POJ 3258 River Hopscotch （二分搜索）

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挑战程序设计竞赛(第2版) 习题例题解同时被 2 个专栏收录

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本文介绍了一种通过移除部分石头来最大化河中跳跃最小距离的方法。在一个直的河流中，通过调整石头的位置，帮助农夫了解如何提高跳跃挑战的难度。

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River Hopscotch

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 8422		Accepted: 3620

Description

Every year the cows hold an event featuring a peculiar version of hopscotch that involves carefully jumping from rock to rock in a river. The excitement takes place on a long, straight river with a rock at the start and another rock at the end, L units away from the start (1 ≤ L ≤ 1,000,000,000). Along the river between the starting and ending rocks, N (0 ≤ N ≤ 50,000) more rocks appear, each at an integral distanceD_i from the start (0 < D_i < L).

To play the game, each cow in turn starts at the starting rock and tries to reach the finish at the ending rock, jumping only from rock to rock. Of course, less agile cows never make it to the final rock, ending up instead in the river.

Farmer John is proud of his cows and watches this event each year. But as time goes by, he tires of watching the timid cows of the other farmers limp across the short distances between rocks placed too closely together. He plans to remove several rocks in order to increase the shortest distance a cow will have to jump to reach the end. He knows he cannot remove the starting and ending rocks, but he calculates that he has enough resources to remove up to M rocks (0 ≤ M ≤ N).

FJ wants to know exactly how much he can increase the shortest distance *before* he starts removing the rocks. Help Farmer John determine the greatest possible shortest distance a cow has to jump after removing the optimal set of M rocks.

Input

Line 1: Three space-separated integers: L, N, and M
Lines 2..N+1: Each line contains a single integer indicating how far some rock is away from the starting rock. No two rocks share the same position.

Output

Line 1: A single integer that is the maximum of the shortest distance a cow has to jump after removing M rocks

Sample Input

Sample Output

这题要添加起始和终点两个石头题目就等效于包括终点石头在内的 n-m+1 个石头且距离都大于二分的答案

写法与上一题类似

AC代码如下：

//
//  Created by TaoSama on 2015-04-22
//  Copyright (c) 2015 TaoSama. All rights reserved.
//
#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <string>
#include <set>
#include <vector>

using namespace std;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 7;
const int N = 1e5 + 10;

int L, n, m, a[50005];

bool check(int x) {
    int last = 0;
    //<=> 选出n-m个间距都>=x
    for(int i = 1; i <= n + 1 - m; ++i){
		int idx = last + 1;
		while(idx <= n + 1 && a[idx] - a[last] < x) ++idx;
		if(idx == n + 2) return false;
		last = idx;
    }
    return true;
}

int main() {
#ifdef LOCAL
    freopen("in.txt", "r", stdin);
//  freopen("out.txt","w",stdout);
#endif
    ios_base::sync_with_stdio(0);

    cin >> L >> n >> m;
    for(int i = 1; i <= n; ++i) cin >> a[i];
    sort(a + 1, a + n + 1);
    a[0] = 0; a[n + 1] = L;
    int l = 0, r = L + 1;
    while(l + 1 < r) {
        int mid = l + r >> 1;
        if(check(mid)) l = mid;
        else r = mid;
    }
    cout << l << '\n';
    return 0;
}