Leetcode 983 最低票价

　　JAVA 分治：

public final int mincostTickets(int[] days, int[] costs) {
        return minCost(days, costs, days.length - 1, new int[days.length]);
    }

    private final int minCost(int[] days, int[] costs, int end, int[] cache) {
        if (end < 0) {
            return 0;
        }
        if (end == 0) {
            return costs[0];
        }
        if (cache[end] != 0) {
            return cache[end];
        }
        int min = Integer.MAX_VALUE;
        for (int begin = 0; begin <= end; begin++) {
            min = Math.min(min, minCost(days, costs, begin - 1, cache) + cost(days[begin], days[end], costs));
        }
        cache[end] = min;
        return min;
    }

    private final int cost(int begin, int end, int[] costs) {
        if (begin == end) {
            return costs[0];
        }
        int travelDay = end - begin + 1;
        int thir = travelDay / 30;
        int seven = (travelDay % 30) / 7;
        int one = travelDay - thir * 30 - seven * 7;
        int cost1 = thir * costs[2] + seven * costs[1] + one * costs[0];
        int cost2 = (travelDay / 7) * costs[1] + (travelDay % 7) * costs[0];
        int cost3 = travelDay * costs[0];
        int min1 = Math.min(Math.min(cost1, cost2), cost3);
        int cost4 = (thir + ((travelDay % 30) > 0 ? 1 : 0)) * costs[2];
        int cost5 = (travelDay / 7 + (travelDay % 7 > 0 ? 1 : 0)) * costs[1];
        return Math.min(Math.min(min1, cost4), cost5);
    }

　　JAVA DP：

private final int cost(int begin, int end, int[] costs) {
        if (begin == end) {
            return costs[0];
        }
        int travelDay = end - begin + 1;
        int thir = travelDay / 30;
        int seven = (travelDay % 30) / 7;
        int one = travelDay - thir * 30 - seven * 7;
        int cost1 = thir * costs[2] + seven * costs[1] + one * costs[0];
        int cost2 = (travelDay / 7) * costs[1] + (travelDay % 7) * costs[0];
        int cost3 = travelDay * costs[0];
        int min1 = Math.min(Math.min(cost1, cost2), cost3);
        int cost4 = (thir + ((travelDay % 30) > 0 ? 1 : 0)) * costs[2];
        int cost5 = (travelDay / 7 + (travelDay % 7 > 0 ? 1 : 0)) * costs[1];
        return Math.min(Math.min(min1, cost4), cost5);
    }

    public final int mincostTicketsDP(int[] days, int[] costs) {
        int[] cache = new int[days.length];
        cache[0] = Math.min(Math.min(costs[0], costs[1]), costs[2]);
        for (int end = 1; end < cache.length; end++) {
            int min = Integer.MAX_VALUE;
            for (int begin = 0; begin <= end; begin++) {
                if (begin == 0) {
                    min = Math.min(min, cost(days[begin], days[end], costs));
                } else {
                    min = Math.min(min, cache[begin - 1] + cost(days[begin], days[end], costs));
                }
            }
            cache[end] = min;
        }
        return cache[cache.length - 1];
    }

　　JS DP：

/**
 * @param {number[]} days
 * @param {number[]} costs
 * @return {number}
 */
var mincostTickets = function (days, costs) {
    let len = days.length;
    let cache = new Array(len).fill(0);
    cache[0]=costs[0];
    for (let end = 1; end < len; end++) {
        let currentMin = Number.MAX_SAFE_INTEGER;
        for (let begin = 0; begin <= end; begin++) {
            let current = cost(costs,days[begin], days[end]);
            if (begin === 0) {
                currentMin = currentMin < current ? currentMin : current;
            } else {
                current = current + cache[begin - 1];
                currentMin = currentMin < current ? currentMin : current;
            }
        }
        cache[end]=currentMin;
    }
    return cache[len - 1];
};

var cost = function (costs, begin, end) {
    if (begin == end) {
        return costs[0];
    }
    let travelDay = end - begin + 1;
    let thir = Math.floor(travelDay / 30);
    let seven = Math.floor((travelDay % 30) / 7);
    let one = travelDay - thir * 30 - seven * 7;
    let cost1 = thir * costs[2] + seven * costs[1] + one * costs[0];
    let cost2 = Math.floor(travelDay / 7) * costs[1] + (travelDay % 7) * costs[0];
    let cost3 = travelDay * costs[0];
    let min1 = cost1 < cost2 ? cost1 : cost2;
    min1 = min1 < cost3 ? min1 : cost3;
    let cost4 = (thir + ((travelDay % 30) > 0 ? 1 : 0)) * costs[2];
    let cost5 = (Math.floor(travelDay / 7 )+ (travelDay % 7 > 0 ? 1 : 0)) * costs[1];
    min1 = min1 < cost4 ? min1 : cost4;
    min1 = min1 < cost5 ? min1 : cost5;
    return min1;
}