i])) digit = i;
    }
    for(int i = l; i <= r; i++) {
        if(s[i] == '?') {
            if(pos == -1 || weight[pos] > weight[i]) pos = i;
        }
    }
    if(~pos) return pos;
    return digit;
}

void dfs(int l, int r, int rt) {
    if(s[rt] != '?') {
        mxdp[rt][0] = s[rt] - '0';
        mndp[rt][0] = s[rt] - '0';
        return;
    }
    int ls = getPos(l, rt - 1);
    int rs = getPos(rt + 1, r);
    dfs(l, rt - 1, ls);
    dfs(rt + 1, r, rs);
    cnt[rt] = cnt[ls] + cnt[rs] + 1;
    if(P < M) {
        for(int i = 0; i <= cnt[ls]; i++) {
            for(int j = 0; j <= cnt[rs]; j++) {
                if(i + j > P) continue;
                if(P - i - j > 0) {
                    chkmax(mxdp[rt][i + j + 1], mxdp[ls][i] + mxdp[rs][j]);
                    chkmin(mndp[rt][i + j + 1], mndp[ls][i] + mndp[rs][j]);
                }
                if(M - (cnt[ls] - i) - (cnt[rs] - j) > 0) {
                    chkmax(mxdp[rt][i + j], mxdp[ls][i] - mndp[rs][j]);
                    chkmin(mndp[rt][i + j], mndp[ls][i] - mxdp[rs][j]);
                }
            }
        }
    } else {
        for(int i = 0; i <= cnt[ls]; i++) {
            for(int j = 0; j <= cnt[rs]; j++) {
                if(i + j > M) continue;
                if(M - i - j > 0) {
                    chkmax(mxdp[rt][i + j + 1], mxdp[ls][i] - mndp[rs][j]);
                    chkmin(mndp[rt][i + j + 1], mndp[ls][i] - mxdp[rs][j]);
                }
                if(P - (cnt[ls] - i) - (cnt[rs] - j) > 0) {
                    chkmax(mxdp[rt][i + j], mxdp[ls][i] + mxdp[rs][j]);
                    chkmin(mndp[rt][i + j], mndp[ls][i] + mndp[rs][j]);
                }
            }
        }
    }
}

int main() {
    scanf("%s", s + 1);
    n = strlen(s + 1);
    scanf("%d%d", &P, &M);
    for(int i = 1; i <= n; i++)
        for(int j = 0; j <= min(P, M); j++)
            mxdp[i][j] = -inf, mndp[i][j] = inf;
    int root = getPos(1, n);
    dfs(1, n, root);
    printf("%d\n", mxdp[root][min(P, M)]);
    return 0;
}

/*
*/