分石子问题简易题解

有N个石子,每个石子重量Qi；按顺序将它们装进K个筐中；求一种方案，使得最重的筐最轻。

样例：
N=9,K=3
9 7 5 6 8 4 3 2 7
16 19 16
最轻的最重筐为19

思路：
二分搜索（PS：这就是传说中的“二分答案”？）
IOI中国国家集训队2005论文《参数搜索的应用》中有详细分析，这里我就不多说了，下面是我的代码。

//2011.11.06
//By LYLtim

#include<stdio.h>
#include<stdlib.h>

size_t N, K;
unsigned *Q, sum;

void Init(void)
{
    size_t i;
    scanf("%lu %lu", &N, &K);
    Q = malloc(sizeof(unsigned)*N);
    for(i = 0; i < N; i++) {
        scanf("%u", &Q[i]);
        sum += Q[i];
    }
}

char Can(unsigned P)
{
    unsigned *Basket;
    size_t i, nB = 0;
    Basket = (unsigned *) calloc(K, sizeof(unsigned));
    for (i = 0; i < N; i++) {
        if (Basket[nB] + Q[i] <= P)
            Basket[nB] += Q[i];
        else {
            if (nB == K - 1) //begin from 0, full.
                return 0;
            Basket[++nB] = Q[i];
        }
    }
    free(Basket);
    return 1;
}

unsigned Search(void)
{
    int start = Q[0], end = sum;
    while (start <= end) {
        unsigned m = (start + end) >> 1;
        if (Can(m))
            end = m - 1;
        else
            start = m + 1;
    }
    free(Q);
    return start;
}

int main(void)
{
    Init();
    printf("%u", Search());
    return 0;
}