uva 12501 Bulky process of bulk reduction 线段树(mid)

UVa Online Judge

　　线段树的应用。【成段更新，成段查询】

　　因为每个位置都要乘上相应的权值，而且乘的大小依次递增，所以就要构建两棵线段树，一棵记录原始值，另外一个就乘上它所在位置的标号就好了。query的时候就直接两部分相减，得到答案。例如，第一棵树的结点记录为a[i]，那么第二棵树的就是i*a[i]了。

　　其实这题不难，不过打上来是为了提醒自己注意延迟标记的更新。这题因为延迟标记更新搞错了，所以就产生了严重错误。同时，这次也要感谢Troy师兄，让我明白了debug还是要靠自己的，不是所有问题都有oj帮你检测代码是否通过，不是所有问题的解决都会有标程给你。所以，要证明一个算法没问题，最好还是自己打个暴力的程序，跑一跑随机的数据，然后跟自己优化的算法作比较。

暴力统计以及随机数据产生的代码：

#define prog 1

#if prog == 0

#include <cstdio>
#include <cstring>

const int maxn = 100;
typedef long long ll;
int a[maxn];

int main() {
    int T;

    freopen("in", "r", stdin);
    freopen("cmp", "w", stdout);

    scanf("%d", &T);
    while (T--) {
        int n, m;

        puts("");
        scanf("%d%d", &n, &m);
        for (int i = 1; i <= n; i++) {
            a[i] = 100;
        }
        while (m--) {
            char op[10];

            scanf("%s", op);
            if (!strcmp(op, "query")) {
                ll ans = 0;

                int l, r;

                scanf("%d%d", &l, &r);
                for (int i = l; i <= r; i++) {
                    ans += a[i] * (i - l + 1);
                }
                printf("%lld\n", ans);
            } else {
                int l, r, d;

                scanf("%d%d%d", &l, &r, &d);
                for (int i = l; i <= r; i++) {
                    a[i] += d;
                }
            }
        }
    }

    return 0;
}

#endif

#if prog == 1

#include <cstdio>
#include <ctime>
#include <cmath>
#include <algorithm>
#include <cstdlib>

using namespace std;

int main() {
    int T;

    freopen("in", "w", stdout);
    scanf("%d", &T);
    printf("%d\n", T);

    srand(time(NULL));
    while (T--) {
        int n = rand() % 10 + 40, m = rand() % 10 + 40;

        printf("%d %d\n", n, m);
        while (m--) {
            if (rand() & 1) {
                int a = rand() % n + 1, b = rand() % n + 1;

                if (a > b) swap(a, b);
                printf("query %d %d\n", a, b);
            } else {
                int a = rand() % n + 1, b = rand() % n + 1;

                if (a > b) swap(a, b);
                printf("change %d %d %d\n", a, b, rand() % 2000 - 1000);
            }
        }
    }

    return 0;
}

#endif

AC代码：

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cstdlib>

using namespace std;

#define lson l, m, rt << 1
#define rson m + 1, r, rt << 1 | 1
typedef long long ll;

const int maxn = 100005;
ll sum1[maxn << 2], sum2[maxn << 2], late[maxn << 2];

void up(int rt) {
    int ls = rt << 1, rs = rt << 1 | 1;

    sum1[rt] = sum1[ls] + sum1[rs];
    sum2[rt] = sum2[ls] + sum2[rs];
}

void down(int rt, int l, int r) {
    if (late[rt]) {
        int ls = rt << 1, rs = rt << 1 | 1;
        int m = (l + r) >> 1;

        late[ls] += late[rt];
        late[rs] += late[rt];

        sum1[ls] += late[rt] * (m - l + 1);
        sum1[rs] += late[rt] * (r - m);

        sum2[ls] += late[rt] * ((ll)l + m) * (m - l + 1) / 2;
        sum2[rs] += late[rt] * ((ll)m + 1 + r) * (r - m) / 2;

        late[rt] = 0;
//        printf("l %d r %d  %lld %lld %lld %lld\n", l, r, sum1[ls], sum1[rs], sum2[ls], sum2[rs]);
    }
}

void build(int l, int r, int rt) {
    late[rt] = 0;
    if (l == r) {
        sum1[rt] = 100;
        sum2[rt] = 100 * l;

        return ;
    }
    int m = (l + r) >> 1;

    build(lson);
    build(rson);
    up(rt);
}

void update(int L, int R, ll key, int l, int r, int rt) {
    if (L <= l && r <= R) {
//        printf("l %d r %d  %lld\n", l, r, late[rt]);
        late[rt] += key;
        sum1[rt] += key * (r - l + 1);
        sum2[rt] += key * ((ll)l + r) * (r - l + 1) / 2;

        return ;
    }
    int m = (l + r) >> 1;

    down(rt, l, r);
    if (L <= m) update(L, R, key, lson);
    if (m < R) update(L, R, key, rson);
    up(rt);
//    printf("%d %d : %lld %lld\n", l, r, sum1[rt], sum2[rt]);
}

ll query(int L, int R, int l, int r, int rt) {
    if (L <= l && r <= R) {
//        printf("query %lld %lld\n", sum1[rt], sum2[rt]);
        return sum2[rt] - sum1[rt] * (L - 1);
    }
    int m = (l + r) >> 1;
    ll ret = 0;

    down(rt, l, r);
    if (L <= m) ret += query(L, R, lson);
    if (m < R) ret += query(L, R, rson);

    return ret;
}

int main() {
    int T;
    char op[10];

//    freopen("in", "r", stdin);
//    freopen("out", "w", stdout);

    scanf("%d", &T);

    for (int cc = 1; cc <= T; cc++) {
        int n, m;

        scanf("%d%d", &n, &m);
        build(1, n, 1);
        printf("Case %d:\n", cc);

        while (m--) {
            scanf("%s", op);
            if (!strcmp(op, "query")) {
                int a, b;

                scanf("%d%d", &a, &b);
                printf("%lld\n", query(a, b, 1, n, 1));
            } else {
                int a, b;
                ll c;

                scanf("%d%d%lld", &a, &b, &c);
                update(a, b, c, 1, n, 1);
            }
        }
    }

    return 0;
}

　　继续学习如何debug！

——written by Lyon