375.GuessNumberHigherOrLowerIi.cpp

/*
 * @lc app=leetcode id=375 lang=cpp
 *
 * [375] Guess Number Higher or Lower II
 *
 * https://leetcode.com/problems/guess-number-higher-or-lower-ii/description/
 *
 * algorithms
 * Medium (40.87%)
 * Likes:    954
 * Dislikes: 1442
 * Total Accepted:    72.3K
 * Total Submissions: 172.5K
 * Testcase Example:  '10'
 *
 * We are playing the Guessing Game. The game will work as follows:
 *
 *
 * I pick a number between 1 and n.
 * You guess a number.
 * If you guess the right number, you win the game.
 * If you guess the wrong number, then I will tell you whether the number I
 * picked is higher or lower, and you will continue guessing.
 * Every time you guess a wrong number x, you will pay x dollars. If you run
 * out of money, you lose the game.
 *
 *
 * Given a particular n, return the minimum amount of money you need to
 * guarantee a win regardless of what number I pick.
 *
 *
 * Example 1:
 *
 *
 * Input: n = 10
 * Output: 16
 * Explanation: The winning strategy is as follows:
 * - The range is [1,10]. Guess 7.
 * - If this is my number, your total is $0. Otherwise, you pay $7.
 * - If my number is higher, the range is [8,10]. Guess 9.
 * - If this is my number, your total is $7. Otherwise, you pay $9.
 * - If my number is higher, it must be 10. Guess 10. Your total is $7 + $9 =
 * $16.
 * - If my number is lower, it must be 8. Guess 8. Your total is $7 + $9 =
 * $16.
 * - If my number is lower, the range is [1,6]. Guess 3.
 * - If this is my number, your total is $7. Otherwise, you pay $3.
 * - If my number is higher, the range is [4,6]. Guess 5.
 * - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay
 * $5.
 * - If my number is higher, it must be 6. Guess 6. Your total is $7 + $3 + $5
 * = $15.
 * - If my number is lower, it must be 4. Guess 4. Your total is $7 + $3 + $5 =
 * $15.
 * - If my number is lower, the range is [1,2]. Guess 1.
 * - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay
 * $1.
 * - If my number is higher, it must be 2. Guess 2. Your total is $7 + $3 + $1
 * = $11.
 * The worst case in all these scenarios is that you pay $16. Hence, you only
 * need $16 to guarantee a win.
 *
 *
 * Example 2:
 *
 *
 * Input: n = 1
 * Output: 0
 * Explanation: There is only one possible number, so you can guess 1 and not
 * have to pay anything.
 *
 *
 * Example 3:
 *
 *
 * Input: n = 2
 * Output: 1
 * Explanation: There are two possible numbers, 1 and 2.
 * - Guess 1.
 * - If this is my number, your total is $0. Otherwise, you pay $1.
 * - If my number is higher, it must be 2. Guess 2. Your total is $1.
 * The worst case is that you pay $1.
 *
 *
 *
 * Constraints:
 *
 *
 * 1 <= n <= 200
 *
 *
 */

// @lc code=start
#include <climits>
#include <cmath>
#include <vector>

class Solution {
public:
    int getMoneyAmount(int n) {
        std::vector<std::vector<int>> minAmount(
            n + 1, std::vector<int>(n + 1, INT_MAX));

        // if the length of range is 1, we will win at a guess, so no cost
        for (int i = 1; i <= n; i++) minAmount[i][i] = 0;

        for (int len = 2; len <= n; ++len) {
            for (int left = 1; left <= n - len + 1; ++left) {
                int right = left + len - 1;
                for (int guess = left; guess <= right; ++guess) {
                    // choose worst scenarios from either left or right side of
                    // guessing
                    minAmount[left][right] = std::min(
                        minAmount[left][right],
                        guess + std::max(
                                    lookupAmount(minAmount, left, guess - 1),
                                    lookupAmount(minAmount, guess + 1, right)));
                }
            }
        }

        return minAmount[1][n];
    }

private:
    int lookupAmount(const std::vector<std::vector<int>>& minAmount, int l,
                     int r) {
        if (l > r || l < 0 || r >= minAmount.size()) return 0;
        return minAmount[l][r];
    }
};
// @lc code=end